An evidence based
approach to improving
discovery and innovation
Peter O’Shea
Queensland University of Technology
Copyright 2010 by Peter O’Shea
All rights reserved. Written permission must be obtained from
the publisher to use or reproduce any part of this book, apart
from short quotes in reviews and articles.
Published in Brisbane, 2010
The author gratefully acknowledges the generosity of others
who have made figures and photos within this book available as
public domain entities. Several public domain photos were
sourced from www.public-domain-photos.com.
Printed in Australia
Table of Contents
1. Introduction
1.1 Book outline
2. Evidence based strategies for improving thinking
and discovery
2.1 Cultivation of mindfulness and vision
2.2 Reflection and belief adjustment
2.3 Shrewd acquisition of appropriate
background knowledge and skills
2.4 A commitment to deliberate practice
2.5 Habitual abstraction of key underlying
principles from new situations
2.6 Engagement with analogies and metaphors
2.7 Giving and receiving care and guidance in
the area of thinking and discovery
2.8 Physical exercise and adherence to a healthy
2.9 Conclusions
3. Developing effective problem solving skills
3.1 A general problem solving strategy
3.2 General problem solving techniques
3.3 Selecting the most appropriate problem
solving technique(s)
3.4 The evidence for studying and practicing
generic problem solving strategies
3.5 Conclusions
4. Developing creativity and innovation
4.1 The inclination towards creativity
4.2 Methods and algorithms for innovation
4.3 Conclusions
5. Practical tips for novice researchers
5.1 Tips for using time productively
5.2 Disseminating research work
5.3 Conclusions
6. Mentoring others in innovation and discovery
6.1 Tips and traps for research mentoring
6.2 Conclusions
7. Conclusions
8. Appendix
9. References
10. Index
Alcoholics Anonymous
Community of Practice
Divide and Conquer
General Problem Solver
Institute of Electrical & Electronic Engineers
Long-Term Memory
Means-End Analysis
Queensland University of Technology
Theory of inventive problem solving
Working Memory
Chapter 1
In 1969 a group of animal trainers at Sea Life Park in Hawaii
embarked on an investigation into the mental capabilities of a
rough-toothed dolphin. These trainers had worked with
dolphins for some time, and knew very well that dolphins had
the ability to mimic the tricks they were shown. They believed,
however, that dolphins might well be capable of much more
than that. This belief prompted them to see if they could teach
a dolphin to go beyond simple mimicry and regularly devise
new tricks of its own.
To achieve their objectives the Sea Life Park staff instigated a
training regime in which the dolphin was given a reward every
time it demonstrated innovative behaviour. As the training
progressed the dolphin came to understand that it was being
rewarded for innovation, and changed its thinking and
behaviour accordingly. This change in thinking and acting
eventually brought the dolphin to the point where it could
devise and perform its own new trick every day (Pryor et al.,
The attempt by the Sea Life Park staff to teach an animal
something as elusive as creativity was a very ambitious
undertaking. Remarkably the attempt was a success, and this
success has powerful implications for us as human beings. We
can all advance our thinking and innovation, and if we have the
appropriate attitudes, extraordinary improvements are
There are many possible ways we could go about trying to
improve our mental capabilities, but research shows that very
few of these ways actually work. The study with the dolphin
provides a clue as to the approach that is needed. The trainers
believed in the dolphin’s potential, and pursued a vision to
develop that potential. Likewise, if we wish to facilitate
intellectual capacity improvements in ourselves or others, we
need to start with a belief in our (or their) potential, and then
pursue a vision to realise that potential.
The reason why belief and vision are critical to the
advancement of thinking is that sustainable improvements
rarely occur suddenly – they usually occur gradually over a
protracted period of time (Manathunga & Wissler, 2003).
Vision and belief are needed to sustain motivation and
commitment during that time, particularly when major
obstacles need to be faced.
Figure 1.1. The training of dolphins has illuminated the process of
discovery and innovation in humans
While belief and vision are critically important for improving
discovery and innovation, there is another factor which is
arguably even more important. This other factor is well
illustrated in the life story of Pedro Bach-y-Rita. Pedro was a
Spanish poet and academic who in 1959, suffered a debilitating
stroke (Abrams, 2003; Doidge, 2008). After the stroke he could
not speak and was unable to move about half of his body.
Pedro's wife had already died but he had two sons, George and
Paul. They were told by medical authorities that their father
would never recover, and that he would need to be
Not wanting to see their father put into a nursing home, one of
the sons (George) brought Pedro back to live with him in
Mexico, where he was studying Medicine. Although he knew
very little about rehabilitation, George decided to try to
facilitate his father’s recovery himself.
George commenced his attempts at rehabilitation by trying to
teach Pedro to walk again. In so doing, he reasoned that his
father would have to roll and crawl before he could walk, and
therefore started putting Pedro through a lot of rolling and
crawling exercises. To try to make the exercises tolerable for his
father, George devised many games which the two of them
played together, much like a father plays with a baby. Through
the many exercises and games they undertook together, Pedro
eventually progressed from rolling to crawling, to standing, to
Spurred on by the successes with his large motor skills, Pedro
himself began to attempt the rehabilitation of his speech. He
started devising and performing mental and vocal exercises to
gradually re-stimulate his speech. Within a few months that
started to come back, and then he slowly and gradually redeveloped his writing. Pedro’s overall recovery was so
successful that after about a year he was able to take up a
lecturing position at City College in New York, and subsequent
to that he also remarried.
Pedro died of a heart attack about five years after his recovery,
and an autopsy was performed on his body. The presiding
doctor at that autopsy was utterly amazed at what she saw 97% of the nerves running from the cerebral cortex to the spine
had been destroyed by the stroke, and so had the other regions
of the brain dedicated to motor control. In spite of this, Pedro
had been able to coax his brain to re-organise itself, so that he
was able to discover anew how to walk, talk, write and
successfully interrelate with others.
How was it that Pedro was able to achieve such dramatic
improvements against all the expectations of the medical
experts? It was partly due to George’s belief and vision. The
medical authorities believed Pedro could never recover, but
George believed he could. George was also wise enough to
know that Pedro’s recovery would need to be gradual, and so
pursued a long-term vision, rather than a short-term fix.
George’s belief and vision were infectious. After a while, Pedro
captured a vision to drive his own rehabilitation, and he
successfully pursued this vision.
The belief and vision factors, alone, however, would probably
not have been enough to ensure Pedro’s recovery. Another
critical factor was at work. Evidence from the neurosciences
suggests that the care factor can impact enormously on a
person’s cognitive functioning.
When a person experiences a deep sense of care, two different
chemicals are released into the brain. The first of these is
dopamine, which acts by lowering the threshold at which the
pleasure centres fire. If these pleasure centres fire when skill
acquisition is occurring, the skill development tends to be
rewarded and therefore strongly reinforced (Olds & Milner,
As well as increasing the likelihood of the pleasure centres
firing, dopamine also reduces the likelihood of the pain centres
firing. This is so because the pain and pleasure centres are in
close proximity and operate within a competitive framework.
When the pleasure centres fire, the pain centres have
diminished ability to operate. As a result, people are more
resilient to obstacles and difficulties when they feel cared for.
The second chemical which can be released when a person has
a deep sense of care is oxytocin. To understand the significance
of this chemical it is important to consider the way the brain
functions. The cerebral cortex is actually a neural network
which can be trained to provide appropriate responses to
particular stimuli. Once the training is done, the appearance of
a particular stimulus often triggers (at a subconscious and
automatic level) the responses which have been established or
programmed during training. Another way of saying this is that
as we progress in our intellectual endeavours, robust mental
habit patterns are established. Once established, these mental
habit patterns tend to be very difficult to change.
Although our mental habit patterns are generally hard to
change, it is important that they do change, since many of them
are flawed. The evidence tells us that there is one circumstance
under which change can occur quite easily – that circumstance
is when oxytocin is released (Freeman, 1995). When this
happens neuronal connections are cleared on a massive scale.
This clearing paves the way for new attitudes, new lines of
thought and new behavioural patterns to form.
The importance of deep care for neural change is well
illustrated in the scenario where two people fall in love. In such
a situation the two people typically experience an oxytocin
release which enables them to rapidly modify old, selfish ways
of thinking and acting. Similarly when parents beget children
they experience a chemical release which allows them to swiftly
adopt new ways of acting which can benefit the child.
More generally, when a person experiences feelings of deep
care, wide scale neural change is facilitated, which in turn
creates a very marked openness to the formation of new
attitudes and new lines of thought. Attitude change and
creativity are therefore facilitated.
In summary, then, if a person experiences a strong sense of
care, they are likely to
be able to acquire new skills more rapidly and deeply,
be more resilient to set-backs,
be more open to changing attitudes, and
be more creative.
Pedro Bach-y-Rita’s story of re-discovering how to walk, talk
and communicate against enormous obstacles is testament to
the power of care. Pedro’s son, George, was prepared to forego
his own convenience to attempt the rehabilitation, and
committed to caring for his helpless father. This was no small
commitment - initially Pedro had to be lifted onto the toilet and
into the shower, and the medical authorities indicated that this
would need to be done for the rest of Pedro's life. In
committing to serve his father the way he did, George made a
profound declaration of his care.
In the early stages of the rehabilitation, George played games
on the floor for many hours with his father. During this time
Pedro would almost certainly have experienced an intense
sense of care. Extraordinarily powerful mental progress ensued,
as Pedro’s brain managed to dramatically reorganise its
The care factor is very important if we wish to maximise gains
in our thinking and discovery. If our goal is to improve our own
capabilities we can benefit enormously by finding others who
are invested in our well being, and who can mentor us.
Similarly, if we wish to help others to improve their capabilities
we should make it a priority to demonstrate our care and
support for them.
CASE STUDY: One year I was talking to one of the PhD
students in our school, and I asked him how his research
was progressing. He told me that he felt things were
going quite badly, and he was quite despondent. The
deflated nature of his demeanour left me wondering
what could be done to help him. I could not think of any
quick and certain solution at the time.
About a year later I ran into the same student, and asked
him somewhat cautiously how he was coping. He
surprised me by telling me that things were going very
well in his studies, and that he had just had a paper
accepted in a prestigious journal.
I was naturally curious to know what had caused his
change of outlook, and asked him to enlighten me. He
told me that he had considered his situation, and after
reflection, realised that he needed more help. His PhD
topic had veered away from his supervisor’s field of
expertise, and he concluded that he needed to look
elsewhere for help. He had searched the internet, found
a person who had the appropriate expertise, and had
then emailed that person to propose a collaboration
which could benefit both of them.
The PhD student agreed to include this man on his
publications in exchange for support and guidance. The
collaboration did eventuate and proved very successful –
a number of high quality publications followed.
In the above story, the student came to his own
realisation that he needed greater care and guidance.
This was a shrewd insight, and one which he followed up
with appropriate action. The result was very rapid
research progress.
1.1 Book outline
This book is dedicated to assisting people to engage with vision,
belief, the care factor, and various other evidence based
principles to improve their ability to discover and innovate. To
this end, Chapter 2 focuses on evidence based strategies for
advancing our thinking and discovery. Chapters 3 and 4
address the improvement of specific aspects of our cognitive
processes, namely problem solving and creativity. Chapter 5
presents practical tips for novice researchers, while Chapter 6
discusses the mentoring of other researchers. Conclusions are
presented in Chapter 7.
Chapter 2
Evidence based strategies for improving
thinking and discovery
The opening paragraphs of Chapter 1 recounted the story of a
dolphin which progressed from simply mimicking tricks to
regularly devising and performing new tricks of its own. As
researchers we need to embark on an analogous journey. We
need to progress our cognitive abilities to the point where we
can routinely synthesise new and creative solutions to the
many problems that confront us.
When I talk to students about the process of improving
thinking I often roll up my sleeves so that they have a clear
view of my upper arm. Then I ask them “How do you think you
get muscles like these?” The students usually laugh because
they generally can’t see much in the way of muscle
development in my arm. I then explain to them that the reason
they can’t see strong muscles is that I have not been doing
anything intentional to build them up. The same principle
holds in the cognitive domain – if we take no deliberate steps
to build up our intellectual muscles, they are unlikely to grow
Normally if someone wishes to build up their physical muscles
they take deliberate and informed action. They may, for
example, start doing weight training exercises, and may also
begin to eat more protein. For many years the intellectual
community remained blissfully unaware that one must follow a
similar path if one is to build up intellectual muscle. Many
people believed that cognitive capacity grew substantially and
automatically during the normal processes of life. In particular
it was believed that if we acquired a basic set of core skills, we
would automatically be able to adapt and transfer these basic
skills to new and unseen situations. This belief was enshrined
in the Bo-Peep Theory of skills transfer, which was so named to
reflect the sentiments in the Little Bo-Peep nursery rhyme
(Perkins & Salomon, 1990):
‘Leave them alone, and they’ll come home,
wagging their tails behind them’.
The theory postulated that we do not need to worry about
explicitly trying to improve our cognitive capacity – rather, like
Bo-Peep’s sheep, we could just be left alone, and would
eventually come home with the requisite ability to deal
effectively with new problem situations.
Figure 2.1. Early scholars believed that, just like Bo-Peep’s sheep, people
would find their own way. The evidence suggests otherwise.
Extensive research has been done to test the validity of the BoPeep theory. The findings from this research are negative. If we
simply pursue routine intellectual activities, we tend to underprepare ourselves for dealing effectively with new and unseen
situations. One of the first studies into this area was done by
Thorndike, who tested students undertaking a course in Latin
(Thorndike, 1923). It had been argued that the acquisition of
competence in Latin would help students to develop mental
discipline, which would have a flow on effect to other
intellectual endeavours. The investigation by Thorndike,
however, showed that after students had completed the Latin
course, their ability to deal with new contexts had not
Thorndike’s investigation was followed up with various other
studies. One such study examined the impact of a Computer
Programming course on students’ abilities to deal better with
new problems. There was significant hope that the findings
here would be positive – it was believed, after all, that
Computer Programming tasks provoked students to solve new
problems, to devise their own testing strategies, and to develop
organised thinking. The outcome here, however, was also
negative – students did not improve their ability to deal with
new problem situations after studying Computer Programming
(Pea & Kurland, 1984).
More and more testing was performed, however, and
occasionally there were positive findings. Students in graduate
Psychology programs, for example, had improved transfer
skills after completing their course (Lehman et al, 1988).
Further studies revealed that there are a small number of
practices which do indeed improve one’s ability to deal with
new problems.
The positive findings on improved transfer under certain
conditions gave rise to the now generally accepted Good
Shepherd Theory of transfer (Perkins & Salomon, 1990). The
practices which have been found to positively dispose students
to dealing more effectively with new problem scenarios are:
cultivation of mindfulness and vision (Langer,
(ii) reflection and belief adjustment (Belmont, 1982;
Butler et al, 2006),
(iii) shrewd acquisition of appropriate background
knowledge and skills (Bransford et al, 1999),
(iv) a commitment to deliberate practice in diverse
contexts (Ericcson, 2005; Scribner & Cole, 1981;
Luria, 1976),
(v) habitual abstraction of key underlying principles
from new problem situations (Gick & Holyoak,
(vi) engagement with analogies and metaphors
(Perkins & Salomon, 1992),
(vii) giving and receiving care and guidance in the area
of thinking and innovation (Palincsar & Brown,
(viii) physical exercise and adherence to an appropriate
diet (Van Praag et al, 1999).
These practices are all important for anyone who wishes to
improve their ability to research and innovate, and the
remainder of this chapter explores each of them in turn.
2.1 Cultivation of mindfulness and vision
Mindfulness pertains to an active and conscious engagement
with one’s thinking and behaviour. To improve thinking one
needs to be mindful of one’s intellectual processes, and how
these processes affect one’s behaviour and achievements
(Langer, 1989).
People who are successful in building up strong physical
muscles think regularly about their muscle development, and
are usually driven by a vision. This vision helps to keep them
mindful of the activities which facilitate muscle growth (such as
weight lifting and personal training). In an analogous fashion,
those who wish to improve their thinking capabilities need to
have a vision which keeps them mindful of the activities which
facilitate intellectual muscle growth.
CASE STUDY: The benefit of embracing a vision for
cognitive advancement is well illustrated in the life of a
woman named Barbara Arrowsmith Young. Barbara
grew up in Canada with a plethora of intellectual
She had difficulty pronouncing words, she had very poor
spatial reasoning, she frequently lost things, she had
poor physical co-ordination, she often found herself in
accidents, she had an extremely narrow range of vision,
she was unable to understand relationships with
symbols, she had great difficulty with grammar and
maths, she was often unable to link cause and effect, she
had dyslexia, and social relationships were highly
problematical for her. Sometimes she felt so
overwhelmed with life that she contemplated suicide
(Doidge, 2008).
Faced with the unpleasant consequences of her flawed
cognitive processes, Barbara decided to pursue a vision
to improve her mental processes. Remarkably, she was
eventually accepted into a PhD program, and within that
program she investigated the problem of how to
overcome intellectual disorders.
While engaged in her research Barbara came across the
work of two important scientists. The first was
Alexander Luria, a neuroscientist who worked with
soldiers whose brains had been damaged by artillery
fire. Barbara identified very strongly with one of the case
studies in Luria’s writings, and she correctly deduced
that she must have the same problem as the subject in
that case study – that is, she realised she had a
physically damaged brain.
The second scientist to impact strongly on Barbara’s
understanding was Mark Rosenzweig. He did
experiments on rats, and observed that the brains of rats
experienced significant physical enhancements if they
were subjected to heavy mental and physical
After reflecting on the work of Luria and Rosenzweig,
Barbara hypothesised that her brain could be healed by
heavy stimulation (i.e. by relentlessly practicing tasks at
which she was very poor). This hypothesis ran counter to
the conventional wisdom of the time. The normal
recourse to dealing with disorders was to try and work
around (or compensate for) weaknesses.
Barbara put her hypothesis to the test and discovered
that she was correct. She found that forcing the brain to
repeatedly do what it was weak at doing provoked the
brain to reorganise and rebuild itself. As she persisted
with her mental exercises her many disorders began to
She found that some disorders were cured by engaging
in intensive and repeated practice in rote memorisation.
Others were cured by relentless practice at intricate line
tracing. Yet others were cured by copious practice at
memorising, followed up by public speaking. Barbara
eventually succeeded in healing her own disabilities, and
then launched into helping others with similar
problems. Along with her husband, Joshua Cohen, she
set up a school in Toronto dedicated to helping those
with intellectual disorders. They identified 19 different
disorders, and devised exercises which could address
these disorders. Her school has helped many people to
successfully overcome their difficulties (Miller, 2008;
Doidge, 2008).
Barbara was able to nurture her vision for cognitive
advancement to completion by using a number of very
sound strategies. She studied the neuroscience
literature, and found solace and inspiration in the truths
she discovered there. She reflected diligently, and was
able to make breakthroughs via this reflection. She faced
obstacles bravely, rather than trying to skirt around
them. She drew others (including her husband) to her
vision, and was ultimately supported by these others.
She also adopted a highly persevering attitude and did
not give up hope, despite the many obstacles she faced.
Barbara nurtured her vision so successfully that
eventually she was able to advance not only her own
cognitive abilities, but also those of others.
As was the case in the above story, pursuit of a long-term vision
causes us to regularly focus on an outcome over a prolonged
period. The neuroscience research indicates that when we do
this our brain allocates specialised neural resources to realise
that outcome (Pascual-Leone & Torres, 1993; Doidge, 2008;
Rock & Schwartz, 2006). These additional resources
substantially increase the likelihood of the outcome being
If we really wish to improve our mental functioning we should
establish and articulate a vision. One such vision could be to
increase our mental capacity sufficiently to be able to
undertake and complete postdoctoral studies which greatly
interest us. Alternatively, our vision could be to improve our
creativity and technical expertise to the point where we become
successful inventors.
There is great scope in the kind of vision we can pursue. It is
vital, however, to ensure that the vision we choose is something
that we are passionate about.
2.1.1 Dealing with obstacles
Regardless of the vision we choose, we will almost certainly
encounter obstacles as we pursue it. We should not be
surprised when we encounter these obstacles, rather, we
should prepare ourselves to deal with them. To this end we
should enlist the help of wise mentors, and we should study
and adopt proven strategies for overcoming the obstacles.
If we do not face obstacles in an informed and determined way
we may find ourselves falling victim to the phenomenon of selfsabotage. When we fall into this kind of trap, we typically start
to engage in a flurry of diversionary activities which direct our
efforts away from the pursuit of our vision. These activities
serve two purposes, the first being to keep our mind off the
issues we do not want to face, and the second being to provide
a convenient excuse in the event of failure (Martin et al., 2003).
Intuitively of course, we know that failure is a real possibility if
we do not face important issues.
Diversionary activities are very common. Research shows in
fact, that self-sabotage inspired diversionary behaviour occurs
in up to 95% of university undergraduate students, and there is
little reason to think the incidence is any less in postgraduate
students (Oenwugbuzie, 1999; Solomon & Rothblum, 1984).
These diversionary activities may be apparently worthy
endeavours in themselves, but they sabotage the pursuit of a
CASE STUDY: At one point in my life I started reflecting
on my career and lamented that it had not gone as well
as I had hoped. I really did not want my disappointment
to continue, and was keen to see if I could somehow
change my situation. I started engaging in reflection
about the cause of my career slump. After some time I
came up with a realisation which surprised me. I had a
clear sense that my problems existed because I had a
strong aversion to doing things that were difficult or
risky. I wanted, rather, to cruise through life.
Instead of trying to face my risk-aversion, I had created
diversions to conceal my inclinations – I engaged in lots
of routine teaching activities, all of them easy but time
consuming. I also avoided serious research because it
was too fraught with risk. With all my diversionary
activities I had no time to attempt the challenging things
that would help me grow.
This revelation about my challenge aversion turned out
to be a pivotal moment for me. Discontent and adversity
had prompted me to seek and find the solution – I
simply had to start challenging myself more. I started in
small ways to take on more challenges, and as time went
on I took on bigger challenges. Life became much more
enjoyable for me as I did this, and importantly, I started
to experience a greater level of success.
There are some tell-tale signs that can help us to identify selfsabotage. If we detect over-committing, busyness,
perfectionism, procrastination, disorganisation, not putting in
effort or choosing performance-debilitating circumstances in
our behaviour patterns, then we may well be guilty of selfsabotage (Kearns et al, 2008). Strategies for overcoming
obstacles and dealing with self sabotage are described more
fully in Section 2.2.
2.1.2 Nurturing our vision
Obstacles and other distracting elements can cause our vision
to fade, and when it does fade, we need to spend time reinvigorating it. If, say, we have a vision to become a
groundbreaking medical researcher, we might read books or
articles about inspiring doctors who have changed the world. If
we wish to become a great electronics inventor, we might start
reading IEEE Spectrum, a magazine which regularly profiles
major breakthroughs in Electrical and Electronic Engineering.
If we have a vision to become a great writer we might read the
works of great novelists. If we wish to find cures which will
change the lives of the poor and needy, we might choose to
work among these needy people.
We also need to find others to support us in our vision. When
Sergey Brin and Larry Page were undergraduates at Stanford
University, they shared a vision with one another – namely, to
make information more globally accessible. After sharing the
vision with one another they began to share it with others, and
ultimately shared it with some sympathetic venture capitalists.
As they shared, others captured their vision and a community
of supporters grew up around them. What resulted was the
Google web-site, which has now been visited billions of times.
In the process of realising the Google vision, founders Sergey
Brin and Larry Page became enormously wealthy and
influential. Like Brin and Page, we need other people to
support and encourage us in our vision.
CASE STUDY: During the 1930s Winston Churchill was
confronted with an enormous challenge. He had to find
a way to overcome the serious threat to British liberty
posed by Adolf Hitler. At the time it was not clear how
this could be achieved – Churchill had to find a way.
Churchill faced some very serious obstacles in pursuing
his vision to overcome Hitler. One of these obstacles was
the initial reluctance of the British people to engage in a
difficult fight. They had only recently emerged from the
ordeal of World War I, and had little enthusiasm for
another costly campaign. Churchill knew that he needed
the support of the people to realise his vision, and
persevered in winning them over.
He took opportunity after opportunity to put the truth
before the British people. After the English Prime
Minister, Neville Chamberlain, returned from a meeting
in which Hitler was appeased, Churchill boldly declared
“You were given the choice between war and dishonour.
You have chosen dishonour and you shall have war”.
Churchill also nurtured his vision by extensive reading,
study and reflection. He read Mein Kampf and studied
the strategies of the Nazi forces. This reading and study
fortified his resolve.
When Hitler’s aggression continued, Churchill argued
that Britain should occupy the strategic port city of
Narvik in Norway and the Swedish iron ore mines of
Kiruna – such an occupation would have dramatically
reduced Hitler’s supply of critically important iron ore.
Churchill was ignored, and instead, the Nazi forces went
on to occupy Norway.
Churchill continued to put his vision before the British
people. In one memorable speech he told them
“the Battle of France is over. I expect that the Battle
of Britain is about to begin ... Upon it depends our
own British life, and the long continuity of our
institutions and our Empire. The whole fury and
might of the enemy must very soon be turned on us.
Hitler knows that he will have to break us in this
island or lose the war. If we can stand up to him, all
Europe may be freed and the life of the world may
move forward into broad, sunlit uplands....Let us
therefore brace ourselves to our duties, and so bear
ourselves, that if the British Empire and its
Commonwealth last for a thousand years, men will
still say, This was their finest hour.”
Churchill’s speeches had an extraordinary impact on the
British people and as a result they willingly entered into
the fight for freedom. This enabled much of Churchill’s
vision to come to fruition, although it did not come to
pass easily – England was bombarded relentlessly in
1940, and about 40,000 people lost their lives.
Gradually, however, Britain and her allies clawed their
way back from near defeat to prevail against Hitler.
Churchill pursued a very grand vision and he used many
effective techniques to successfully nurture it. He read
widely, and drew on the truth and inspiration that he
found in literature. He studied and reflected carefully.
He also shrewdly enticed many others to his visionary
cause, and drew on the support of those he recruited.
2.1.3 Seeking inspiration from positive role models
To maintain vision, it is important to draw on the inspired
example of others. Some of the greatest sources of inspiration
are people we have not met and will never meet. They may not
even be alive, but we can still find powerful inspiration by
reading their biographies, studying their work and reflecting on
how they were able to achieve what they did.
We can find inspiration not only in the pages of history, but
also in the lives of great contemporary thinkers. Exposure to
these exemplary role models can have a powerful motivational
effect on us.
CASE STUDY: As a young man, Henry Ford was greatly
inspired by one of the luminaries of his age, namely
Thomas Edison. Ford read about the works of Edison,
followed his career, and eventually sought and gained
employment at the Edison Detroit company. Ford rose
to the level of Chief Engineer at Edison’s company, and
while in that role began his own personal research into
gasoline car engines.
When Edison heard about the gasoline engine
experiments he personally spoke with Ford and asked
many probing questions. At the end of all these
questions, Edison banged his fist on the table and said
“Young man, that’s the thing. You have it! Your car is
self contained and carries its own power plant”.
Ford later claimed that “That bang on the table was
worth worlds to me. No man up to then had given me
any encouragement. I had hoped that I was headed
right. Sometimes I knew that I was, sometimes I only
wondered, but here, all at once and out of a clear sky, the
greatest inventive genius in the world had given me
complete approval. The man who knew most about
electricity in the world had said that for the purpose, my
gas motor was better than any electric motor could be.”
Ford remained grateful all his life for the inspiration and
encouragement of Edison. The two became great friends
and in their later years, even bought houses next to one
another in Florida. When Edison advanced in years and
became wheelchair bound Ford bought a wheelchair as
well just so that the two of them could have wheelchair
races around their adjoining properties.
The inspiration Ford found in Edison proved very
pivotal. It helped him to successfully pursue his vision to
invent and popularise a practical motor car. The
fulfilment of that vision ultimately changed the way we
While famous artists, writers and scientists are an undoubted
source of inspiration, so are many others closer to us. Some of
the most potent sources of inspiration can be found among
peers. The power of peers to influence is well documented. In
1995 Judith Rich Harris wrote a paper about the influence of
peers on children (Rich Harris, 1995). The paper presented
evidence to suggest that peers have a greater influence on the
development of children than parents. The paper received a
great deal of attention, and although its findings are highly
contentious, the American Psychological Association honoured
the paper with the prestigious George A. Miller award.
We can also find inspiration in many non-peers. To exploit
what opportunities come our way, we need to start to focus on
the positive qualities in those we meet. This is important
because when we do dwell on the positive attributes of others,
they tend to manifest in us. The corollary is sadly true as well –
if we focus on the negative qualities in others, they tend to
assail us, and become part of our character.
2.2 Reflection and belief adjustment
A woman was working with some young people and was
concerned that some of them might be underperforming
because of a lack of belief in themselves. When she had them
all together she therefore spoke to them and said “Stand up if
you think you are dumb”. After a while Johnny stood up.
She said “Johnny do you really think you’re dumb?” He said
“No. I just felt sorry for you standing up all by yourself”.
Beliefs and attitudes can greatly affect our intellectual progress,
and the hapless (albeit fictional) woman in the above story
understood this.
Reflection is a powerful tool for scrutinising our beliefs and
attitudes with a view to improving them. Systematic reflection
also helps us to refine our thinking processes.
Few people would vote for a politician who refused to be
accountable. A lack of accountability tends to breed corruption,
which in turn can wreak havoc in people’s lives. People
therefore want politicians’ actions to be scrutinised. Our
thought processes and beliefs have much greater power over us
than politicians, but ironically, many of us fail to hold our
mental processes accountable. The research shows that when
we do hold our beliefs and thought processes up to proper
scrutiny, our thinking can improve considerably (Belmont,
1982; Butler et al, 2006).
It is important to point out at this juncture that novices to the
area of reflection often struggle with it initially. This struggle
may well occur because:
reflection does not provide an immediate sense of
gratification, and
the notion of reflection is often presented to novices
with very few models or worked examples.
CASE STUDY: For many novice students and
researchers the process of reflection is initially quite
foreign, and they need to have it demonstrated to them
in very concrete ways. In some countries there is a
tradition of having successful academics present a Last
Lecture. In such a lecture a Professor is asked to pass on
their wisdom to others, assuming that this is the last
chance they will have to do so.
If done well, a Last Lecture can be an excellent way for
an academic/researcher to communicate their most
significant reflections, and so provide effective models
from which others can learn.
On September 18th 2007, world renowned Virtual
Reality expert Randy Pausch provided a stunning
example of a well executed Last Lecture. Pausch’s Last
Lecture achieved significant poignancy because he gave
it shortly after finding out that he really did have very
little time left to live – he had just discovered that his
pancreatic cancer was terminal. This lecture by the
Carnegie Mellon Professor inspired multitudes worldwide, with about 6 million people watching it within a
year of its release. A book derived from the lecture also
topped the New York Times bestseller list. Pausch’s
reflections can be seen on You-tube at
Pausch explains in the video that before he arrived at
Carnegie Mellon he had managed to achieve all of his
childhood dreams, a fact which gave him a considerable
sense of fulfilment. From that time on he knew that his
mission was to help others fulfil their dreams. In his
presentation he gave his insights into
(i) how he achieved his own dreams,
(ii) how he motivated others, and
(iii) how he tried to draw the best out of those he
was guiding.
Pausch’s reflections managed to touch and inspire not
only those at Carnegie Mellon, but millions of people all
over the world.
The following subsections attempt to provide some further case
studies to illuminate the notion of reflection. These sections are
only an introduction – it is important that novices seek out
more examples and further insights through reading and
discussions with others.
2.2.1 Identifying mental blocks
Reflection can be very useful in helping us to identify major
mental blockages. The notion of a mental block is best
explained with an example.
CASE STUDY: A PhD student once recounted to me that
when he was an undergraduate, he spent one of his
exam preparation periods teaching himself a new
computer programming language rather than studying
for his exams. When I asked him why he did it, he said
that he was anxious about commencing his study, and
found it hard to face the anxiety. He started learning a
new programming language because it made him feel
less guilty about not studying.
In the above story, the student had a mental blockage –
namely an anxiety about study. The student did not want
to face this anxiety, and what he subsequently did was
all too common – he engaged in diversionary activity
which helped him to take his mind off the issue he really
needed to face.
The kind of diversionary activity described above is
symptomatic of self-sabotaging behaviour. If we detect such
behaviour, it is necessary to look for the attitudinal blockage or
flawed belief which is triggering it. Reflection can help in this
Mental blockages may come in the form of risk aversion,
anxiety, laziness, fear of failure, or a variety of other issues. To
identify these blocks we should use reflection, and ideally these
reflections should be shared. That is, after looking to ourselves
for the answers, we should air our own perceptions with wise
and learned colleagues, counsellors or friends. In addition to
providing objective feedback on our insights, others may well
be able to see tendencies in us which are hidden from our own
Removing blockages by adjusting our beliefs
and attitudes
Once a block is identified, it is necessary to take action to
remove it. A useful strategy is to challenge the beliefs and
attitudes underpinning the blockage repeatedly. In doing this,
it is crucially important to give ourselves time to rise to the
challenge. Human beings have great difficulty changing
attitudes and beliefs suddenly – we need time to be able to
gradually embrace the required changes (Kearns et al, 2008).
Courageous, honest and persistent reflection (ideally combined
with on-going counselling sessions) can provide clues on how
to adjust our beliefs and attitudes, and thereby deal with
blockages. The following story illustrates some of these points.
CASE STUDY: At one stage I had to manage a situation
with someone who failed to write up the results of their
work in a timely fashion. The delay in the writing went
on for weeks and months, and so I knew there was a
major problem.
I pressed the issue of the overdue work on several
occasions and eventually we had a revealing discussion.
The person told me that they had a writing block, but
they did not know why. They said that they really wanted
to find out why, and decided that they would do some
serious reflecting on the issue, asking me to support
them in it. I agreed to this and they did indeed go away
and spend time in reflection.
Sometime later, the person confided in me that they had
uncovered the reason for the block. They said that
whenever they had tried to write previously, they had
been frustrated by a mass of jumbled and disorganised
thoughts. This had caused them to get stressed, and they
were discouraged from doing any further writing. That
is, the person’s belief was that they would be confronted
by disorganisation and discouragement whenever they
started writing.
Reflection on this problem had prompted them to realise
that this belief was ill-founded. They could overcome the
discouragement if they simply wrote down all their
initial thoughts and organised them later. That is, they
could do the editing in a second stage. They told me that
they had started doing this, and that it was starting to
The advantage of sharing reflections with one another
(as happened in the above example) is that it not only
helps us to clarify our own thoughts, but also triggers
productive reflections in others. The above reflections,
for example, impelled me to start thinking about my own
strategies for writing. I had spent much of my life not
wanting to write. I actually pursued a career in
engineering and the physical sciences so that I would not
have to write much (little did I know!). When I started
my PhD, though, I realised that I would have to do some
serious writing, and so I made a decision to embrace the
writing process. I then started to enjoy it more and
more. As I reflected on why this had occurred, I realised
that it was because I too had learned to progress the
writing in stages.
When I write now I record all my thoughts (jumbled as
they might be) very quickly, and I typically generate a lot
of text. This tends to give me a sense of achievement.
When I come to the next pass at the writing, I read the
previous version and reflect on it by asking myself many
questions - Is the draft clear? Is it factually correct? Is it
interesting? How can I improve it? As I answer these
self-posed questions I begin to change the manuscript
substantially, and the new version is generally a
significant improvement on the previous draft. The fact
that I have made an improvement gives me a further
sense of fulfilment. Each new draft (and there are many
of them) is by my reckoning an improvement on the
previous one, and the continuous improvement tends to
provoke positive feelings in me about the writing
Some blocks can stubbornly resist removal because they are
strongly supported by many years of ill-founded beliefs and
dysfunctional attitudes. In such cases it can be helpful to
identify the reasons we first developed the inappropriate
attitudes and beliefs. Once these reasons are identified there is
a better chance that we can deal with them. The following case
study illustrates these points.
CASE STUDY: Many years ago I participated in a
positive thinking course which promoted the use of
affirmations to achieve life goals. The key message of the
seminar was that if we repeatedly make affirmations we
come to believe them, and if we believe them, they
eventually become a reality in our lives.
After the seminar I devised some affirmations and
commenced faithfully reciting them. Since I wanted to
become a better singer, one of these affirmations was: “I
am a fantastic singer”. One day, as I was reciting this
affirmation, I felt substantial anger rising up inside of
me, and I said to myself “No I’m not. I’m a terrible
singer”. I then had vivid recollections of someone telling
me that my singing was poor when I was a child. At that
point I realised that a part of me had believed it ever
As I reflected on the negative emotions that
accompanied my childhood memory, I concluded that I
had been carrying around anger for many years without
realising it. I knew that this was unhealthy, and I made a
decision to let the anger go.
A short time later, an unusual turn of events occurred,
and I found myself in a position where I was singing
right next to the very person who had told me my
singing was poor as a child. At the end of one of the
songs that person turned to me and said “I’ve witnessed
a miracle. You sang every note on key”. I was stunned. It
was then that I realised my unresolved anger had not
only been unhealthy, it had also kept my mental
processes bound up. It had therefore inhibited my
singing ability.
This case study illustrates, among other things, the
importance of responding appropriately to feedback. If
we receive feedback and respond positively to it, we tend
to improve. If, on the other hand, we receive feedback
and respond negatively to it, our attitudes, beliefs and
subsequent mental progress can be badly affected
(Hattie, 1999).
As a child I chose (albeit subconsciously) to respond to
early feedback I received about my singing in a negative
way. This undermined my ability to believe in myself
and my progress in singing stagnated as a result. Later
in life I changed my attitude. I decided to put some
energy into improving my singing rather than into
blaming someone who gave me honest feedback. That
was the trigger for my improvement.
Many of us suffer the ill effects of negative childhood
experiences. We may be stilted in our cognitive functioning
because of anger towards parents, family members or friends.
We may be unwilling to take risks because our early
experiences made us believe us that we could not be loved if we
failed. If we are brave and persistent, though, we can uncover
our flawed attitudes, change our beliefs, and gradually progress
in improving our mental capabilities. Reflection and
counselling can help in this regard.
A useful strategy for dealing with blockages is to look at the
areas which cause us the most grief. In particular, we should
look at areas where recurring patterns of grief, frustration and
anger occur. Then we need to start searching for unhealthy
responses we might have made to others in those areas.
Remarkable changes can occur when we deal with these
blockages, particularly if we start to deal with the negative
responses we have made as young children.
Scheduling time to reflect on improving
thinking and discovery
There is a key point to consider when engaging with reflection.
Just as weight lifting does not cause instant muscle growth, so
reflection does not necessarily produce instant revelations
about how we can solve problems or make improvements in
our mental processes. Reflection stimulates our conscious and
subconscious mind to start finding answers for us. Long after
our conscious mind has ceased to ponder, our subconscious
mind can be at work in a process known as incubation (Wallas,
1926). Because of incubation, answers can come to us at the
most unexpected moments.
Research has shown that the quality of ideas that come to us in
incubation tends to be dependent on the amount of time spent
reflecting on the problem before we stop consciously thinking
about it (Dodds et. al., 2009). A significant time investment is
therefore required for reflection if we are serious about
improving our thinking and discovery. This is entirely
analogous to a bodybuilder who must spend long periods of
time lifting weights in order to see physical muscle gains. The
amount of time needed for reflection will vary with the
individual, and should be determined from experience. If
inadequate improvement is obtained, we should try increasing
the allocated time.
For those who are not experienced in reflection it may be useful
to be guided by trying to answer some self-posed questions.
Examples of these kinds of self-posed questions are listed
Am I progressing well in my studies/research?
If I am not progressing well, what are the reasons I am not
Who do I see around me who is progressing well, and what
cognitive and behavioural strategies are they using in their
What concrete steps could I take to make at least some
progress today?
If I look back at my life, when did I experience a lot of success?
What was I doing to foster that success?
Figure 2.2. Spending time alone to reflect helps to improve thinking.
2.2.4 Maintaining a reflective journal, or writing
papers on thinking and innovation
Reflective journals are a common tool used to stimulate
reflection. Typically, a person records their reflections in an
ongoing way in the journal. It is best if the journal is not an end
in itself, but is used to stimulate shared reflection with peers.
This shared reflection can be achieved, for example, with
journaling groups in which peers come together to discuss their
most recent reflections. PhD students may also find it helpful
to regularly discuss the reflections in their journal at supervisor
There are two key desired outcomes for journaling. The first is
to stimulate us to find new and better ways to think. The
second is to keep a record of our thought processes.
CASE STUDY: Many of the world’s most eminent
researchers keep systematic records to document the
evolution of their thinking and to stimulate reflection.
Alexander Graham Bell, the inventor of the telephone, is
one of those who did keep such records, and it is just as
well that he did.
Bell and a competitor filed separate patents for the
telephone in the US on the same day, and there was a
significant dispute over whether it was Bell or his
competitor who really deserved the credit for the
invention of the telephone.
During a period of about twenty years, The Bell
Telephone Company had to defend over 600 legal
challenges to the primacy of the telephone patent. It is
not entirely surprising that Bell’s patent was challenged
– a great deal was at stake. The patent rights for the
telephone were estimated to be worth about $25 million
in 1878.
The Bell Telephone Company essentially succeeded in its
many court battles, largely due to the existence of Bell’s
journals and family letters. Those journals recorded
Bell’s evolution of thought as he developed the
telephone, while letters from his rivals acknowledged his
prior work. This documentation swung the decisions of
the courts in Bell’s favour.
Bell’s journals therefore served two purposes. First, they
helped him to clarify and refine his thoughts. Second,
they helped to establish the legitimacy of his intellectual
Practicing reflection during problem solving
It is highly advantageous to reflect on our thinking during the
process of problem solving – this can help us to critically
evaluate and improve our problem solving strategies. For
beginners in this kind of reflection, it can be helpful to have a
structure which guides the process. One such structure is the
Task Evaluation and Reflection Instrument for Student Self
Assessment (Belski, 2009). This instrument uses three key
Before attempting to solve any problem, write down
the anticipated level of difficulty of the problem (on a
scale of 1-5).
(ii) Solve the problem and then re-rate the level of
difficulty experienced in actually solving the problem
(again on a scale of 1-5).
(iii) If there is a discrepancy between the ratings provided
in Steps (i) and (ii), reflect on why this discrepancy
occurred. Write down these reflections, along with
recommendations on how you could go about solving
this type of problem better in the future.
It has been found that in most cases where this instrument is
used, the scores given in Steps (i) and (ii) tend to be different.
This discrepancy tends to set up a state of questioning in the
problem solver, which instinctively prompts them to engage in
reflection (Belski, 2009).
2.2.6 Crisis and adversity
It is not only voluntary mechanisms which stimulate reflection.
Some involuntary stimuli can also be very effective. At some
stage in our life we all face some crisis or adversity which
causes us pain. Work by Paulo Freire among the very poor in
Brazil highlighted the fact that when people become aware of
the root causes of their adversity and sense a means to deal
with these root causes, they can make exceptionally rapid
progress (Gadotti, 1994). This was evidenced by Freire’s efforts
in teaching poor sugarcane workers in South America. Once
these workers realised that being able to read and write could
help them to achieve a less problematical life, they were infused
with stunning levels of motivation – 300 of them became
competent in reading and writing within just 45 days (Gadotti,
When we do experience adversity (of any kind) we may well
start to reflect on the root causes of that adversity, and on
mechanisms for dealing with the root causes. What can follow
is very significant growth.
Figure 2.3. Desert like experiences can stimulate effective reflection.
2.3 Shrewd acquisition of appropriate
background knowledge and skills
Research performed between 1950 and 1990 produced
invaluable insights into how human beings acquire problem
solving expertise. This research was spearheaded by Herbert
Simon, one of the most accomplished and diverse researchers
of the 20th century. He won the Nobel Prize in Economics,
pioneered the development of Artificial Intelligence, laid key
foundations for Complex Systems Theory, and wrote many
groundbreaking and heavily cited papers in the area of
Mathematics, Cognitive Psychology, and Decision Theory.
In 1957 Simon and his co-worker, Alan Newell, developed a
pioneering computer program called the General Problem
Solver (GPS). This program attempted to mimic the problem
solving strategies of human beings.
The GPS program employed generic problem solving strategies
to solve new and unseen problems. While it was successful in
solving basic problems, it proved incapable of solving many
advanced problems which humans could solve relatively easily.
The failure of the GPS program to match human problem
solving capabilities propelled Simon and others to further
investigate the way in which humans acquired problem solving
It was ultimately discovered that early machines like GPS
underperformed because, unlike humans, these machines did
not accumulate pertinent background information during the
course of their operation. Well functioning humans, on the
other hand, do tend to accumulate large stores of relevant
background knowledge and skills within their long-term
memories (Sweller et al, 1998). These large stores of
background information are vitally important for problem
The importance of background knowledge for problem solving
became clear through investigations in the realm of chess (De
Groot, 1965; Chase & Simon, 1973). Studies showed that expert
chess players had very similar generic problem solving
strategies to those of novices. The experts differed greatly from
the novices, however, in the amount of knowledge and
experience they had. The experts were found to devise their
moves by subconsciously recognizing previously encountered
chess board patterns, and by drawing on their prior experience
with these patterns.
Simon concluded from his studies that to develop expertise one
needed to not only acquire generic problem solving skills, but
also to accumulate large chunks of domain specific information
in long-term memory. This information had to be in a form
that could be efficiently accessed by the brain, and generally
took the form of coded mental patterns. Simon’s investigations
indicated that to become an expert in a given field one needed
to have about 50,000 chunks of coded information (or
Subsequent investigations focused on mechanisms for
facilitating the rapid acquisition of schemas in pursuit of
problem solving expertise. Simon found that the process of
studying worked examples was a very effective means for
rapidly acquiring schemas (Zhu & Simon, 1987). Worked
examples are essentially well organised and well
communicated solutions to appropriate problems which are
provided by others. If one properly studies these examples one
implicitly starts to recognise which problem solving steps are
needed to solve given problems.
CASE STUDY: In 1983 a new method of instruction was
trialled for the teaching of algebra to Chinese middle
school students. In this new method the students simply
studied the many and varied worked examples which
had been compiled by a teacher. The day to day role of
the teacher was minimal – there were no formal lectures
and almost no formal explanations.
It was found that the students studying the worked
examples without day to day teacher intervention
outperformed a similar class which was taught via
traditional means. In fact, the students who obtained
their guidance by studying only the worked examples
were able to effectively master three years of algebra in
just two years (Zhu & Simon, 1987).
It was also found that the students studying the worked
understanding. This understanding appeared to be
facilitated because the provision of solutions along with
the problems gave students more scope to observe and
discover important underlying principles themselves as
they studied. This impacted positively on student
progress because the act of discovery tends to create a
rush of adrenaline which reinforces skill acquisition
(Rock & Schwartz, 2006).
By contrast, it was found that when novices tried to solve
new problems without guidance from worked examples,
they were often so pre-occupied with trying to solve the
problems they paid little attention to absorbing
underlying principles as they went.
The relatively poor outcomes that tend to occur when novices
try to solve problems by themselves can be explained by
considering the cognitive architecture of the human brain.
Research into this architecture reveals that there are two key
structures in the brain which have relevance for problem
solving. These two structures are commonly referred to as the
working memory (WM) and the long-term memory (LTM)
(Anderson, 1983).
The WM is where conscious processing and data transfer tends
to occur, while the LTM is the structure where subconscious
processing tends to occur.
The WM has very limited capacity, and this has significant
implications for the rate at which new information or concepts
can be acquired. At any one time the WM can accommodate
only about seven pieces of elementary information (say the
seven digits of a telephone number). Moreover, the data
typically cannot reside in the WM for more than about 30
seconds, unless rehearsing occurs (Cowan, 2001). If the new
information is being processed rather than simply being stored,
it is thought that the WM may only be able to deal with two or
three pieces of information at a time (Kirschner et al, 2006).
Because new information almost always passes through the
WM before reaching the rest of the brain, the limitations of the
WM are very significant. Because of these limitations the
demands on cognitive processing need to be kept low for
novices. Obtaining guidance from worked examples is one way
to keep these demands low. While novices are studying a
worked example their minds are not consumed with having to
find the solution. Rather, they can focus on gradually and
purposefully extracting critically important underlying
principles from the given solution - overload of the WM is
generally therefore avoided.
By contrast, when novices begin by solving problems on their
own they often flounder. This is so because problems tend to
prompt humans to set goals, and these goals must be managed.
The goal management process tends to consume a lot of the
WM’s cognitive resources, leaving very little for the purposes of
extracting important underlying principles (Sweller et el, 1998).
It is not only Simon and his co-workers who uncovered
evidence for the importance of studying examples. Sweller and
Cooper independently identified the so-called worked example
effect (Sweller & Cooper, 1985).
CASE STUDY: Traditionally it has often been assumed
that a good strategy for improving problem solving skills
in a given area is to grasp some basic theory in that area,
and then start solving problems which apply that theory.
Sweller and Cooper’s investigations led them to believe
that this approach would be ineffective because when
novices were faced with new problems, they typically
wasted the bulk of their limited cognitive resources
trying to manage the problem solving process.
They argued that a ‘mastery via studying worked
examples’ approach would work better. They set up an
experiment in which novices learned to solve algebraic
problems largely via engagement with worked examples.
This process involved four steps.
understanding of the relevant algebraic
The novices then studied a series of worked
examples and asked relevant questions until
they believed they understood the examples.
The novices were then asked to explain the
goal of each example problem as well as the
kind of operations used in each step of the
The novices then solved similar problems
Sweller and Cooper found that the above approach
worked very successfully. From their investigations they
also identified the importance of studying many and
varied worked examples. That is, it was not simply
observing one or two examples which facilitated skill
acquisition. Rather, effective long-term understanding
was fostered by studying many examples, with enough
variations within those examples to convey all the
pertinent underlying principles.
The worked example effect has been validated in many
different domains by numerous independent investigators
(Hilbert & Renkl, 2007; Gergets et al, 2004; Atkinson et al,
2000). In different domains, the worked examples will of
course take on different forms. In non-mathematical
disciplines the examples may, for example, take the form of
stories which illustrate important principles or they may be
model essays.
The notion of studying worked examples is not new – books
have traditionally provided examples for readers. What is
comparatively new, however, is the evidence that people need
to study many more examples than was previously thought to
be necessary.
If novices study many well chosen and well varied examples
they tend to advance quickly in their competence, and the
relevant schemas eventually build up to a critical mass. Once
the critical mass is reached in the build up of schemas, the
schemas themselves are able to provide the person with
internal guidance in problem solving. That is, an expertise
reversal effect occurs, whereby the novice transitions to an
expert (Sweller et al, 1998). When this point is reached there is
no further need for external guidance (via worked examples or
any other means). In fact, if external guidance is provided at
that point performance tends to deteriorate because attention
is split between the internal and external sources of guidance.
If we do build up a large body of schemas, it is then much
easier for us to grasp new concepts and make new discoveries
of our own. It needs to be noted, though, that schema
acquisition takes time. Expertise development typically
therefore requires substantial amounts of time even for those
who are gifted (Singley & Anderson, 1989).
CASE STUDY: Michael Faraday is thought by many
scientists to be the greatest experimental researcher who
ever lived. He did numerous groundbreaking experiments
in Physics, Chemistry and Electromagnetism. He is
probably best known for inventing the electric motor and
the electric dynamo (or generator).
Faraday went on to inspire many others, most notably
Thomas Edison. During his time as a telegraph operator, a
young Edison became very interested in the operation of
the telegraphy equipment. In a bid to find out more about
the pertinent electrical science, he bought the works of
Faraday and devoured them. A colleague of Edison’s
remarked that after Edison bought and read Faraday’s
works “his mind was on fire”.
Edison thoroughly studied Faraday’s many experiments
and repeated a large number of them himself. By studying
and repeating many of Faraday’s experimental examples,
Edison rapidly built up his expertise as an experimental
researcher. His sound background knowledge then allowed
him to embark on new experiments of his own.
Edison’s own experimental research subsequently became
so successful that telegraph companies were eventually
prepared to employ him for inventive work. His big
breakthrough came when he invented the quadruplex
telegraph, a device which could send telegraph messages in
both directions with just one pair of conductors.
The quadruplex telegraph netted Edison $10,000 in patent
rights, and enabled him to fund facilities for further
research. Edison went on to become extremely successful.
He invented, among other things, the first practical electric
light bulb, the first device for recording sound and the first
motion picture camera.
In his approach to acquiring background knowledge and
skills, Edison showed great wisdom. In his early career he
thoroughly studied and repeated the many and varied
examples provided by Faraday. This strategy almost
certainly helped him to rapidly build up a substantial body
of relevant schemas. With these schemas in place he was
well situated to grasp new concepts and make new
discoveries of his own.
Building up background knowledge and skills
by engaging with goal-free problems
The study of worked examples is not the only way to efficiently
build up background knowledge. Engagement with goal-free
problems is an alternative way.
Goal-free problems are open-ended problems in which the
goals are not precisely defined. An example of a conventional
problem might be to find a particular angle in a geometric
figure, whereas a goal-free problem would be to find whatever
angles one can in that same geometric figure.
Goal-free problem solving tends to be effective because it does
not waste the WM’s limited resources trying to manage
attainment of a specific goal. These resources can therefore be
dedicated to absorbing important underlying principles.
CASE STUDY: For many months I worked with a PhD
student and repeatedly asked him to do a statistical
analysis of a simple processing operation that he was
employing in his work. The statistical analysis was not
trivial, but he was clever, and I felt that it should be
within his capabilities. Every week, however, he came
back without having done it. He indicated that it was too
After reflecting on the impasse with the student, I
changed tack in my supervision strategy. I started to feel
that an open-ended (goal free) task might be more
effective. I therefore asked him to do an adaptation of
any existing derivation to a slightly different context. I
let him choose the particular derivation and the new
context himself, but I told him that I wanted some
results by the end of the week. By leaving the problem
open-ended, I knew that he would not be able to say that
the problem was too difficult, because he could choose
the context himself, and he could make it as simple as
To my surprise (and delight) he came to me at the end of
the week and showed me his results - he had successfully
completed the first part of the statistical analysis that I
had been asking him to do for months. Interestingly,
when the problem was made open-ended he started to
make good progress.
2.4 A commitment to deliberate practice in
diverse contexts
CASE STUDY: Alvaro Pascual-Leone is a neuroscientist
who conducted important experiments into the nature of
skill acquisition. He charted the brain maps which
developed over time as blind people attempted to use
Braille. Over the period of a year, these blind people
engaged with Braille by practicing two hours a day in
class, followed up with one hour of homework. The
students worked 5 days a week, from Monday to Friday.
Pascual-Leone found that the brain maps for Braille
reading would enlarge very significantly from Monday to
Friday, but would return substantially to their original
size by Monday (Pascual-Leone & Torres, 1993). That is,
the skill acquisition which occurred between Monday
and Friday appeared to be transitory. It seemed to
disappear during the week-end break.
The brain maps taken on the Mondays remained almost
unchanged until the students had practiced for about 6
months. Between 6 months and 10 months, the skill
acquisition became less and less transitory, with the
Monday and Friday brain maps becoming more and
more similar. Once the Monday brain maps reached a
peak at around 10 months they were quite stable – they
did not change even when the people took a two month
break. Pascual-Leone concluded that long-term practice
and focus was needed to engender lasting change in
people’s brains. That is, he concluded that sustained
practice was crucial to reliable skill acquisition.
Pascual-Leone’s research concerned itself mainly with the
development of a very specific skill. Other research has
examined the impact of sustained practice on development of a
broad cluster of skills (i.e. on development of expertise within a
given field). This research has shown that development of a
high level of expertise in an area requires about 10,000 hours
of deliberate practice (Ericcson, 2005). Note that it is not
simply practice that is required, but deliberate practice. The
latter is practice which is:
driven by a vision,
informed by copious amounts of feedback,
repeated frequently with continual monitoring of
mentally demanding and engaging,
characterized by regular striving beyond what has
previously been achieved,
guided by substantial amounts of reflection.
Malcolm Gladwell points out in his book, Outliers: The story of
success, that super-achievers such as Mozart, Bill Gates, The
Beatles and chess champion, Bobby Fischer, all engaged in
enormous amounts of deliberate practice before becoming
famous (Gladwell, 2008).
CASE STUDY: Roger Federer is one of the greatest
tennis players ever. His interest in the sport was ignited
at the age of four when he watched Boris Becker win
Wimbledon. From that point on, Federer began to watch
tennis matches on TV for hours at a time. He thus began
his engagement with tennis by studying many and varied
examples. He soon began to practice three times a week,
and by the age of six had become the best in his age
group. Federer was passionate about tennis, and
frequently articulated an intention to become the best in
the world. Many people scoffed at his lofty ambitions
(even his coach), but he was undeterred.
In his practice sessions Federer adopted a different
approach to most of his peers. Whereas others would
routinely practice skills at which they were already
competent, he would regularly experiment and push
himself in new areas. As a result, he built up an
impressively broad range of capabilities, and this may
well explain why he is considered by many experts to
have had no weaknesses on the tennis court.
While Federer developed competence quickly, he had to
practice for many thousands of hours (spanning a period
of about twenty years) before he reached his goal of
becoming world number one. During these years of
training he benefited from much feedback, being
coached by a number of different people. Federer also
reflected habitually, as is evident from his many
Tellingly, Federer’s journey to the top of his field
incorporated all the essential elements of deliberate
practice. He was driven by a vision to become the best in
the world, he began by studying many and varied
examples, he practiced intensely over a long period, he
received copious amounts of feedback, he regularly
‘pushed the envelope’ in his practice and he reflected on
his progress often.
2.4.1 Thorough practice
Research indicates that practice tends to foster the automation
of skills. If one pushes the envelope within practice in a
thorough and diverse way not only is automation built up, but
so is flexibility (Perkins & Salomon, 1992). This subsection
explores the issue of thorough practice, while the following one
discusses diverse practice.
To progress in thorough practice we typically need to change
our attitudes. In particular we need to move towards an
attitude of seeing challenging or time consuming mental tasks
as mechanisms for growth. Successful body builders
understand that new physical muscle is built up by first
breaking down existing muscles. Because of this understanding,
many body builders actually derive a great sense of satisfaction
from feeling pain as they lift weights. The pain triggers them to
think about the fact that new muscle is starting to form – their
minds are more focussed on the reward of new muscle growth
than on the momentary pain.
Those of us who are intent on building intellectual muscle need
to emulate the attitudes of successful body builders. We need to
keep our eyes on the reward of increased cognitive capacity, not
on the inconvenience of engaging with difficult or time
consuming problems.
CASE STUDY: When I started doing my PhD I began
reading articles in the top ranked international journal
in my field, namely the IEEE Transactions on Signal
Processing. When I started to read these articles I was
staggered at the complexity of the mathematical
derivations in many of them. I found a lot of these
papers impenetrable. Nonetheless, my supervisor made
it clear to me that the standard in these papers was the
standard that he wanted me to attain. His insistence
eventually helped me to see that the need to master
mathematical derivations was an opportunity to grow.
In trying to grapple with doing derivations, I started
looking at the very simple ones. I asked myself if I could
transfer some of the very basic techniques in these
simple derivations to the related problems that I was
studying. I found that in some cases I could. I modelled
my derivations on the existing ones, and made
adjustments to suit the problems I was investigating.
This helped me to start mastering simple derivations.
Then I started looking at slightly more complicated
derivations. Again, I asked myself if I could transfer
some of the existing techniques to my area of
investigation. Again the answer was yes.
I gradually attempted more and more complex
derivations, and as I did my confidence started to build.
I often did the derivations by adapting existing
derivations to new contexts. I continued to use this
approach and eventually produced mathematical
derivations that were sophisticated enough to be
accepted in the IEEE Transactions on Signal
The approach described in the previous case study is a task
variation strategy. This is a phenomenon whereby an overall
outcome is achieved via performing a set of tasks, with each
new task being slightly more complex than the previous one. To
accomplish each new task the person must transfer
understanding from existing knowledge (possibly acquired
during the previous task). Task variation is known to accelerate
thorough skill acquisition, and also to help people to develop
habit patterns of skills transfer (Schilling et al, 2003).
2.4.2 Diverse practice
To make progress in diverse practice, it is frequently necessary
to change our attitudes. In particular we need to move towards
an attitude in which we see all areas of thinking and discovery
as relevant.
CASE STUDY: Isaac Newton’s life bears testimony to the
power of diversity in thinking and discovery. Newton
created revolutions in four separate areas: mechanics,
mathematics, physics, and universal gravitation
(Morrow, 1999). These revolutions changed the world,
and yet he spent much more time writing on theology
and philosophy than he did on the physical science
advances for which he is best known. He also spent large
amounts of time studying chemistry, and working in
high profile administrative roles (such as President of
the Royal Society, Member of the British Parliament,
and Master of the Royal Mint).
One might wonder how Newton could embrace so many
different areas and achieve so much. It was precisely
because of his diversity that he was probably able to
achieve so much. This diversity honed his ability to see
the common simplifying principles, and his
preoccupations with theology and philosophy almost
certainly heightened his reflective powers and sense of
Figure 2.4. Isaac Newton’s thinking showed enormous diversity.
While we may not rise to the levels of achievement that Newton
did, we can all improve our cognitive prowess by increasing our
diversity of engagement.
There is another critical point to make about diversity. There is
an intriguing physiological benefit to habitually building up
skills in new areas – namely, the longevity of our brain cells.
Research shows that the more intensely we embrace the
development of new skills, the longer our brain cells tend to
live (Gould, 2000). If we wish to preserve our mental
functioning into old age, then, we need to value opportunities
to acquire skills in new areas.
CASE STUDY: James Cameron is one of the most
successful movie makers in history. He created Avatar,
Titanic, The Terminator, Terminator 2: Judgement
Day, Aliens, The Abyss and True Lies. Two of these
movies, Titanic and Avatar, became the two highest
grossing movies of all time. Why has Cameron’s
commercial success exceeded that of so many of his
His biographer, Rebecca Keegan, pointed out in The
futurist: The life and times of James Cameron, that
Cameron is unique among directors in that:
(i) he is only interested in doing things that are hard,
(ii) he is intensely engaged in very diverse areas.
In summary, he systematically engages in thorough and
diverse practice.
As a young man James Cameron was greatly interested
in drawing, painting, writing, physics and astronomy.
He decided that rather than focus on just one of these
areas, he would pursue all of them. To this end he
enrolled in formal college courses in diverse areas such
as Physics, English, and Philosophy.
After college he began to realise that science fiction
movies were a realm which incorporated all of his areas
of interest. This inspired him to start writing film
scripts. At the same time, he also began to do his own
research into cameras so that he could see how they
Cameron, in fact, does not refer to himself as a director,
because within his movies he is engaged in much more
than simply film direction. He is an artist, creator,
writer, director, inventor, researcher and producer. In
Titanic, for example, he drew the sketches produced by
Leonardo de Caprio’s character, Jack. He wrote the
scripts for The Terminator, Titanic, Avatar and The
Abyss. He also co-wrote the scripts for Aliens,
Terminator2: Judgment Day and True Lies. To realise
his filmmaking vision for Titanic, Avatar, Terminator 2:
Judgement Day, and Ghosts of the Abyss he researched
and co-invented new underwater cameras and remote
Ultimately, Cameron’s commitment to thorough and
diverse practice has paid off in major technological
breakthroughs and in extraordinary commercial success.
2.5 Habitual abstraction of key underlying
principles from new situations
There are many skills which we need to master in life.
Efficiencies in the mastery process can be achieved by routinely
abstracting the important principles from any given situation,
in readiness for applying them to other contexts.
CASE STUDY: During the 16th and 17th centuries various
scientists studied the motion of physical bodies. Gallileo
provided detailed mathematical descriptions of the
motion of uniformly accelerated bodies. Huygens
mathematically characterised the motion of pendulums.
Hooke, Halley and Kepler provided mathematical
descriptions of the motion of planets and other heavenly
Aware of the need to advance the work of all these
scientists, Christopher Wren offered a small financial
reward to Halley and Hooke if they could provide a
unifying theory for all these existing results. Wren
stipulated that the new theory needed to not only unify
the existing results, but to also show how force and
motion were related.
Halley then took Wren’s challenge to Isaac Newton.
Newton’s proceeded to work feverishly on the problem
and ultimately abstracted four key underlying principles
from all the existing work. These four principles
included his three laws of motion and the law of
universal gravitation. Newton showed that these four
key principles could not only be used to explain existing
results, but they could also predict an enormous range of
new physical phenomena.
Newton’s articulation of these key underlying principles
triggered extraordinary new learning in the scientific
community. These principles enabled buildings and
bridges to be designed and built much more efficiently.
They enabled mechanical devices to be designed more
elegantly. Indeed, much of the industrial revolution was
empowered by Newton’s newly articulated laws
CASE STUDY: In the early 1980s Palincsar and Brown
attempted to understand why some children
comprehended very effectively as they read and why
others didn’t.
As they performed their investigation they abstracted a
key underlying principle – those who comprehended
effectively reflected as they read, while those who
comprehended poorly did not engage in reflection. That
is, the good readers would slow down and reflect if they
did not understand a passage. The poor readers, on the
other hand, would not slow down when they did not
The extraction of the important principle underlying
comprehension sparked significant new learning.
Palincsar and Brown reasoned that if they intervened to
help weak readers to reflect they might be able to
improve achievement levels. They therefore embarked
on an intervention where the students were carefully
guided through the reflection process during reading,
The results were remarkable - the students improved not
only in their reading subject but also in other areas such
as science (Palincsar & Brown, 1984).
CASE STUDY: Genrich Altshuller was born in
Uzbekistan in 1926. He showed a natural talent for
invention as a child, and was even granted his first
patent while still as school. At the age of 20 he
commenced work in the Inventions Inspection Division
of the Soviet Navy. His job was to inspect patents and
abstract general principles from them which could help
others to invent.
Altshuller studied more than 200,000 patents, and
through this study realised that patent applications
rarely corresponded to real inventions. Most were
simply incremental advances on prior work. When
Altshuller did find genuine inventions, he tried to extract
the important underlying principles. His efforts enabled
him to discover forty key principles which seemed to
underlie most inventions (Altshuller, 1984).
Altshuller believed that his insights into invention might
be able to help improve Russian industry, which was still
trying to recover from the ravages of World War II. He
therefore took some of his ideas to Joseph Stalin. He
received a frosty reception, however, and was
imprisoned in a Russian Gulag above the Arctic Circle.
While in prison, Altshuller had the opportunity to
converse with many other intellectuals and academics.
These conversations helped him to deepen his already
substantial insights into creativity and invention.
Altshuller articulated many of his ideas in writing, and
this work eventually came to receive a great deal of
attention (Altshuller, 1984). The so-called TRIZ
methodology that he developed is now used widely in
industry to stimulate invention and creativity. It is
discussed more fully in Chapter 4.
Edward de Bono was another pioneer who has affected
contemporary thinking through his efforts to extract important
principles from new situations. In the late 1960’s he sought to
determine what underlying principles existed in creative
thinking and creative problem solving. De Bono’s
investigations and insights led to the popularisation of many
algorithmic techniques for stimulating creativity (De Bono,
1967; De Bono, 1992). De Bono’s techniques are discussed
further in Chapter 4.
Formal study for facilitating competence in
Certain disciplines appear to be well suited to developing skills
in abstraction. Within the scientific disciplines, the study of
Mathematics appears to be quite fruitful in this regard. A
survey of employers and managers in (SIAM, 2009), for
example, found that mathematicians were highly valued
because they:
had well developed skills in abstraction,
were able to analyse underlying structures, and
had logical thought processes.
The notion that the study of Mathematics enhances problem
solving skills (arguably through the fostering of skills in
abstraction) appears to be supported by a 2007 article in
Science (Sadler & Tai, 2007). The study in that article carefully
examined the impact of various high school study programs on
success in university. It was found that if students had studied
Mathematics in high school, those students tended to perform
significantly better not only in university level Mathematics,
but also in Biology, Physics and Chemistry. On the other hand,
students who studied Physics at high school tended to do better
in university level Physics, but not in Chemistry or Biology or
Mathematics. Similarly, students who studied Biology or
Chemistry at high school tended to do better in the same
discipline at university, but not in the other disciplines.
Within the social science disciplines, the study of Psychology
appears well suited to improving problem solving skills
(Lehman et al, 1988). One might speculate that this is because
the study of Psychology gives people practice at trying to
abstract principles about why human beings behave and think
the way they do.
2.6 Engagement with analogies and
CASE STUDY: When Leonardo da Vinci considered how
to facilitate human flight he drew on two analogies. The
first was that of a bird flying. From his study he
concluded that birds relied not only on flapping their
wings for flight, but also on riding thermal wind
currents. He therefore designed a hang glider with large
wings that could ride the wind currents like birds.
In trying to generate lift off the ground, Leonardo looked
to a second analogy - that of the Archimedes screw. The
latter was a device which was used to draw water up
from a low-lying region. It consisted of a screw-shaped
blade encased in a cylinder. When the screw was
manually turned it drew water up the cylinder. Leonardo
recognised that if one were to manually (or
mechanically) turn a screw in the air, it would create an
analogous thrust of air upwards. This analogy gave him
the idea for his helicopter.
When the Wright brothers developed their flying
machine they incorporated both of Leonardo’s ideas (as
well as some new ideas of their own). They made a plane
with large wings which could ride on the wind. (These
wings were also shaped with a camber so as to induce
upward thrust as the plane moved forward). The
brothers additionally placed rotating blades (i.e. a form
of rotating screws) at the front of the plane to create
forward thrust. Analogy featured strongly, therefore, in
the development of the aeroplane.
CASE STUDY: It is well known that hot air is more
buoyant than cold air, and therefore tends to rise. As
mentioned already, Leonardo da Vinci noticed that birds
often took advantage of this phenomenon by hovering
with outstretched wings above hot air pockets so that
they could rise effortlessly.
Scientists have recently created maritime thermal
gliders which operate on an analogous principle to that
used by birds. These gliders exploit the fact that there
are temperature gradients in the ocean. Deep ocean
water is cold (2-4 0C), while surface water has a much
higher temperature because it is warmed by the sun.
Thermal gliders are filled with special fluid which
becomes less as the temperature decreases. When these
gliders are positioned deep down in the ocean the
decreasing density of the fluid increases the buoyancy of
the glider and so it rises effortlessly. When the glider
gets closer to the ocean surface the warm temperatures
cause the fluid to become less dense and so it sinks.
Because of its fluctuating buoyancy the glider has a
tendency to regularly move up and down in the water.
An adjustable rudder on the glider is able to direct some
of the upward and downward movement into horizontal
motion as well. As a result, the glider can navigate up,
down and horizontally, with very little energy
Because they exploit buoyancy effects just like birds,
thermal gliders are highly efficient. They are, in fact,
about 1,000 times as efficient as equivalent gasoline
powered motor vehicles. The extreme energy efficiency
of these kinds of thermal gliders was amply
demonstrated in 2009, when a small vessel successfully
crossed the Atlantic from New York to Spain. It was
powered by just a simple battery (Spectrum, 2010)!
Analogies and metaphors tend to provoke us to identify and
apply important underlying principles. Below are some simple
practical techniques which can be used to foster engagement
with analogies and metaphors.
We can get into the habit of making summaries after
reading an article or chapter in a book. The advantage
of making summaries is that it typically requires us to
engage more fully with the content. In these
summaries it is helpful to include a) a discussion of
the important principles demonstrated or revealed in
the article/chapter, b) a list of some analogous
contexts where these important principles are
applicable, and c) an identification of an idea in the
article/chapter can be applied to our own work.
(ii) We can start to use more analogies and metaphors
when we talk to others, or when we are explaining
concepts to others. This produces a number of
benefits. Firstly, it is likely to provoke us to find
suitable analogies and metaphors ourselves – this will
assist our current and future understanding. Secondly,
analogies and metaphors are effective teaching tools,
and so our explanations are likely to facilitate better
understanding in others.
(iii) We can look for role models who excel in the use of
analogies and metaphors. When we find these role
models, we should study the way they organise and
structure their thinking and communication. That is,
we should use those role models as living worked
(iv) We can look for literary styles which effectively
communicate analogies and metaphors to others. We
can then incorporate some of these styles into our
own writing.
Engagement with analogies and metaphors helps us to identify
the common structure and linkages within our world – this not
only helps us to organise and improve our cognitive processes,
it also helps us to build up our sense of wonder.
2.7 Giving and receiving care and guidance in
the area of thinking and discovery
Giving care and guidance via reciprocal
In general, mental progress is accelerated when we oscillate
between the roles of novice and expert (Durell, 1959). We often
begin our understanding as a novice who draws on the
experience of an expert source, be that a human being, a book,
a video or a computer program. If we then attempt to step into
the role of expert and teach what we know to another person,
we are often confronted with the fact that our understanding
needs to deepen. Trying to teach what we know therefore
drives us to better understanding.
Of course, we always need to keep acquiring new skills, and so
we must regularly revert to the role of novice. An ongoing
commitment to oscillating between the roles of novice and
expert is therefore a wise strategy for making rapid mental
CASE STUDY: Research has shown that if people selfmonitor their comprehension levels as they read or
study, their understanding tends to increase (Palincsar
& Brown, 1984). The particular comprehension
monitoring activities which have been found to be
effective in this regard are
question generating,
summarizing and
While high achievers tend to perform the above four
activities naturally during reading/study, lower
achievers do not.
In 1984 Palincsar and Brown decided to see whether
explicit interventions could help under-achievers engage
more fully with the above four activities. They initiated
an experiment in which students worked in pairs to
assist one another to monitor comprehension in their
reading. One of the students in the pair initially acted as
the expert to guide the other, and after a while that
student changed to the role of novice, being guided by
the other. That is, the students regularly alternated
between expert and novice roles.
In the intervention, a teacher gave the students very
clear instructions on how to provide the assistance - the
students were required to guide one another in the areas
of question generating, clarifying, summarising and
predicting as they read. As the students started to
supervise one another in these strategies, their levels of
reading comprehension began to improve. This had a
flow on effect, and they also began to improve
significantly in other areas of study, such as science
(Palincsar & Brown, 1984).
The reciprocal supervision had actually increased the
students’ self-monitoring skills, which had a positive
impact on other subject areas as well.
The reciprocal supervision approach pioneered in (Palincsar &
Brown, 1984) can be used to advantage by PhD students in
reading groups. These groups are comprised of a team of
students who work through an advanced coursework textbook
or set of research papers together. The students take it in turns
to teach one another material from the text/papers. An expert
facilitates the group and guides students in research and
innovation strategies. The students can also take it in turns to
supervise one another’s activities and approaches.
Reciprocal supervision is an example of an initiative in which
people can help one another to improve not only their mastery
of subject matter, but also their cognitive capacity. One of the
key principles behind reciprocal supervision is that when we
help others to improve their capabilities, there is a pay-off for
us – we tend to increase our mental effectiveness as well.
2.7.2 Helping others to attain the right attitudes
To think and innovate effectively we need the right attitudes. In
helping one another to progress, then, we need to do more than
just help one another to acquire skills. We need to find ways to
lead one another into an ongoing renewal of attitudes. The
story in the next paragraphs helps to illustrate this point.
CASE STUDY: There was a young girl who grew up in
the desert of Arizona with her mother and father. Her
life received a significant jolt one day when her father
failed to come home. Many days passed without the
father coming home, and in fact he never came home.
The girl was very distressed that her father had left her,
and had not even bothered to tell her why. Her world
was shattered.
After some time, the young girl received a letter from her
father. In the letter the father explained that he had
developed terminal cancer some time back. When he
received the diagnosis he had considered his situation,
and had decided not to put his wife and child through
the agony of seeing him suffer and die – so he left.
The father explained in the letter (sent after his death)
that since his diagnosis he had spent his time building a
new house in the desert, a house which he now wanted
his wife and daughter to have. He had built this house
for them because he hoped that it would help them to
know how much he loved them.
When the young girl went to see the house she was
amazed - it was a dwelling of breathtaking beauty, built
like a palace. It did indeed help the young girl to see how
much her father had cared about her.
After reading the letter and seeing the house, the
daughter’s attitude changed dramatically. Her feeling
changed to one of deep gratitude and she went to live in
the new house her father had built for her. She even
continued to live there after her mother died.
In this true story the daughter’s attitude changed
profoundly forever because of the deep and selfless care
of her father. This is the key to eliciting attitude change.
If we wish to help others to change attitudes we need to
find ways of demonstrating kindness and care. There are
many ways we can do this. We can go out of our way to
tell someone they have done a good job. We can give of
our time to help others with their endeavours. Attitudes
can change with even small gestures of kindness.
Once we have demonstrated kindness and care we can also
bring about attitudinal change by challenging others. Another
true story helps to illustrate this point.
CASE STUDY: A man was teaching in the US and one of
his young students regularly came to school with
bruises, incurred at the hands of his father. The teacher
became enraged at what he was seeing, so much so that
he struggled to contain his own thoughts of violence. He
kept experiencing desires to beat up the father. As the
teacher reflected, however, he realised that he had to
deal with his own issues before he could make any
progress in helping the student.
The teacher struggled for some time and was eventually
liberated from his own thoughts of antagonism towards
the father. After he had managed to face and deal with
his own attitudes, he went to visit the father. At the start
of this visit the teacher explained who he was. He went
on to say that he knew the father really cared about his
son because of the many thoughtful and generous things
that he did for him. The teacher then started to name the
father’s generous acts. The teacher also, however, put a
challenge to the father, appealing to him to come along
to Alcoholics Anonymous (AA) with him, because it
could help the son even more.
The father was moved by the teacher’s care, and also by
his challenge. The two of them did end up going to AA
together, and as a result, a number of lives began to
change for the better.
In the above story the teacher was able to facilitate an
attitude change in the father because he first
demonstrated care towards the father (as well as to the
son). If others know we care about them, they are much
more likely to be able to respond to our challenges.
2.7.3 Providing structure to our care and guidance
Many of the examples given earlier in this chapter relate to the
efforts of individuals. We can generally accomplish more as
part of a large community, though, than we can alone. In
thinking and innovation, we need to be able to give and receive
care and guidance. This need is the driving force behind the
growing world-wide interest in communities of practice (CoPs)
(Lave & Wenger, 1991).
CoPs typically form because of people’s desire to self-organise
with others who have the knowledge, skills and support
mechanisms they are seeking (Berkana, 2008). They involve
groups of individuals who voluntarily band together to care for
one another in their various endeavours.
In their work on CoPs, Lave and Wenger analysed the
dynamics of intellectual engagement within communities, and
they articulated the notion of legitimate peripheral
participation (LPP). According to the LPP phenomenon,
newcomers to a community tend to participate on the margins
or periphery. During these early stages the novice members
draw very heavily on the example, wisdom and nurture of the
experts. As time progresses, the novices tend to become much
more actively involved in the community, and they tend to then
progress to the point where they themselves become experts.
The time the novices spend on the periphery of the community
appears to be a necessary part of their initiation, and hence the
term legitimate peripheral participation. This observation
about LPP parallels the consistent finding from the Cognitive
Psychology research that novices tend to benefit greatly by first
studying examples (Sweller et el, 1998). It is only after novices
have engaged with many and varied examples that they tend to
become experts.
There is a great deal of benefit in becoming a part of a
community of practice around discovery and innovation.
Within the research domain these CoPs may take the form of
research laboratories or research centres, or they may be
informal structures. These CoPs have many advantages, some
of which are listed below:
CoPs enable novices to be exposed to many and varied
expert research role models.
(ii) CoPs provide opportunities for many and varied
research experts to mentor novices. This mentoring
tends to deepen the understanding of the mentors.
(iii) CoPs incorporate social interaction dynamics into the
research skill acquisition process. This is important as
social interactions can greatly assist our thinking and
discovery (Vygotsky, 1978).
The literature on communities of practice provides numerous
examples where people acquire skills much more rapidly
because of the guidance and nurture they receive from experts
in the community. The power of CoPs derives very significantly
from the fact that they facilitate many and varied sources of
guidance and nurture. Part of the initial motivation for
investigating CoPs came, in fact, from Lave and Wenger’s
relationships often gained more from a community of peers
than they did from the master. Much more information about
CoPs is provided in (Lave & Wenger, 1991).
2.8 Physical exercise and adherence to a
healthy diet
For a number of years I served as one of the Directors of
Postgraduate Research Studies at QUT. Within that role I
became all too aware of the struggles that many postgraduate
students experience. Experiments would fail, theoretical
analyses would prove unsolvable, family crises would arise, etc.
These difficulties caused some students to fall into depression,
which made mental progress very difficult. The evidence
suggests that physical exercise helps to mitigate against
depression, and so promotes better long-term cognitive
functioning (Singh et al, 1997).
Exercise also tends to stimulate the creation of new neuronal
stem cells, which leads to more effective brain regeneration
(Van Praag et al., 1999). For this reason the pursuit of physical
exercise is particularly important for older people. This is so
because as we age there is a greater tendency for the brain cells
to die - new cells therefore need to be created. This new cell
regeneration is strongly stimulated by physical exercise.
Exercise is not the only factor that impacts on neural health.
Diet is also important. We need a healthy diet so that the brain
is supplied with all the essential nutrients. Our diets should be
rich in fruit, vegetables, whole grains and healthy fats so that
we have abundant access to important bodily nutrients.
The Omega-3 essential fatty acids found in fish are particularly
important for proper brain maintenance. A deficiency in these
kinds of fats can impair a person’s ability to function mentally,
and may even lead to depression. A study in 2008, for example,
suggested that fish oil based Omega-3 fatty acids were just as
effective in mitigating against depression as low dose Prozac
(Jayazeri et al., 2008).
2.9 Conclusions
This chapter has identified and discussed eight key evidence
based practices for improving our ability to think and discover.
These practices are:
cultivation of mindfulness and vision,
reflection and belief adjustment,
shrewd acquisition of appropriate background
knowledge and skills,
(iv) a commitment to deliberate practice in diverse
(v) habitual abstraction of key underlying principles
from new situations,
(vi) engagement with analogies and metaphors,
(vii) giving and receiving care and guidance in the area
of thinking and discovery,
(viii) physical exercise and adherence to an appropriate
The remaining chapters of this book explore these and other
evidence based practices further. Chapters 3 and 4 look more
fully at how to develop effective problem solving and
innovation skills. Chapter 5 provides tips and traps for novice
researchers, while Chapter 6 addresses the issue of mentoring
others in discovery and innovation. Chapter 7 presents the
book’s conclusions.
Chapter 3
Developing effective problem solving
Problem solving practice is pivotal to effective cognitive
advancement. Accordingly, it is pertinent to look at the many
techniques that humans can use to solve problems, and to
extract and articulate the important principles that underlie
these techniques. This chapter attempts to do precisely that.
Section 3.1 lays the foundation for the chapter by outlining a
general problem solving framework. Section 3.2 discusses the
principles underlying many common approaches to problem
solving, while Section 3.3 is devoted to recommendations for
selecting the most suitable problem solving approach for a
particular problem. Section 3.4 examines the evidence for and
against the study of generic problem solving strategies, and
conclusions are presented in Section 3.5.
3.1 A general problem solving strategy
In 1945, George Polya, a mathematician from Stanford
University, wrote a book about systematic procedures for
solving problems. The book, How to solve it, has become one of
the most influential treatises on generic problem solving ever
written (Polya, 1945). In his book, Polya introduced a general
problem solving strategy which has since become widely
accepted. This strategy is outlined below.
Take steps to make sure you understand the problem.
Devise a plan to solve the problem.
Enact the plan.
Reflect on your progress and revise your plan if
If the 4-step plan above fails then find a related problem which
you can solve. Use this solution as a launching pad for solving
the original problem of interest.
As well as providing a general strategy for solving problems,
Polya’s book describes many specific candidate problem
solving techniques (Polya, 1945). Various other authors since
Polya have devised additional problem solving methods, and
the following section discusses some of these many different
3.2 General problem solving techniques
Research the problem of interest and
analogous problems
We need to seek efficiencies in our problem solving, and as far
as possible, we should exploit the prior efforts of others. When
we are confronted with an important new problem, it is
advantageous to search the literature to determine whether or
not anyone has solved this problem before. According to (TRIZ,
2009), about 90% of all problems encountered have been
solved before, albeit in a different field or setting. Fortunately,
the task of searching for these solutions has become easier in
recent times. With the help of the internet one can simply enter
keywords into electronic databases.
Some useful databases for doing research are Web of Science,
Science Direct, Proquest, IEEE Explore, Informaworld,
Informit Search, EBSCO Host and CSA.
If a search reveals no existing solution to the problem, it does
not mean that the literature is unable to provide any useful
insights. The solutions to analogous problems can sometimes
illuminate the process of solving the problem of interest. It is
therefore advisable to consider analogous problems and to
search for solutions to them. The literature may also be able to
provide solutions to part of the problem, or to part of an
analogous problem.
CASE STUDY: A number of researchers have looked at
the problem of how to make robots move elegantly and
efficiently. Some innovative solutions have been
obtained by looking to analogies from nature.
Amir Shapiro, for example, has looked at the problem of
enabling robots to climb walls, slither through pipes and
move along ceilings. He has created a wall climbing
robot which facilitates its climbing by secreting glue to
hold its legs temporarily in position as it climbs. This
type of robot was inspired by the way a snail releases a
trail of mucus as it moves. To climb rough walls Shapiro
developed a different type of robot which has fishhooks
attached to each of its legs, analogous to the way claws
protrude from the paws of a cat.
To build a robot to slither through pipes, Shapiro looked
to the snake. He created a new robot which can produce
two travelling wave movements, one in the horizontal
direction and one in the vertical direction. The two
combined motions produce a slithering or screw-like
motion which allows the robot to project itself forward.
This is useful for practical scenarios in which a robot is
required to move through narrow caves and pipes.
To create a robot which can move along ceilings Shapiro
conceived an entity which shoots arrows attached to
strings, enabling the robot to pull itself along the ceiling.
This approach was inspired by Spider-man!
Another researcher, Professor Mandyam Srinivasan, has
looked at the problem of how to make small robotic
planes move nimbly as they land in confined areas. He
has drawn inspiration from the way honey bees control
their flight so effectively. He found that bees regulated
their speed relative to the ground by ensuring that
images of the ground move across their eyes at constant
speed. This is often referred to as the principle of
‘constant optical flow’. Srinivasan has found that a
similar principle can be used for robotic planes as they
try to land – that is, small onboard computers can be
used to ensure that images of the ground move across
the plane’s visual sensors at a constant speed
(Srinivasan et al, 2001).
3.2.2 Trial and error
In the trial and error approach one simply guesses an initial
candidate solution and then tests whether or not this solution
is valid for the problem at hand. If it is not, then another
candidate solution is trialled. The process can be repeated until
a correct solution is found.
Sometimes one is not seeking an exact solution, but rather a
best available (optimal) solution. If one is seeking an optimal
solution, there are a number of candidate search algorithms
available. These algorithms include Gradient Search Methods
(Snyman, 2005) and Genetic Algorithms (Baricelli, 1957).
Gradient search methods employ systematic processes to
extract and exploit trends in the trial and error process.
Typically, they make the search faster by using structural
information underlying the function or process to be optimised.
These methods tend to find solutions quickly, but there is no
guarantee that they will find the best possible solution. They
tend to work best if a good initial guess is found first via the
trial and error method.
Genetic algorithms are based on an evolutionary process in
which the solution becomes progressively better with time. The
power of genetic algorithms is that they tend to yield good
approximations to the optimal solution relatively quickly. They
tend to take a long time, however, to converge to the truly
optimal solution.
CASE STUDY: The International Space Station is a
research facility designed to operate in low earth orbit.
There were a number of significant challenges in
designing the Space Station. One such challenge was
how to ensure that humans within the facility could be
protected from dangerous gases. To help to meet this
challenge NASA developed an artificial Nose (ENose).
The ENose was conceived because the human nose was
unsuitable for reliable monitoring in space – the nose of
a human could only detect certain hazardous
contaminants when their concentration levels were well
beyond safe limits. By contrast, NASA’s Enose could
detect many chemicals at extremely low concentrations
(as well as at very high concentrations). Moreover,
unlike the human nose, the ENose was not prone to
odour fatigue. That is, the ENose did not become
insensitive to smells that persisted for a long period of
The ENose was designed to have within it many artificial
films (sensors) which could be categorised into 16
different types. The films were made from different
types of insulators impregnated with carbon particles,
with these particles effectively transforming the films
into partial conductors of electricity.
The films in the ENose were all designed to either shrink
or swell when particular chemicals impinged upon them.
If they swelled, the carbon particles moved further apart
and the conductivity of the material decreased.
Conversely, if the material shrank the particles came
closer together and the conductivity increased.
When a gas impinged on the various films in the ENose
a computer detected the electrical changes which
occurred in all of the different film types, and from this
information the processor was able to deduce the nature
of the gas and its level of concentration.
A key problem which needed to be solved to make the
ENose work reliably was, “What materials should be
used to make the films if the performance of the ENose
is to be optimal?” This problem was solved by using trial
and error. Initially a physical trial and error process was
used in which various materials were trialled and tested.
At a later stage, a computer based trial and error method
was used, with theoretical models of the films being
systematically trialled via software. This trial and error
process proved very reliable and led to an ENose which
could detect hazardous gases far more reliably than
humans could.
Break a large complex problem down into
small solvable problems
Many problems can be conquered best by solving one part of
the problem at a time. The solutions to the sub-problems are
then re-combined to produce a final solution. This approach is
sometimes known as the divide and conquer (DAC) approach.
CASE STUDY: DAC is central to many powerful
algorithms, most notably the Quicksort Algorihm
(Hoare, 1961) and the fast Fourier transform (Cooley &
Tukey, 1965). These algorithms have been named among
the 10 most significant computational algorithms of the
20th Century. This case study describes the Quicksort
algorithm and its use of the DAC principle.
The Quicksort procedure was introduced to provide a
computationally efficient way to sort a list into
alphabetical or numerical order. The steps in the
algorithm are:
Choose an element from the list – this element
is referred to as the pivot.
(ii) Rearrange the list so that there are two sublists, one containing all the elements above the
pivot, and one containing all the elements
below the pivot.
(iii) Take the two sub-lists, and for each of them
create a new pivot and two new sub-lists.
Continue to repeatedly create more new pivots
and pairs of sub-lists until the original list is
completely sorted. (This step essentially
involves a repeated application of the DAC
The Quicksort technique is very simple in concept, and it also
turns out to be very efficient in terms of computation. The DAC
approach in this case therefore provides computational as well
as conceptual benefits.
3.2.4 Means-end analysis
A related technique to DAC is Means-end Analysis (MEA),
which has been found to be one of the key generic problem
solving techniques instinctively used by humans (Sweller,
1994). MEA is similar to DAC in that it systematically devises
and pursues sub-goals en route to reaching the final goal.
The key rationale behind MEA is that the problem space in
many practical problems is too large to search, and so one
cannot simply use an unguided process of trial and error.
Instead, one needs to find an efficient (albeit) sub-optimal way
to extract a useful solution. Consider the example of trying to
devise a chess move within a chess match. It would be
impractical to mentally trial and evaluate every possible chess
move each time a chess piece needed to be moved. The MEA
approach provides a viable practical alternative.
In MEA there is considered to be a problem space with:
an initial state (eg. the initial board layout in a game
of chess),
(ii) a goal state (eg. the checkmate condition) and
(iii) various intermediate states which are achieved by
actions (eg. chess moves).
If there is an action which can achieve the final goal then it is
implemented immediately. In the chess scenario, this would
mean that if there is an obvious move which can achieve
checkmate, then that move should be made. If no such action is
possible or apparent, then one should articulate a sub-goal. In
chess, this sub-goal might be to capture a valuable chess piece
such as a queen, castle, or bishop. If there is an action (move)
which can immediately achieve this sub-goal, then that action
should be taken. If no such action is possible or apparent, then
one should articulate a further sub-goal. In the chess scenario,
this might be to plan a set of three moves which will set up
capture of a valuable chess piece.
Sub-goals are repeatedly pursued in MEA until some sub-goal
is achieved. Once the low level sub-goal has been achieved the
higher level sub-goals are pursued. This process is repeated
until the final goal is attained. MEA has been found to be quite
successful in solving many problems, although it is ineffective
for some very complex real world problems.
3.2.5 Seek ideas and solutions from others
There are many ways that we can seek and gain ideas from
others. It can, of course, be done by simply having spontaneous
discussions with friends and colleagues. Such informal
discussions can be surprisingly effective.
CASE STUDY: Two of the most important
breakthroughs of the 20th century were the discovery of
DNA structure and the invention of the transistor. There
were some remarkable similarities in the way both
breakthroughs were made, as discussed below.
The transistor is a critically important constituent
component in almost all electronic computers, hi-fi
systems and telecommunications equipment. Its
development in 1947 effectively triggered the electronics
and computer revolutions.
The transistor was first developed by a team at Bell Labs.
These team members were seeking to create a new
device which could replace slow and bulky existing
devices such as relays and vacuum tubes. Two members
of the Bell Labs team, John Bardeen and Walter
Brattain, hypothesised that a transistor could be made
by exploiting the so-called “surface or field effect” in a
semiconductor material. They tested out their idea
experimentally and tried to create the required effect by
pressing a pair of narrowly separated gold strips onto a
semiconductor material. They applied appropriate
electrical signals to test their new device and found that
it worked exactly as they had hoped. In this way they
produced the first ever transistor.
They discussed their successful experiment with William
Shockley, one of their co-workers. Shockley reflected on
their experiment and on their hypothesis about the
“surface or field effect’. He had a conviction that
Bardeen and Brattain were wrong about why the
transistor actually worked. He set about devising his
own theory to explain the operation of their transistor.
Within a few weeks Shockley had come up with a
convincing alternative explanation for the operation of
Bardeen and Brattain’s transistor. His theory revolved
around the so-called “bipolar junction effect”.
Shive, another co-worker at Bell Labs, did further
experiments and confirmed that Shockley’s theory was
correct, while that of Bardeen and Brattain was
predominantly wrong. Shockley’s new understanding of
how the transistor worked led to the creation of a much
more stable and practically reliable transistor, which
went into mass production within about two years. For
their efforts, Bardeen, Brattain and Shockley all won the
Nobel Prize.
The development of the first commercially viable
transistor was made possible by the fusing of Bardeen
and Brattain’s experimental work with the theoretical
insights of Shockley. Interestingly, this successful fusion
was unplanned – it occurred through the informal
sharing of ideas.
DNA was well known to be the building block of life in
the early 1950’s. It is not surprising, then, that there was
a great impetus at that time to unlock the secret of
DNA’s underlying structure. James Watson and Francis
Crick were working on solving this problem at
Cambridge, as were Rosalind Franklin and Maurice
Wilkins at Kings College, London.
In 1953 Watson payed a visit to Franklin to see if she
was interested in working with himself and Crick.
Franklin, however, was not at all open to the idea. After
getting a refusal from Franklin, Watson ran into Wilkins
by chance. Because Franklin was leaving King’s College
the Laboratory Director had insisted that all her DNA
results remain at Kings. Franklin’s data therefore ended
up in the hands of Wilkins, and among this data was a
stunningly clear X-Ray diffraction image of DNA.
Franklin had already correctly deduced the double helix
form for DNA from this image, but had not produced a
theoretical model. Wilkins showed this image to Watson,
who immediately recognised not only the double helix
structure, but also a means to produce a sound
theoretical model.
Watson and Crick submitted their model for DNA
almost immediately to the journal, Nature. In a deal
done between the Laboratory Directors at Cambridge
and Kings College, three papers on DNA structure
appeared in the same 1953 issue of Nature. The first was
by Watson and Crick, while the third was by Franklin.
Watson, Crick and Wilkins went on to win the Nobel
Prize in 1962 for their contributions to the
characterisation of DNA structure. Franklin, sadly, was
ineligible for the Prize at that time because she had died
in 1958.
Much like the development of the transistor, the
discovery of DNA structure was made possible by the
fusing of experimental results from one group with
theoretical insights from elsewhere.
Many people have sought to source and share ideas in
systematic pre-planned ways. Perhaps the best known
systematic technique for enlisting the insights of others is
brainstorming (Rickards, 1999). In this approach, a group is
formed to generate a large number of ideas, the rationale being
that among the many ideas generated there should be at least
one good one. The problem is defined and relayed to all
participants via a memo or email at least two days before the
brainstorming session, thus enabling participants to think
about the problem in advance.
In brainstorming sessions there is an emphasis on welcoming
all ideas, and unusual ideas in particular. To this end there is
often a rule that no new idea should be criticised. The best of
the many ideas presented may also be combined to form one
very well regarded idea, with this then providing leverage for
further ideas.
Although group brainstorming is heavily used, and is typically
enjoyed by participants, there appears to be little evidence that
it is an efficient approach for generating high quality ideas or
solving problems (Rickards, 1999). It appears to be limited
because of factors such as:
social loafing (the tendency of individuals to
contribute less to a task when they are in a group),
(ii) production blocking (the tendency to be blocked from
devising new ideas when someone else is speaking)
(iii) an unwillingness on the part of many participants to
give ideas because they fear being judged by the group.
Because of the abovementioned problems, a number of
variants of traditional group brainstorming have been
proposed. Electronic brainstorming is one such variation in
which email is used to facilitate idea collection. The facilitator
emails the problem of interest to the group members, who then
send back their ideas to the facilitator directly. Because the
participants have less visibility of the other group members, the
approach tends to mitigate problems with social loafing,
production blocking and fear of being judged. It also allows
group members an arbitrary amount of time to reflect on the
problem before submitting their ideas.
It is possible to not only seek ideas from others, but also
advanced solutions. The soliciting of solutions has been made
easier in recent times by the establishment of problem solving
e-communities. One example of this approach is the
community facilitated by InnoCentive, a company which takes
research and development problems and poses them as open
challenges on its web-site (Innocentive, 2009). Cash rewards of
up to US$100,000 are offered as an incentive to solve the
problems. The problems are typically provided by companies
referred to as seekers, and the solutions are provided by
thinkers and inventors known as solvers.
3.2.6 Incubation
Incubation is a process within problem solving whereby a
person temporarily puts aside his/her efforts at solving the
problem. It is believed that the subconscious mind then
continues to work on the problem, delivering the solution at
some later point in time. Wallas laid some of the earliest
foundations for our current understanding of incubation with
his five-stage model for creative problem solving (Wallas, 1926).
The five stages of this model are:
preparation, where the person focuses their mental
efforts on the problem,
incubation, during which time the person ceases to
consciously think about the problem,
intimation, when the person gains a sense that the
solution is imminent,
illumination or insight, where the solution suddenly
presents itself, and
verification, where the solution is verified consciously
and then implemented.
Some empirical evidence suggests that the period of incubation
prevents a person from becoming obsessed with inappropriate
solution paths, and helps them to forget misleading
information (Smith, 1981).
There are various factors which seem to increase the
effectiveness of incubation (Dodds et al, 2009). In particular,
longer periods of preparation tend to yield more productive
outcomes, and incubation tends to be more effective for high
achieving thinkers than for low achieving thinkers. The clues
given immediately before or during the incubation period also
positively affect the quality of the outcomes (Dodds et al, 2009).
CASE STUDY: The most commonly cited example of
incubation is probably Archimedes’ eureka discovery.
Legend has it that King Hiero II of Syracuse had
commissioned some craftsmen to make a gold crown for
him, and had supplied them with all the gold they
needed to make it. After the king received the crown he
started to suspect that the craftsmen had stolen some of
the gold for themselves, and had made the crown partly
with gold and partly with less valuable silver. The king
asked Archimedes to investigate the matter for him.
The crown weighed the same as the gold initially
provided by the king, and so Archimedes knew that if it
was made partly of silver (a less dense metal than gold)
the volume of the crown would have to be larger than the
volume of the original gold. He did not initially know,
however, how to measure the volume of an object with
an irregular shape such as a crown.
Some time after his initial ruminations on the problem,
Archimedes settled into a bath tub. As he sank into the
tub, he noticed the displaced water overflowing. This
was the clue which precipitated his discovery of how to
measure the volume of the crown. He could do it
indirectly by immersing the crown in water and
measuring the volume of the water subsequently
displaced. That was Archimedes’ eureka moment, and it
came to him via the process of incubation.
3.2.7 Express the problem in different forms
One of the first steps to effective problem solving is to properly
understand the problem (Polya, 1945). To facilitate
understanding of the problem, it can be useful to express it in a
number of different forms. One should consider the following
possibilities for enhancing understanding:
draw a picture or diagram with appropriate symbols
and labels,
(ii) construct a table,
(iii) use a list,
(iv) construct physical models,
(v) use a mind map (Buzan, 2000).
CASE STUDY: In 1769, James Watt invented and
patented a highly practical steam engine. This invention
ushered in the industrial revolution which changed the
The concept of the steam engine originated as early as
130BC, when Hero of Alexandria successfully
demonstrated a crude steam turbine. Many people
contributed advances to Hero’s original device, and one
of them was the English engineer, Thomas Newcomen.
In the Newcomen engine, steam was guided into a
cylinder, and then condensed with cold water. As the
steam condensed, a vacuum was created and
atmospheric pressure forced a piston to move
While at the University of Glasgow in 1765, James Watt
was given the task of repairing a Newcomen engine.
When he was given this physical model to work with,
things became clear in Watt’s mind. He realised that
about 80% of the heat in each new injection of steam
was used up re-heating the cylinder after a prior cycle of
condensation and cooling. Watt therefore proposed that
before attempting to condense the steam, the latter
should be siphoned off into a separate chamber through
a valve. With this arrangement the old issue of steam
could be cooled, while the main cylinder was maintained
at the same temperature as the new burst of incoming
The use of a physical model helped Watt to properly
conceptualise the problem of how to create a practically
viable steam engine. Once this occurred the solution
followed relatively quickly.
Mind maps are a particular type of diagram in which words,
concepts and activities are visually represented around a key
central word or concept. An example is shown in Figure 3.1.
This figure shows a mind map of de Bono’s thinking hats. i.e. it
graphically illustrates the various perspectives from which one
can consider a problem.
The mind map representation appears to have a number of
advantages over conventional representations. Firstly, because
a mind map is an integrated representation of text and
graphics it tends to be relatively effective at promoting
comprehension and stimulating thought. Second, mind maps
tend to promote a more holistic engagement with the problem
of interest than conventional notes or problem statements. The
latter often require the reader to scan the page from left to right
and from top to bottom, whereas mind maps promote a
broader scanning which captures linkages between constituent
Black Hat
Red Hat
Blue Hat
Thinking Hats
White Hat
Yellow Hat
Green Hat
Figure 3.1. A mind map to represent de Bono’s six thinking hats
There is some evidence to support the effectiveness of mind
maps. In particular, studies have found that when
undergraduate students engage with the mind mapping
technique, they tend to improve their memory recall (Farrand
et al, 2002).
3.2.8 Root cause analysis
Many problems pertain to the malfunction or failure of systems.
These systems can be in areas such as manufacturing, business,
education, sport and psychological development. Root cause
analysis is a particular type of approach to failure analysis in
which one seeks to determine not just immediate causes for
failure, but root causes. The rationale is that problems are
much less likely to recur if one deals with root causes.
To develop good root cause analysis skills we often need to
retrain our minds. The retraining is needed so that we are more
adept at linking actions to long-term consequences. This
retraining can be stimulated by studying many pertinent
examples, by appropriate reflection, and by practice in solving
root cause analysis problems.
CASE STUDY: When I was a young child I loved the
sense I got from being able to float in the water and
always looked forward to going to the swimming pool. I
was not, however, very good at swimming. As I got older
I lamented the fact that I was such a poor swimmer and
decided to try and improve. Despite my efforts I really
struggled. I found it very hard to understand why it was
that others could glide through the water so easily, but I
could not. I was, nonetheless determined to get better,
and decided to just keep persevering.
My strategy was to gradually try and build up the
distance I could swim. When I started I could swim one
length of a 50 meter pool, albeit with significant
difficulty. With great effort and anguish I built this up to
4 lengths of the pool. The process of swimming those 4
lengths, however, was very stressful, and I was
exhausted by the time I finished. I found the 4 length
limit very difficult to go beyond for a long time.
One day, in the middle of my 4 length swim a memory
from my childhood flashed suddenly into my mind. It
was the vivid memory of seeing someone else who was a
poor swimmer, and of my scoffing very disrespectfully at
their incompetence. Given my own incompetence now as
a swimmer, I realised I had been hypocritical, and made
a decision to revoke the scoffing attitude. When I made
that decision, I was surprised to detect an immediate
change occurring in me – I felt a significant amount of
tension disappear from my body as I swam. Suddenly,
swimming seemed more effortless, and instead of
swimming the usual 4 lengths, I swam 20 lengths.
During that swim I seemed to have solved the problem
of identifying why my swimming had been so poor. The
root cause of my incompetence appeared to lie in a
judgmental attitude formed in my childhood. That is, in
order to find the solution to my problem I needed to
look for long-term links between cause and effect. This
is frequently the case in failure analysis.
This case study also supports the contention made in an
earlier chapter that when we dwell on negative aspects
in others, those aspects tend to assail us. The corollary is
fortunately true as well. When we dwell on the positive
characteristics of others, those characteristics tend to
grow in us.
Another technique commonly used for identifying root causes
of failure is the Five whys method. In this technique one asks
“Why did the failure occur?” five times in succession. Each new
time the question is answered, however, one seeks to find a
progressively deeper underlying cause.
3.2.9 Work backwards
In some important problems one is presented with a final
outcome (or outcomes) and the task is to find out how the
outcome was achieved. One example of this type of problem is
a crime scene investigation for a murder – in this case the task
is to work backwards from the crime scene to determine who
committed the murder, how they did it, and for what purpose.
In other problem scenarios there may not be such an obvious
pre-empting of the working backwards approach. If
conventional forward thinking problem solving strategies fail,
though, the working backwards from the goal approach
should be considered. The working backwards approach is
illustrated in the simple example below.
Suppose I was paid on Tuesday and spent 20% of my pay on
Wednesday. Suppose also that I spent $15 of my pay on
Thursday. If I had $525 of my pay left on Friday, then how
much did I get paid originally?
Working backwards,
On Friday I still had $525.
On Thursday I spent $15, so at the start of Thursday I had $540.
On Wednesday, I spent 20% of my pay, so 80% of my original
pay must have been $540. My original pay must have been
$540 times 100/80.
My original pay was therefore $675.
3.2.10 Assumption reversal
As discussed in (Polya, 1945), one of the crucial steps in solving
any significant problem is to properly understand the problem.
An important aspect of this understanding is a clear
appreciation of the underlying assumptions upon which the
solution will be based. In the assumption reversal approach
one begins by formally articulating these assumptions, then
reversing these assumptions one by one, and finally evaluating
the implications of the assumption reversal. Assumption
reversal helps to eliminate false pre-conceptions, and can open
up new paths for investigation.
CASE STUDY: King Nebuchadnezzar II was one of the
rulers of ancient Babylon, and under his reign Babylon
achieved extraordinary heights. The magnificent
hanging gardens within the city were one of the seven
wonders of the ancient world. What was perhaps most
impressive of all about Babylon, though, was its system
of protective walls. These walls were 87 foot thick, 350
feet high, and had a perimeter of 60 miles – they were
considered to be impenetrable.
Cyrus, the king of neighbouring Persia, was keen to
extend his territory and wondered how he could prevail
against the might of Babylon. Eventually, Cyrus came up
with a plan. He ordered the Persian soldiers to dig a
channel to divert the Euphrates river away from its path
through Babylon. The soldiers then marched through
the riverbed, under the walls of Babylon, to capture the
city. The usual assumption in ancient warfare was that
one had to go over the walls to capture a city. Cyrus
decided instead to go under the walls. Assumption
reversal therefore proved pivotal to toppling one of the
grandest empires in human history.
CASE STUDY: In the late 1940s four friends started to
meet together regularly in an English pub. After a while
their humorous banter took on a life of its own and they
started to record their meetings together. Some
influential radio personalities heard these recordings
and offered them a chance to do their own show on
British radio.
The four friends were Spike Milligan, Peter Sellers,
Harry Secombe and Michael Bentine. Their radio
broadcasts eventually became known as the Goon Show,
This program turned into one of the most successful and
influential shows ever to play on BBC radio. It was
broadcast over and over again internationally. Groucho
Marx was a fan, and many comedians (including John
Cleese and others in the Monty Python team) cite it as
an important influence on their development as
Why is it that the Goon Show became so successful? It
was partly because Milligan, the writer, used a
systematic approach to solving the problem of how to
make people laugh. One of the key techniques he
exploited in his approach was assumption reversal.
Milligan knew that a key to making people laugh was to
have story lines which disrupted their conventional
expectations (or assumptions). He therefore reversed
the conventional assumptions of audiences on many,
many levels. Some of these numerous expectation
(assumption) reversals are listed below.
Several of the characters had unconventional
names – eg. Lord Hairy (Neddy) Sea Goon,
Bluebottle, Grytpype-Thynne, Eccles, Major
A lot of the characters had unconventional
(silly) speaking voices, acted out very ably by
the cast members.
(iii) There were many unusual and elaborate sound
effects incorporated into the show to augment
the silly voices.
(iv) Many of the inanimate objects in the scripts
had absurd functions – there were exploding
sausages, a pair of bananas which were used as
binoculars, 1918 calendars which were
dropped into Germany during 1916, and which
thereby caused World War I to end two years
early, etc.
The locations were highly varied – the
characters roamed all over the world.
(vi) The characters regularly breached usual social
protocol. Grytpype-Thynne, for example,
would sometimes disrupt people’s polite
conversations and tell them that he did not
wish to listen to them.
(vii) The episode titles were often unusual, eg. “The
first man on the Goon”.
(viii) Highly unusual things regularly happened to
the cast members. Sometimes, for example, a
cast member would be blown up, only to
return later. In one memorable episode
Bluebottle was blown up by the exploding
sausages and then mused, “Is that why they
call them bangers?”
(ix) Characters would interact with one another in
very unusual ways. Sometimes one character
would announce that they were leaving the
room, and a door would slam. They would,
however, not have left the room, but a
different character would have left.
Because of the many, many assumption/expectation
reversals incorporated into the Goon Show the humour
was described as ‘anarchic’.
3.2.11 Induction and deduction
Induction: In induction, one seeks to extract a generalised
solution by first considering some particular (and hopefully
representative) examples. Consider the following illustrative
Given the following sequence of numbers,
rn  2,5,9,14...
find the 50th entry in the list.
One can readily solve this problem by induction. One can see
from the first few numbers in the series that the difference
between consecutive numbers on the list continually increases
by one. It is therefore possible to determine the following
generalised formula for the nth number in the list:
r1  2
r2  2  (2  1)
r3  2  (2  1)  (2  2)
rn  2  (2  1)  (2  2)    (2  (n - 1)).
rn  2n  (1  2    n - 1)
(n)(n - 1)
(because (1  2    n - 1)  (n)(n - 1)/2, according to the formula
given in (AP, 2009)).
 2n 
Substitution of n=50 into the above formula yields the value for
the 50th number on the list:
r50  100 
50  49
 1325.
Deduction: Deduction involves drawing a logical conclusion or
arriving at a logical solution from that which is known or
assumed. In mathematics, deduction is the kind of technique
which is used to simplify expressions and equations. In police
investigations, observation and deduction are often used to
solve crimes.
CASE STUDY: In “The adventure of the dancing men”,
Sherlock Holmes was tasked with solving the mystery of
who shot Hilton Cubitt and his wife, Elsie. Hilton had
enlisted Holmes’ help to investigate the disturbances
which were occurring with his wife. She had regularly
been receiving messages with a series of little dancing
men on them, and every time she received one she
became traumatised.
When Homes examined all the messages, he studied
them and concluded that the messages were a
substitution code in which the letters of the English
alphabet were substituted with characters of little
dancing men with different shapes. By determining
which characters appeared most frequently in the
messages (and assuming that these characters
corresponded to the most commonly written characters
in normal English usage) Holmes deciphered the code.
As soon as Holmes cracked the code, he realised that
there was significant imminent danger to Elsie. He
therefore hurried to the Cubitt house to avert the
danger. When he arrived he found Hilton Cubitt dead
from a bullet to the heart and Elsie seriously wounded in
the head. The investigating policeman believed that it
was a murder-suicide, but Holmes did not agree. His
observations led him to deduce other causes.
Holmes noticed that there was a bullet hole in the
window sill, and there were bullets in both Hilton and
Elsie. There were thus three bullets fired, but only two
chambers in the Cubitt revolver were empty. Holmes
also noticed that there was a trampled flowerbed
adjacent to the window, and so deduced that there was a
third person involved – the person who had been
sending the messages with the little dancing men.
After cracking the code, Holmes was able to deduce from
the messages that the name of the person sending the
messages was Abe Slaney, and that he lived at the
nearby Eldridge farm.
Holmes lured Slaney to the Cubitt home by sending a
message to the Eldridge farm, signed by Elsie. When
Slaney arrived at the home, he was arrested, and at that
point Slaney told the full story. He had been a former
lover of Elsie who had been trying to woo her back. He
had sent the coded dancing men messages, and had
become highly agitated at Elsie’s refusal to leave her
husband. He finally sent her a threatening message and
then went to visit Elsie. When Slaney arrived, Hilton had
shot at him, and Slaney retaliated by shooting and
killing Hilton. Elsie had then shot herself in dismay.
The above story illustrates the use of both deduction and
induction to solve a crime. Holmes used logical
deduction to determine that there must have been a
third person involved at the scene of the crime. That is,
there were three bullets at the crime scene and only two
bullets fired from the Cubitt gun. There was no other
gun in the room and the Cubitts had possession of only
one gun, so a third person must have been involved.
Holmes used induction to crack the substitution code of
the little dancing men. That is, the messages were just
particular and representative examples of coded English.
From these representative examples, Holmes inductively
inferred the general form for the code. He did this by
determining the characters used most frequently in the
messages, and then assumed that these corresponded to
the most frequently used letters in the un-coded English
alphabet. i.e. they were assumed to be the letters “e”, “t”,
3.3 Selecting the most appropriate problem
solving technique(s)
The following guidelines may be used in attempting to select
the right problem solving technique(s) for a given problem.
They are adapted from (Halpern, 1997).
1. For ill defined problems: express the problem
in a variety of different forms and include a visual
2. For problems with a limited number of
possible solutions: consider the trial and error
3. For problems with fewer paths leading away
from the goal than from the starting point: use
the working backwards approach.
4. For mechanical/materials engineering
problems: use TRIZ (see the next Chapter).
5. For complex problems: try means end analysis,
deduction, induction, and divide and conquer.
6. For failure analysis: use root cause analysis.
7. For complex mathematical problems: consult
the books of Polya (Polya, 1945) and Shoenfeld
8. For creative problem solving: use assumption
reversal, lateral thinking and/or TRIZ (see the next
9. For all problems: Early in the problem solving
process, use research, analogies and expert
consultations. Use incubation to help facilitate
solution, and actively seek clues wherever possible.
Reflect intermittently on your progress and reevaluate your plan for obtaining a solution.
3.4 The evidence for studying and practicing
generic problem solving strategies
In recent years it has become very popular to study generic
problem solving strategies such as those described in Section
3.2. The research suggests that much of the study of general
problem solving strategies is ineffective (Shoenfeld, 1985). In
particular, studying these techniques in isolation tends to be
relatively fruitless.
The research suggests that to promote effective development of
problem solving expertise one needs a broad strategy. One
such broad strategy is outlined below (Shoenfeld, 1985; Sweller
et al, 1998):
study and practice problem solving as part of a
wider strategy which incorporates reflection,
begin your attempts at developing different
problem solving strategies by studying and
articulating the strategies of experts (also seek to
articulate these strategies in fine detail)
persevere at studying and practicing problem
solving over a long period of time, because
problem solving expertise tends to develop slowly
and gradually,
study and practice problem solving strategies (at
least initially) within a specific problem solving
domain (eg. Mathematics), rather than in a
general sense.
3.5 Conclusions
This chapter has begun by providing a 4-step overarching
strategy for problem solving. This 4-step methodology is a
simplified version of the much broader strategy which is
needed to build up problem solving expertise. The broader
strategy is outlined in Section 3.4.
The advice in Chapter 2 about improving thinking is also highly
relevant for improvement of problem solving. As alluded to in
Chapter 2 we need to be armed with a vision because problem
solving skills develop slowly, and there are likely to be obstacles
along the way. We need reflection because when we solve
problems we must discover how to use our cognitive resources
wisely and productively. We need to acquire copious amounts
of background knowledge because much problem solving
involves the subconscious scanning of relevant prior
We need to practice problem solving in a thorough and diverse
way so that we obtain practice in transferring our skills to new
and unseen problem scenarios. We need to systematically use
analogies, metaphors and abstraction so that we can obtain
efficiencies in our mental development and processing. We
need to engage the whole person and so we need physical
exercise to accompany our mental exercises. Additionally we
need to be part of a community of problem solvers who can
help and guide one another.
This chapter has also provided various problem solving
‘arrows’ which we can add to our ‘quiver’ of thinking
techniques. These techniques are listed below.
research the problem of interest and analogous
trial and error,
(iii) divide and conquer,
(iv) means-end analysis,
seek ideas and solutions from others,
(vi) incubation,
(vii) express the problem in different forms,
(viii) root cause analysis,
(ix) work backwards (as well as forwards),
assumption reversal,
(xi) induction and deduction.
Finally, the chapter has provided suggestions on which
problem solving strategy to use in a given situation.
Chapter 4
Developing creativity and innovation
Creativity is not merely an innate ability, but it is something we
can learn. This chapter addresses the issue of how to go about
improving our ability to create and innovate.
To realise improvements in our creativity two key elements are
needed – first, we need to have the proper inclination towards
creativity, and second, we need to use the right methodologies.
The first section of this chapter looks at how to foster the
proper inclination, while Section 4.2 discusses the kinds of
methodologies we can use to enhance creativity.
4.1 The inclination towards creativity
CASE STUDY: In the 1850s, a young man named
Thomas started school in Milan, Ohio. Thomas’s teacher
was quick to notice that the boy’s mind tended to
wander, and described the boy as muddle-headed.
Thomas’s mother, Nancy, was alarmed when she learned
of the teacher’s attitude towards her son, and decided to
take Thomas out of school and educate him herself.
The son grew up to become extremely successful. He
built Yankee Stadium in New York, he invented the first
device for recording sound, he co-invented the first
commercially viable electric light bulb, he developed the
first commercial electric power distribution system and
he co-invented the first motion picture camera. He was
granted more US patents than anyone else in history.
The son was in fact, Thomas Edison.
Towards the end of his life, Edison revealed one of the
key reasons for his success. He said “My mother was the
making of me. She was so true and so sure of me, and I
felt I had something to live for, someone I could not
Edison was strongly affected by his mother’s care and
belief. Moreover, in his adult life he seems to have
followed her example of believing in and guiding others.
Using his own resources, he invested heavily in premises
at Menlo Park, New Jersey, where he established large
private research laboratories. He did this at a time when
it was unheard of for an individual to do such a thing. He
filled those laboratories with people he believed in,
effectively creating a community of practice around
discovery and innovation.
Edison successfully guided the people in that community
in their creative practice, and his efforts were
breakthroughs emanated from Menlo Park, and Edison’s
research laboratories became models which would
subsequently be copied by many others.
Edison made many significant mistakes in his life. He
himself acknowledged that he failed to respect Nikola
Tesla, one of his most famous employees. Despite his
flaws, however, he still managed to cast many positive
influences. Through his inventions and initiatives, he
was instrumental in birthing the electricity industry, the
music industry and the film industry. He also had a
significant influence on Henry Ford and on the creation
of the automobile industry.
The story of Thomas Edison’s childhood underscores the
importance of nurture, belief, and guided practice in
fostering discovery and innovation. Edison’s mother
believed in her son’s potential, and committed strongly
to realising that potential through her long-term nurture
and guidance. Edison was greatly impacted by that
belief, guidance and nurture, and replicated it in his own
life to extraordinary effect.
An inclination towards creativity is to some extent hereditary,
but it is also partly determined by environmental factors. As
alluded to in the previous case study, some of the pivotal nongenetic factors which foster an inclination towards creativity
nurture and physical affection,
guidance, and
deliberate practice.
The importance of nurture and physical affection: Nurture
and physical affection help to transmit a sense of care. If this
sense of care is strong enough, the neuro-modulating chemical,
oxytocin, is released into the brain and a massive number of
neuronal connections are cleared (Freeman, 1995). This
clearing paves the way for the formation of new connections, so
that new lines of thought and new attitudes can form. This is
precisely the kind of environment where creativity can flourish.
The importance of belief: When someone believes in our ability
to accomplish a task (or we believe in our own ability) that
belief tends to prompt us to imagine ourselves doing it. Now
the social science research tells us that when we imagine
ourselves accomplishing a task we become more likely to
actually accomplish it (Gregory et al, 1982). Belief therefore has
a tendency to propel us to success. This is one of the key
reasons that belief in our (or others) ability to develop
creativity is so important.
CASE STUDY: A New York publisher was concerned
about the dearth of creativity among some of his staff
and decided to hire a team of psychologists to investigate
the matter. The psychologists studied the different staff
over a period of a year and came to a simple conclusion
– the only key difference between the creative and noncreative staff was in the area of belief. Those who
believed they were creative, engaged creatively, whereas
those who believed they were not creative failed to so
engage (Hoover, 2009).
The importance of guidance: As discussed previously, the
cognitive resources we have in our conscious working memory
are very limited. Novices therefore need to be guided strongly
by example. To acquire a creative disposition, therefore,
novices need to observe and study one or more role models
over a substantial period of time.
The importance of deliberate practice: As suggested in
Chapter 2, deliberate practice is very important for skills
development, and the development of creative skills is no
exception. As a very rough rule of thumb, about 10,000 hours
of deliberate practice are needed to become a creative expert
(Gladwell, 2008). If we engage in this kind of practice creativity
will become much more automatic for us.
When and how to develop a creative disposition: Ideally,
parents transmit the pivotal elements in (i)-(iv) to us during
childhood, thereby stimulating an inclination towards
creativity (Sandford, 1985). If we do not receive these key
elements in childhood, though, we can still receive them later
in life. If we become engaged in a community of practice, for
example, we have opportunities to receive the missing elements
from others in the community - creativity can then blossom as
a result. A necessary pre-condition for this flowering to occur,
though, appears to be a willingness to forego anger and
resentment towards parents for the ways in which they might
have failed (Sandford, 1985).
Those communities of practice which have strengths in the
areas of nurture, appropriate physical affection, guidance, and
belief have a particular appeal for fostering creativity. Such
communities are also places where we can start to imbibe
creative methodologies from others.
CASE STUDY: Isaac Newton was born in Lincolnshire,
England, three months after his father had died. The
pain of losing his father was exacerbated when, at the
age of three, he ‘lost’ his mother to her new husband.
When his mother remarried she left Isaac in the care of
his grandmother.
The effective loss of both his father and mother early in
life would seem a very poor natural environment for
nurturing a creative disposition. Yet we know that Isaac
went on to demonstrate one of the most formidable
creative minds in human history. Was this a
coincidence? The evidence would suggest not.
Mihaly Csikszentmihalyi performed a groundbreaking
study in which he investigated the background of over
90 people who had made a very substantial creative
contribution to society (Csikszentmihalyi, 1996). These
people included Nobel prize winning scientists, eminent
writers, medical pioneers, renowned composers, great
architects and respected politicians. The investigations
revealed that an unusually large number of these superachievers had lost a father early in life.
Why would the loss of a father have contributed to
heightened creativity? It may be partly because such a
loss convinced people that they had a great need, and in
response those people proactively sought nurture from
others around them. That is, they developed a strong
habitual tendency to seek assistance from communities
of creative practice.
Regardless of our life circumstances, we can all adopt an
attitude in which we acknowledge our need and
proactively seek help to meet that need.
4.2 Methods and algorithms for innovation
Chapter 2 noted the importance of acquiring background
knowledge for improving discovery and innovation. To become
effective in creative practice, one needs to acquire thorough
background knowledge in diverse areas. This is well illustrated
in the life of Leonardo da Vinci, who had extensive knowledge
in Art, Music, Science, Mathematics, Engineering, Architecture
and Literature. His broad and thorough knowledge enabled
him to successfully pull together ideas from many different
In addition to acquiring background knowledge, one needs to
develop thorough background skills in diverse areas. These
skills are developed through the study of worked examples and
through practice. Deliberate practice of creativity is particularly
important for those of us who have been schooled in disciplines
which tend to emphasise convergent thinking.
CASE STUDY: Traditional training in the mathematical
and physical sciences can tend to create a predisposition towards convergent thinking. Within these
disciplines, therefore, it is advantageous to take
deliberate steps to engender some divergent and
unconventional thinking.
When I teach Engineering students I talk to them about
the importance of regularly summarising material we
have just covered. I follow this up by asking students to
voluntarily review (summarise) the previous week’s
work in front of their peers. To motivate them to engage
in a divergent way I offer a packet of Tim-Tam biscuits
to any students who can review the material within the
context of a contemporary rap.
Some students have responded quite positively and
creatively to this initiative. The lyrics from an example
rap, devised to summarise the topic of electrical
capacitors, are provided below.
“If you had one shot and one opportunity to win a box of timtams for sayin a rap in front of your whole ENB120 lecture
would u do it,
Wake up in the morning feeling like Mr O’Shea,
We rock up to our lecture, its gonna be really gay,
Ladies and gents I’m dropin a bombshell,
U just add capacitors when the’re in parallel,
Before we start singing the rest of the verses,
when capacitors are in series u got to add their inverses,
We will rap on cause we are savage,
Capacitance equals charge on voltage,
We were talkin about LEDs,
That’s because we are all VIPs,
I don’t see what’s all the fuss,
Cause Peter O’Shea ain’t got nothin on us,
Now I know right now you think these boys are my hero,
But the initial potential difference of a capacitor is zero,
Peter, Peter, you thought you could jam,
But we’ll be chowing down on a tim-tam, ...
Now boys and girls we have reached the end of our rap
We can’t believe we get a box of tim-tams for sayin this crap”
Jake Milburn and Johnathan Morgan
Chapter 3 described many commonly employed convergent
problem solving techniques. The following sub-sections are
devoted to divergent problem solving methods.
4.2.1 Lateral thinking
The term lateral thinking was first used by Edward de Bono in
his book: The use of lateral thinking (de Bono, 1967). De Bono
has claimed that the purpose of lateral thinking is to change
concepts and perceptions. Specifically, lateral thinking’s raison
d’etre is to change the common perceptions which exist in the
mainstream consciousness. As an illustrative example, consider
the nine dots puzzle shown in Figure 4.1. In this puzzle, one has
to join all nine dots by drawing four continuous straight lines,
but one is not allowed to lift the pen from the paper while
Figure 4.1. The nine dots puzzle. One has to join all the dots by drawing
four continuous straight lines without lifting the pen from the paper.
The solution is provided in the Appendix. In order to
successfully solve the puzzle one has to draw the lines partly
outside of the nine dot box. The prevailing perception in the
mainstream consciousness, however, is that the lines should be
confined to being within the box. As a result, few people
manage to solve the nine dots puzzle without some prompting.
Although the nine dots puzzle is a problem where lateral
thinking (or thinking outside the box) is needed, it is not an
especially important problem. There are, though, many
important real world problems which can only be solved by
lateral thinking, and there is thus heavy world-wide interest in
such types of thinking (De Bono, 1992).
De Bono has argued that the human brain is a thinking system
which often settles for outcomes which are good, but well short
of what is possible. The techniques underpinning lateral
thinking are designed to help the brain escape from good
solutions to much better solutions (De Bono, 1992).
Three of the best known techniques for stimulating lateral
thinking are Provocation, Challenge and Random Entry.
These techniques are discussed below.
Provocations are stimuli which are introduced to provoke
new ideas and new patterns of thinking. The provocations
which are introduced must not conform to conventional
mainstream perceptions.
CASE STUDY: One illustration of the provocation
process is provided in a story told by de Bono (De Bono,
2009). He was talking to a group of young people and
asked them how they might estimate the height of a
building. One of them suggested laying the building on
its side and measuring it. This unconventional
suggestion served as a provocation for further idea
One cannot lay a building physically on its side, but one
can lay it conceptually on its side, say, by taking a
photograph, cutting the building out of the photo and
laying it on its side. To help with the height estimation,
one could place a box twenty yards from the building
before taking the photo. In that photo the distance
between the box and the building would represent
twenty yards, and so proportionality could be used to
estimate the building’s height.
Challenge is a mechanism whereby one challenges the way
things have always been done. The case study below illustrates
the concept.
CASE STUDY: A certain man rented out boats on an
Austrian lake, and his clients payed by the hour. If his
clients returned the boats late they had to pay for an
extra hour. The man noticed that his clients seemed to
be preoccupied with watching the clock as they rowed so
that they could be sure they would not be late.
One day the man thought about the situation and started
to realise that it did not have to continue to be this way.
He started to challenge the way things had always been
done. His thoughts turned to the famous people who
lived in the beautiful houses on the lake shore, and he
began to take pictures of these houses and to create a
map of where those houses were. He decided to put this
map (along with the pictures of the houses) in the boats
before he rented them out.
After placing maps in the boats, the boat owner found
that the clients became very enthusiastic about visiting
the homes of the rich and famous. Some of the most
spectacular houses were furthest from the boat jetty, and
so the clients tended to take the boats out for longer,
with very little concern about the increased cost. It was a
win-win situation, because the vendor started to make
more money, and the customers started to enjoy their
boat rides more (Mann, 2009).
Random entry is the process of using a randomly selected
word or phrase to open up new avenues of thinking.
CASE STUDY: This case study pertains to an initiative
developed by the author, after seeing an advertisement
for the popular TV medical drama, Grey’s Anatomy. The
title of this show served as the random entry, and
various other words and ideas followed on from this
seed phrase. The first progression was to change the title
to O’Shea’s Anatomy.
Because of the use of the author’s name in the revised
title (and the author’s background in Engineering), the
next progression was to morph the original medical
drama into an Engineering drama. This then prompted
the question of how such a drama might be useful. In
response it was decided to create a new drama centred
on solving engineering problems, which could be viewed
by students as part of their training.
To help engage students in the process, several different
strategies were proposed for the series. These strategies
using students to assist in devising and
filming the series, and
actively incorporating the student audience
into post-episode discussions.
One of the first episodes developed for O’Shea’s
Anatomy was an attempt to expose students to the
problem of setting up their own consulting company.
One solution to this problem was fortuitously provided
by two engineers (Vladimir Bigdan and Jonathon
Hardy), who had on their own initiative, set up their own
company in the third year of their Engineering degree.
The episode served as a mechanism for showcasing the
entrepreneurial strategies of these two students. To
provide a human interest component, the episode was
laced with farce and melodrama.
The now completed episode begins by showing Bigdan
and Hardy in an office working for O’Shea’s consulting
firm. The two employees are shamelessly unethical, and
spend much of their time playing video games and
drinking beer. After they are warned that they stand to
be sacked if their attitudes don’t improve, they defiantly
retort that they still have that picture of O’Shea with the
CEO’s daughter.
A surprise turn of events sees the CEO die unexpectedly,
and Bigdan and Hardy get sacked. The two of them then
start to worry because they do not have any job
prospects, especially without a reference. In a
subsequent scene, Bigdan walks up to O’Shea’s office
with a six-pack of beer, and knocks on O’Shea’s door. He
intends to try and charm a reference out of O’Shea, but
the latter opens the door, takes the beer, and then slams
the door in Bigdan’s face. Bigdan does not get a chance
to ask for anything.
Bigdan and Hardy realise that their only hope for work is
to start up their own consulting company, and at that
point they begin to discuss how they are going to go
about doing it. Their discussions at this point mirror
what they actually did in real life.
After finishing the discussion about how they intend to
go about establishing their own company, the two disappear from the screen. The next part of the episode cuts
to a screen with the words, “Two years down the track”.
Shortly after these words flash across the screen, there is
a display of a newspaper headline which reads “New kid
on the block puts O’Shea Consultancy out of business”.
The next portion of the episode has O’Shea walking
down the corridor to Bigdan’s office with a six-pack of
beer, hoping to plead for a job. Bigdan, however, opens
the door, takes the beer and then slams the door in
O’Shea’s face. A persistent and desperate O’Shea
continues to plead for a job through the glass door of
Bigdan’s office.
The drama has been effective in engaging students on a
number of levels. Firstly, it has enabled students to see
how two of their peers solved the problem of setting up
their own company. Secondly, it has provided some
significant moments of humour.
After completing the first episode of O’Shea’s Anatomy some of
the author’s colleagues pointed out to him that he had created a
series title with a suggestive double entendre. The author was
unaware of this double entendre, and in response decided to
change the name of the drama series. It subsequently became
known as Engineering Underbelly.
4.2.2 Brainstorming
The notion of brainstorming was discussed in Chapter 3 in the
context of sourcing ideas from others. Brainstorming, however,
does not always have to involve others – it is possible to
brainstorm by oneself. That is, one can simply try to devise and
record as many ideas for a problem scenario as possible.
Interestingly, brainstorming by individuals tends to produce
better results than brainstorming in a group (Sweller, 2009).
This appears to be due to the fact that individuals are not
subject to the problems of
social loafing (diminished responsibility when in a
production blocking (being prevented from devising
new ideas when someone is talking) and
fearing being judged by others.
The effectiveness of individual brainstorming may well explain
the success of Leonardo da Vinci, who appears to have devised
many of his creative ideas alone.
To promote creativity in brainstorming, unusual ideas should
be encouraged, and tools such as random entry can be used to
assist in the idea generation process. One should aim for a long
list of ideas, and defer analysis of the ideas until later.
Note that while groups tend not to be effective for idea
generation, they can be effective for idea appraisal.
4.2.3 Engagement with goal-free problems
As stated in Chapter 2, goal-free problems are open-ended
problems in which the goals are not precisely defined. The use
of goal-free (ill-defined) problems tends to facilitate creativity
because the problem solver is not constrained to any particular
solution path. In this sense, goal-free problems are similar to
It is not only loosely structured problems which prompt people
to investigate multiple trains of thought, but also unstructured
environments. A wise mentor will therefore ensure that a part
of the nurturing environment of a mentee is loosely structured.
CASE STUDY: As a young man, Orson Welles developed
such a reputation for creative genius that Hollywood
offered him what is generally regarded as the greatest
deal ever offered to an unproven film director. He struck
a deal with RKO Studios whereby he was financed to
create a major movie with full artistic control (i.e.
without studio intervention). The movie Welles created
for RKO was Citizen Kane, a movie which regularly tops
critics’ polls as the best movie ever made.
How was it that Welles was able to demonstrate such
cinematic brilliance at his first attempt? It was partly
due to his nurturing environment. This nurture was
provided initially by his parents, who placed a great deal
of belief in him. Welles has been quoted as saying, “The
word genius was whispered into my ear, the first thing I
ever heard, while I was still mewling in my crib”.
Substantial nurture was also provided through his
education. Welles attended Todd School for Boys, and
benefited from the care and guidance of a wise teacher
named Roger Hill.
Hill ensured that some of Welles’ educational
environment was unstructured, giving the boy some
freedom to pursue his own interests. In response Welles
chose to focus on theatrical pursuits and instigated
various experimental productions at the school. This
open-ended component of his scholastic environment
unleashed Welles’ creative talents, and helped to forge
the remarkable skills which would later make him
4.2.4 Humour
“We can be heroes” was an Australian TV series about five
fictional characters who were all nominees for Australian of
the Year. The nominees were all played by the same man, Chris
Lilley. One of the characters he played was a 16 year old girl
called Ja’mie. She was nominated by her School Principal
because she sponsored 85 Sudanese children with Global
Vision and did the 40 hour famine every week. Ja’mie claimed
that the latter not only helped to raise money for the
sponsorship but also kept her “looking hot”.
Because she held the Australian record for the number of
children sponsored, Ja’mie was asked to be the face of Global
Vision in Australia, and was also commissioned to talk about
sponsoring children at her school assembly. During that
assembly Ja’mie berated the students for not using their money
for sponsorship, and said that each dollar not donated meant
one dead child. She also said there were probably a thousand
children dead because the Principal had organised a costly ski
trip instead of giving the money to Global Vision.
Shortly after learning that she had been shortlisted as a state
finalist for Australian of the Year, Ja’mie got some bad news.
Her Principal informed her that a flood had hit the village of
her sponsor children, and that all but two of the children had
been killed.
Ja’mie became very upset and said it was the worst day of her
life. She immediately called Global Vision and demanded that
she be allocated another 100 children within a week. When the
Global Vision representative equivocated, Ja’mie angrily
explained that she no longer held the record for sponsoring
children, and that if she didn’t get these new children
immediately, someone else was going to become Australian of
the Year.
Many people laughed at the antics of Ja’mie’s character
because she was such a contradiction. One would normally
expect someone sponsoring children to be caring and giving.
Ja’mie was vain and self absorbed in the extreme. As was the
case with “We can be heroes”, humour is often generated by
communicating scenarios which are incongruous or
Of course, the incongruous and unexpected scenarios which
arise in humour are rarely useful in a practical sense – they are
simply funny. In real life, however, many unconventional and
unexpected ideas do actually lead to creative and
groundbreaking solutions. It is therefore important to practice
thinking in unconventional ways, and developing a sense of
humour provides a suitable stimulus for this kind of practice.
CASE STUDY: Robin Williams, the Academy Award
winning comedian/actor, is widely regarded as a comic
genius. Interestingly, in his youth he spent a significant
amount of time listening to, and memorising the comedy
albums of Jonathan Winters. This is not only an
illustration of the effectiveness of developing humour by
studying examples, but also suggests a useful synergy that between comedy and memorisation.
Significant research evidence indicates that practice in
rote memorisation can help build up peoples’ memory
capacity, which in turn increases the rate at which
people can absorb new information (Peck, 2006). The
idea of memorising comedy sketches has appeal for
many of us because of the potential for improving our
social interactions.
4.2.5 TRIZ – the theory of inventive problem solving
As with many other skills and capabilities, novices can learn
creativity effectively and efficiently by example. This was amply
demonstrated in the life of Genrich Altshuller. He was a
Russian engineer who spent much of his early career inspecting
inventions patents (i.e. example inventions). The inspection of
a huge number of patent applications led him to abstract and
subsequently document many systematic strategies for
facilitating novelty and invention.
A key feature of the TRIZ methodology is the use of the Forty
Principles of Invention (Altshuller, 1973). One of these
principles is presented below, along with examples which
illustrate the use of the principle (Mazur, 2009).
Principle A: Convert harm into benefit. With this principle, one
seeks inventions which can
convert harmful factors into helpful ones,
eliminate the effects of a harmful factor by
neutralising it with a different harmful factor, and/or
(iii) increase the extent of the harmful action until it
becomes beneficial.
Examples of inventions which employ this principle are:
an electronic noise cancellation device in which
unwanted noise is cancelled by artificially subtracting
a copy of the noise from itself,
the use of explosives in the building industry,
an invention which solves the problem of pouring
sand or gravel in very cold climates where freezing
tends to inhibit effective pouring; if extreme freezing
is used (with say liquid nitrogen), then the problem
disappears because the material then becomes brittle,
and is therefore amenable to pouring,
an invention for surface heat treatment; this
invention was devised by noting that high frequency
current was ineffective for the conventional heating of
metal, because the metal only became hot on the
surface. This disadvantage was turned to advantage
by using high frequency current for surface heating,
Further examples of the Forty Principles of Invention are given
in (Mazur, 2009). From his analysis of patent abstracts
Altshuller also devised one of the chief over-arching principles
of invention:
A key to invention is the shrewd removal of apparent
Altshuller compiled a list of the various contradictions that
arise when one is trying to invent. These contradictions are
summarised in his matrix of contradictions, a two dimensional
array in which the rows are represented by the desirable design
system features, and the columns are represented by the
undesirable (contradictory) features. The list of all 39 possible
features, both desirable and contradictory, are given in Table
The matrix of contradictions is a 39 by 39 element matrix, and
at the intersection of any given row and column, the
Principle(s) of Invention is listed which can resolve the
apparent contradiction. An example of the use of the matrix is
given in the following paragraph.
CASE STUDY: Consider the problem of excessive wear
on aeroplane wheels as they land on the tarmac. The
wear occurs largely because of the sudden jolt on the
wheels when the aeroplane touches the ground. This
creates massive amounts of friction, which generates
heat and burns up the rubber on the wheels.
The naive solution to the burning rubber problem is to
simply slow the aeroplane down as much as possible
before landing. It would be much more desirable,
however, to have a solution which did not impose such
limitations – one which allowed the aeroplane to land at
any speed.
The desired feature in this example is speed (Parameter
9), while the undesirable feature is loss of material
(Parameter 23). If one looks at the intersection of these
two parameters in the contradiction matrix one finds
that the first Principle of Invention listed is Prior Action.
This suggests the strategy of pre-spinning the aeroplane
wheels just prior to landing so that the change in velocity
of the wheels is minimal when the aeroplane touches
down. Because there is much less of a jolt when the
wheels are pre-spun, the wear on the wheels is
correspondingly less.
The methodology for shrewd removal of contradictions is
summarised in Figure 4.2. As depicted in the figure,
abstraction (or generalisation) and concretisation (or
specialisation) are both used as key tools for determining
inventive solutions. The generalisation of the problem is
facilitated by analysing the problem in terms of the 39
engineering parameters and the corresponding contradictions.
The generalised solution is obtained by using the contradiction
matrix to determine the relevant Principle of Invention(s). The
specialised solution is achieved by finding a concrete way to
apply the relevant Principle of Invention(s) to the problem at
Figure 4.2. An overview of the Contradiction Matrix Methodology.
4.3 Conclusions
This chapter has provided some strategies that we can pursue
to help cultivate creativity and innovation. Firstly, there is
significant advantage in our becoming part of a community of
practice of innovators, where we can give and receive example
and nurture. We can also benefit from reading the literature on
creativity, and from reflecting on great creative breakthroughs.
If we wish to heighten our grasp of innovation methodologies,
we should study and practice the algorithms that are known to
heighten creativity. This chapter has outlined some of these
algorithms, namely provocation, challenge, random entry,
brainstorming, engagement with goal-free problems,
development of a sense of humour and the theory of inventive
problem solving (TRIZ). We also need to work on devising and
practising our own strategies for innovation.
Table 4.1. The 39 Engineering Parameters
Weight of moving object
Weight of non-moving object
Length of moving object
Length of non-moving object
Area of moving object
Area of non-moving object
Volume of moving object
Volume of non-moving object
Tension, pressure
Stability of object
Durability of moving object
Durability of non-moving object
Energy spent by moving object
Energy spent by non-moving object
Waste of energy
Loss of substance
Loss of information
Waste of time
Amount of substance
Accuracy of measurement
Accuracy of manufacturing
Harmful factors acting on object
Harmful side effects
Convenience of use
Complexity of device
Complexity of control
Level of automation
Chapter 5
Practical tips for novice problem solvers
and researchers
5.1 Tips for using time productively
Research studies show that ‘time on task’ is linked to
achievement (Hattie, 2009). The evidence also shows, however,
that achievement is strongly dependent on how that time is
spent (Ericsson, 2005). This section discusses evidence based
strategies for wisely using one’s time.
Be reluctant to give up - persevere to the end
Studies show that the brain has an extremely low capacity
working memory. As a consequence information can only pass
into the conscious part of the brain at a very slow rate (Sweller
et al, 1998). If one wishes to accumulate a high degree of
competence, then, one has to persevere for a long period of
time. Einstein understood this very well and quipped that:
“It’s not that I’m so smart, it’s just that I stay with
problems longer.”
Sadly, many people do not emulate Einstein’s attitude. They
give up on their problem solving endeavours too quickly. Some
give up because they assume that they are only making slow
progress because they are ‘dumb’. Some give up because they
want ‘quick fixes’ and decide that it is not worth persevering
over a long period of time.
Instead of giving up, we need to commit to our endeavours for
the long-term and we need to find ways to make sure our time
investments are efficient. The following paragraphs describe
further evidence based principles which can help us to do just
Engage the imagination
CASE STUDY: In 1905 Albert Einstein was perplexed by
a dilemma and he wanted to talk to someone about it.
He therefore went to visit his friend, Michele Besso.
Einstein had deduced that the classical mechanics
theories of Isaac Newton and the electromagnetic
theories of James Clarke Maxwell could not both be
correct. Einstein and Besso discussed the issue for
hours, but they could not resolve the discrepancy.
Einstein became so exasperated that he decided to give
up thinking about the problem.
As he ventured home, Einstein was travelling on a
streetcar in the city of Bern. As he looked back at the
city's clock tower he imagined that the streetcar was
speeding away from the clock tower at the speed of light.
It then struck him that light from the clock tower would
not be able to catch up to his street car, and so the clock
hands would appear to him to be stationary. If there was
a clock in the streetcar, however, it would appear to be
functioning as usual. As he continued to imagine these
possibilities he had a startling revelation. Time was not
invariant! It depended on the speed of the observer.
After this critically important moment of illumination
characterise his new understanding. The theory of
relativity, one of the most famous scientific theories of
all time, was thus born.
One of Einstein’s great strengths was the way he
practiced using his imagination. Even after giving up
deliberate attempts at problem solving, his imagination
was continuing to trigger ideas.
Regular engagement of the imagination is a powerful way to
persevere with the solving of difficult problems. This is so
because use of the imagination tends to increase fluency. That
is, it tends to increase the number of different trains of thought
we have (Sweller, 2009).
The evidence also indicates that imagination can powerfully
foster the automation of important skills. Normally
automation of a skill is achieved by repeated practice, which
typically occurs through conventional study or through
relevant physical activity. With the imagination-based
approach, though, a person spends a significant amount of
time running over the relevant procedure mentally in their own
mind, and as they do so, less and less conscious effort is
ultimately required to execute the procedure (in either their
mind or in a physical way) (Cooper et al, 2001). Interestingly,
the use of imagination based automation is more effective than
conventional study techniques (Leahy & Sweller, 2008).
Scaffold progress as much as possible
Because of the limitations of human cognitive architecture,
mental progress can be slow, and it is easy to become
discouraged as a result. It is therefore important to find ways to
assist our progress. This assistance can be obtained in a
number of different ways.
Firstly, we can take steps to deliberately build up extensive
background knowledge. This can be done by studying and
practicing many and varied examples within our area of focus.
Secondly, we can ‘piggy back’ on the prior efforts of others.
Rather than starting from first principles to solve difficult
problems we can try and find related problems which have
been solved previously. We can then adopt those approaches
(with some modifications) to help us solve our problem.
CASE STUDY: The development of the printing press by
Gutenberg ranks as one of the most significant
technological breakthroughs in history. Gutenberg made
the breakthrough in no small part by building on the
prior efforts of others.
The key idea for the printing press came to Gutenberg
while he was at a wine festival. He observed the winepress forcing coloured liquid (wine) out of the grapes
and realised that he could use an analogous solution for
creating a printing press. That is, he could use a
mechanical device to press ink against paper.
The other critical idea Gutenberg used to create his
printing press was derived from the work of stamp
makers. These stamp-makers had a number of blocks
representing the various letters of the alphabet, and
these blocks could be assembled together at will to form
arbitrary words for a stamp. Gutenberg adapted their
idea to make blocks of inked letters which could be
moved around in his press to create any sequence of
text. He then used a mechanical device to press these
blocks against paper. The pressing process could be
done repeatedly by the mechanical device so that
printing could occur quite quickly.
Thirdly, we can engage in goal-free problem solving. In
practical terms, this means that when we are confronted with a
problem we start to articulate all the relevant information we
currently possess (possibly in writing), without dwelling too
much on how to obtain the final solution. We then start to
think about what we can deduce from what we know. As we
deduce new knowledge we then think about what we can
deduce from that new information, and so on.
Use varied activities and approaches
The evidence shows that the brain responds preferentially to
novelty and variation. For this reason, we should vary the
nature of our intellectual activities on a regular basis. We
should be cautious, for example, about reading for long periods
of time. If we are reading, it may well be better to break after
every 15 to 20 minutes to perform an alternative activity
(Mittendorf & Kalish, 1996). This activity could involve writing
down the things that were unclear in the latest portion of the
reading, or articulating how the ideas we have read about can
be used to stimulate new avenues of investigation.
Even small periods of alternate activities tend to positively
affect the engagement of the brain and the refocusing of
attention – typically only about 5 minutes is necessary for
attention to be restored. If these types of activities are used to
break up extended periods of reading it also provides us with
the opportunity to make our own links between prior
knowledge and new knowledge, something which is vital for
deep and lasting skill development to occur (Ormrod, 1994).
We can also increase the chance of making regular progress if
we vary the type of research activity we pursue. If, say, we are
failing to see any answers in our theoretical analyses, we might
choose to do some writing, perform some experimental work,
develop some useful computer code, or gainfully read some
literature. We can return to the theoretical analysis at a later
It is not only the nature of the activities which should be varied
- the location should be changed regularly as well. Studies
suggest that changing the surroundings during study prompts
the brain to become more alert and therefore more effective
(Carey, 2010).
Maintain the level of challenge and keep the emotions positive
Research shows that challenge plays an important part in
fostering achievement (Hattie, 2009). Without challenging
ourselves regularly we are unlikely to progress adequately in
our cognitive development.
Importantly, evidence from the neurosciences has also shown
that the brain functions best under the simultaneous
conditions of high challenge and low stress (Reardon, 1999).
Challenge cannot, therefore, be provided in isolation. It must
be issued in concert with mechanisms which keep the emotions
positive (and therefore reduce stress). Researchers, then, need
to regularly try and push the envelope in their activities, but
they also need to seek out mechanisms for stimulating positive
emotions .
Music is one tool which can powerfully foster positive
emotional engagement. Studies show that classical music has
the potential to alter mood and intellectual arousal, which can
in turn promote improved reasoning ability. Evidence for this
phenomenon was provided in a well publicised article in
Nature in 1993. That article reported that the spatio-temporal
reasoning ability of university students was enhanced
subsequent to listening to the Mozart Sonata for Two Pianos in
D Major, K448 (Rauscher et al, 1993).
The reasoning enhancement associated with the ‘Mozart Effect’
lasted no more than about 15 minutes, corresponding possibly
to the dwell time of the emotional stimulation. The improved
reasoning seems to occur if the music is perceived to be
energetic with a positive emotional quality (Thompson et al,
There are many ways through which we can foster positive
emotions. Music, humour, social relationships, physical
exercise, and creative expression are some such ways.
Figure 5.1. Studies show that listening to Mozart’s music can enhance
CASE STUDY: Richard Feynman was one of the most
highly regarded scientists of the twentieth century. Such
was his reputation that when he gave his first
postgraduate seminar at Princeton University,
luminaries such as Albert Einstein and John von
Neumann attended.
Feynman went on to win a Nobel prize in Physics in
1965. He also gained international fame when he
publicly explained why the Challenger Space Shuttle
disaster of 1986 occurred.
When he was at the Los Alamos laboratories during the
1940s, he was a relatively junior scientist and was
consequently given little to do. Rather than fall victim to
boredom, Feynman proactively used humour, music and
creative expression to set up his own positive (and
challenging) milieu. He performed numerous practical
jokes on his colleagues. He used his genius, for example,
to crack the codes of a number of safes in the
laboratories, and then left baffling messages in those
safes to confound his colleagues.
He further bemused his co-workers by going to isolated
sections of Los Alamos where he played mesa drums in
traditional American Indian fashion. He also used to
dance and chant. His co-workers thought that there was
a mysterious ‘Injun Jo’ in the Los Alamos area.
Engage in reflection
Reflection is pivotal to intellectual advancement (Hattie, 2009).
While some people reflect effortlessly, others do not. For those
in the latter category it can be helpful to follow a structured
plan to prompt reflection (Palincsar & Brown, 1984). This plan
involves breaking from regular activities to:
1) pose questions,
2) summarise what has been read,
3) clarify the material just covered with a view to linking it
to existing knowledge, and
4) predict how one can apply any newly gained insights.
It is not only conscious reflection which is useful, but also subconscious reflection. When working on a challenging problem,
we should take regular and extended breaks during which we
refrain from consciously attempting to solve our problem.
These breaks can serve as periods of incubation where
subconscious reflection takes place. Such periods tend to assist
us by helping us to forget misleading solution paths. When we
go back to our problems we may well find that we have a fresh
Stay connected and solicit feedback
Interactions with peers and mentors have a strong effect on our
levels of engagement and achievement. We therefore need to
make regular contact with others. Preferably, we should not
limit our social interactions to one or two people, but rather,
we should be engaged in a broader community of practice
around discovery and innovation. Such a community can be a
place where we can receive critically important feedback on our
5.2 Disseminating research work
All researchers and students need to present their work to
others, and it is important that this dissemination occurs
effectively. To exploit what opportunities come our way, we
should be aware of the substantial existing body of evidence on
how to communicate information to others.
If we decide to use Power Point (PP) or other multi-media
software to present our findings, there is significant merit in
adhering to the five evidence based principles outlined below
(Mayer, 2001; Chandler & Sweller, 1992):
The signalling principle: The title on every slide
should explain the key idea on that slide. This tends
to ready the listener to absorb the relevant concepts.
Titles should be concise, informative and in large type,
like a newspaper headline. A sample title might be
“Artificial sweeteners increase risk of cancer”.
The segmentation principle: Information should be
presented in a slow and steady stream so as not to
invoke cognitive overload in the audience. This
implies that each slide should be limited in
information content, and all slides should contain
about the same amount of information. It can be
helpful to do the slide design in the slide sorter view,
so that one can monitor the flow of information
throughout the presentation.
The modality principle: People respond best to
presentations which contain both visual and audio
components. The effectiveness of dual mode
presentation derives from the fact that the mind has
two relatively independent processing channels – one
for visual signals and one for auditory signals (Paivio,
1986). In support of the modality principle,
investigations have explicitly shown that people
respond better to presentations which involve
animation and narration (corresponding to both
visual and aural modes) than to presentations with
animation and text (Mayer, 2001).
The split attention principle: In order to avoid
splitting the attention of the audience, one should
resist using two different forms of information within
the one modality, unless they are integrated. This
principle has implications for both the aural and
visual domains. In the aural domain background
music should not be played concurrently with
narration (Moreno & Mayer, 1999). Similarly, in the
visual domain, graphics and text should not be used
together unless they are integrated. (See Figure 5.1
which shows an illustration of graphics and text
which is integrated, and an alternate illustration in
which they are not integrated).
Splitting of attention also occurs under the special
circumstance where one views and hears the same
word simultaneously. In giving presentations,
therefore, one should studiously avoid narrating onscreen text.
The coherence principle: Only the key ideas should be
included in a presentation. Extraneous material tends
to divert attention away from the more crucial ideas.
If one makes a presentation and decides not to use PP there are
various practical alternatives. Whiteboards, overhead
transparencies, and camera based projections of handwriting
and drawing can all be used. These alternatives have the
advantage that when one uses them it is difficult to produce
new material suddenly, and it is also difficult to produce a lot of
uninspiring bulleted text. It is more natural to produce
informative annotated diagrams.
To improve presentation skills one can also use the ‘microteaching’ approach. The first stage in microteaching is to videotape a sample presentation. The second stage is a reflective one
in which the presenter and a number of peers or students
watch the video and critique it. There is strong evidence that
this kind of approach has a positive impact (Hattie, 2009).
Triangle height=36
Triangle base =15
Length of hypotenuse
(slanting side of
triangle)= 39 .
Figure 5.1. (a) An illustration of integrated text and graphics, (b) an
illustration of non-integrated text and graphics.
Figure 5.2. People tend to learn effectively via pictures and diagrams: A
picture of ‘Fractal broccoli’ illustrating images reproduced at smaller and
smaller scale in nature.
5.3 Conclusions
Novice researchers need to scrutinise the way they spend their
time. The evidence suggests that they should be persevering
because intellectual progress tends to be slow. Studies also
show that they should engage in a diverse range of activities,
embrace the incubation process, be part of a community of
research practice, and give much rein to their imagination.
In developing their presentation skills, novice researchers are
well advised to use the microteaching approach. They should
also follow the evidence based principles outlined in (Mayer,
2001) and (Chandler & Sweller, 1992).
Chapter 6
Mentoring others in innovation and
Teaching and mentoring others how to discover and innovate is
much like teaching and mentoring in other areas - there are
certain general principles which are particularly relevant. The
following case study illustrates some of these principles.
CASE STUDY: Joel Osteen is one of America’s most
sought after speakers and mentors. He fills large
stadiums almost wherever he goes. His books regularly
top the New York Times best seller list and he has been
interviewed by some of the highest profile journalists in
the world. He has been interviewed, for example, on
“Larry King Live” and on “Sixty Minutes” in the US.
When Joel is asked how it was that he became a
successful speaker and mentor, he recounts a part of his
life story. He explains that he grew up with a gifted
father whose life work was to teach and mentor others,
and who wanted his son to follow in his footsteps. Joel,
however, had other plans. When the time came to go to
college, he went off to follow his natural interest – audio
and video production.
After some time studying at college Joel returned to his
home town and asked if he could work on creating video
productions of his father’s speaking. The father agreed,
and Joel worked in this capacity for 17 years.
After 17 years, the father became seriously ill and had to
go to hospital. From his sick bed, the father asked if his
son could replace him in one of his speaking
engagements. Curiously, something in Joel’s heart
changed, and he agreed. Very shortly after Joel did this
first speaking assignment, his father died. Before he
died, however, the father was deeply gratified to know
that his son had substituted for him.
Joel, who was very close to his father, was grief stricken
at losing his parent. Strangely, he also felt compelled to
continue to fill in for him. What happened as Joel did
this was remarkable. He rapidly became enormously
successful, and people came from far and wide to listen
to him and to be mentored by him.
Joel declares that a key reason for his success was the
training which effectively took place as he produced his
father’s videos. In the process of his weekly editing Joel
would repeatedly study his father (typically watching
each video about four times so that he could critically
appraise it). Joel therefore studied many and varied
examples over a protracted period of about 17 years.
In light of the evidence presented in Chapter 2 about the
power of studying many and varied worked examples, it
is not surprising that Joel acquired such high levels of
expertise. Joel of course, eventually progressed beyond
simply studying examples to actually practicing them
himself. Ultimately he even began to teach and mentor
others how to become good teachers and mentors. All of
these strategies are in line with the evidence outlined in
earlier chapters - begin by studying many and varied
examples of an activity, then engage in deliberate
practice, then teach others how to do it.
A final lesson to be learned from the story of Joel Osteen
is the importance of connecting with socially relevant
others in a community of practice. Joel was strongly
connected to his father (and to others) and was able to
learn from him (and them). From his father and others
he learned not only strategies, but also how to impart
care and belief.
6.1 Tips and traps for mentoring others in
discovery and innovation
Many volumes could be written about what mentors can do to
enhance the chances of their mentees’ success. This section
attempts to provide but a few key pieces of advice.
1. Articulate a vision: We are very unlikely to become great
mentors overnight - we need to work at it long-term. To help
sustain us we should articulate and pursue a vision.
When we do articulate a vision we must also commit to
nurturing it. Chapter 2 describes various techniques which we
can use to ensure that this nurturing occurs. We can seek out
positive role models, we can read inspiring stories and we can
resolve to face and deal with obstacles bravely and persistently.
2. Engage in a community of supervisory practice: Mentors
need to learn the art of mentoring by observing many and
varied examples. It is important, therefore, to link with other
more experienced mentors who can provide that example. It is
advantageous to take as many opportunities as possible to
observe and study these people at work. It is also advisable to
seek out video resources to tap into the inspiration and
example of others who cannot be observed physically.
When participating in a community of practice it is pertinent to
keep in mind that we advance our skills effectively by studying
many and varied examples. A common trap is to think that
studying a few examples is enough – falling into this trap limits
one’s potential.
3. Commit to a cycle of continuous and gradual improvement:
People tend to acquire skills gradually, and so one should not
be too ambitious in the first instance. Learning to develop good
mentoring skills takes a substantial amount of time, even for
someone who is gifted. It is therefore necessary to embrace an
attitude of patience and perseverance.
In seeking to continuously improve one’s mentoring it is
advantageous to be guided by copious amounts of feedback.
Some feedback can be sourced from quantitative data such as
student completion rates and the number of high impact
journal papers produced or other measurable outcomes.
Feedback can also come from qualitative mentee evaluations
and peer feedback. Conversations with mentees are yet another
important source of feedback.
4. Follow evidence-based practices: Research studies suggest
that our instincts and beliefs about skill acquisition are often
flawed (Pashler et al, 2009). It is important, therefore, to
consult the evidence.
6.2 Conclusions
When one begins to mentor others in discovery and innovation
one is embarking on what is potentially a very rewarding
journey. To reap the best possible outcomes from this journey
it will be necessary to negotiate substantial obstacles, and it is
therefore advisable to be armed with a long-term vision. It is
also important to appreciate that mentoring is about helping
others, and practical demonstrations of care are of the utmost
New mentors can benefit greatly from being part of a
community of supervisory practice where they can draw on the
example and inspiration of others. They can and should also
acquaint themselves with the evidence on how to foster
discovery and innovation in others. Finally, new mentors need
to be patient - slow and gradual improvement is the norm.
Mentors also need to help those in their care to use their time
wisely. To this end they should help their mentees to acquaint
themselves with the evidence on how to acquire skills rapidly
and effectively.
Chapter 7
The cognitive potential of humans is enormous, and it is the
three critical elements of belief, care and vision which unlock
this potential. The story of Nancy and Thomas Edison in
Chapter 4, and the story of George and Pedro Bach-y-Rita in
Chapter 1 bear testimony to the importance of these elements.
If we wish to positively impact on discovery and innovation in
either ourselves or others it is highly advisable to embrace and
nurture these three elements.
Improving discovery and innovation is a journey, and if we are
willing to adopt the right attitudes, it is an exciting journey.
This book has attempted to provide a stimulus for the reader to
embark on that journey, and to negotiate the path as fruitfully
as possible. To ensure this fruitfulness, it is important that we
commit to evidence based strategies. If we wish to engender
improvements in our own cognitive processes, the key practices
to pursue are those given in Chapter 2. In summary, these
practices are:
cultivation of mindfulness and vision,
reflection and belief adjustment,
shrewd acquisition of appropriate background
knowledge and skills,
(iv) a commitment to deliberate practice in diverse
(v) habitual abstraction of key underlying principles
from new situations,
(vi) engagement with analogies and metaphors,
(vii) giving and receiving care and guidance in the area of
thinking and innovation,
(viii) physical exercise and adherence to an appropriate
This book has also provided advice on how to go about
improving our problem solving and innovation skills. This
advice is summarised in the following list.
For all problems, early in the problem solving process,
we should use research, analogies and expert
consultations. We should also use incubation to help
facilitate a solution, and during the incubation period
we should actively seek clues. We should reflect
intermittently on our progress and re-evaluate our
plan for obtaining a solution.
(ii) For ill-defined problems we should express the
problem in a variety of different forms and include a
visual representation.
(iii) For problems with a limited number of possible
solutions we should pursue the trial and error
(iv) For problems with fewer paths leading away from the
goal than from the starting point we should consider
using the working backwards approach.
(v) For complex problems we should investigate the use
of means end analysis, deduction, induction, and
divide and conquer.
(vi) For failure analysis we should use root cause analysis.
(vii) For mathematical problems we should follow the
advice in Polya’s book, “How to solve it” (Polya, 1945).
(viii) For creative problem solving and innovation we
should use lateral thinking (including provocation,
challenge, and random entry). We should also use
brainstorming (at an individual rather than group
level), TRIZ, and we should seek to develop a sense of
humour and engage regularly with goal free problems.
It is also important to remember that discovery and innovation
are social phenomena, and to achieve our potential, we need to
link with others who can give and receive help. These others
can help us not only to develop better thinking techniques, but
they can also help us to change our attitudes. Attitude changes
are critically important as they can assist us to embrace greater
challenges, respond better to feedback, see greater relevance in
our intellectual endeavours, believe more in others, care for
one another better, and sustain vision more effectively.
This book has provided a discussion of the key areas involved
in improving our discovery and innovation skills – these
discussions, though, are only a beginning. Those who are
earnestly seeking to improve the discovery and innovation
skills need to continue with their own investigations, and
discover all that they need for their own unique situations.
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abstraction, 15, 55, 58, 69,
95, 114, 133
adaptation, 46
adversity, 11, 20, 37
aeroplane wheels, 114
Alcoholics Anonymous, 5
analogies, 16, 59, 60, 61, 69,
71, 93, 95, 133, 134
anger, 31, 32, 33, 100
animal, 6
animation, 125
anxiety, 28, 29, 143
apprentice, 67
architecture, 41, 101, 137,
arrows, 96
assessment, 132, 138
attention, 25, 40, 44, 125,
126, 145
attitude, 31, 49, 51, 64, 65,
85, 97, 131
aural, 125
automation, 49, 116, 119
autopsy, 8
background knowledge, 15,
39, 40, 69, 95, 101, 102,
balance, 121
belief, 6, 7, 8, 9, 12, 13, 97,
99, 100, 129, 133
Biology, 58
blind, 47
blocks to learning, 28, 29
boats, 105
body building, 16
Bo-Peep Theory of learning
transfer, 13
brain, 8, 9, 11, 40, 41, 47, 52,
68, 99, 104, 118, 121, 139,
143, 144
British Parliament, 51
bullet, 91
business, 48, 57, 85, 106,
busyness, 20
camera, 97
care, 9, 10, 11, 12, 64, 65, 99,
121, 129, 132, 133, 134
cerebral cortex, 8, 9, 16
challenge, 20, 29, 65, 105,
116, 121, 134
checkmate, 76, 82
Chemistry, 58
chess, 39, 76, 82, 83, 138,
childhood, 26, 85, 97, 100
children, 10, 24, 33, 105,
139, 144
chunks, 40
clues, 29, 81, 93, 134
cognitive load, 140, 142
coherence principle, 126
collaboration, 11
comedy, 112
comfort, 121
communication, 61
communities of practice, 66,
company, 80, 106
complex systems, 39
complexity, 50, 119
Computer Programming, 15
conscious, 16, 29, 33, 41, 119
content, 61, 63, 125
continuous improvement,
creative problem solving, 57,
81, 93, 134
creative thinking, 57
creativity, 6, 10, 12, 19, 46,
56, 57, 97, 98, 99, 100,
109, 112, 115, 117, 139, 145
crime, 86, 91
critical mass, 44
current, 19, 61, 81, 113
cylinder, 83
deduction, 90, 91, 93, 96,
deliberate practice, 48, 100
depression, 68, 138
diet, 16, 68, 69, 133
digits, 41
discovery, 16, 40, 81, 97, 141
disorganisation, 20
diverse practice, 15, 47, 49,
51, 69, 133
diversionary activities, 19,
divide and conquer, 75, 93,
doctor, 8, 21
dolphin, 6, 13
drawing, 40, 91, 103, 104,
education, 39, 57, 85
efficiency, 19, 139
electric light bulb, 97
emotions, 31
engagement, 16, 46, 52, 61,
69, 71, 84, 116, 119, 121,
engineer, 56, 83, 112
ethics, 106
eureka, 81
evaluation, 132, 138
evidence, 10, 12, 14, 24, 46,
68, 69, 70, 80, 81, 84, 94,
112, 124, 129, 132, 133
expert, 26, 39, 40, 62, 63,
67, 93, 100, 134
expertise reversal effect, 44
fail, 26, 68, 87
fear of failure, 29
feedback, 29, 31, 48, 121,
131, 134, 138
fish, 68
Invention, 56, 112, 113
General Problem Solver, 5,
generic problem solving
strategies, 39, 70, 94
genetic algorithms, 73
goal, 11, 45, 46, 76, 77, 82,
87, 93, 109, 110, 116, 134,
gold, 81
Good Shepherd Theory of
learning transfer, 15
Google, 21
grade, 19
gravel, 113
guidance, 11, 42, 44, 67, 97,
99, 100, 121, 141
habit patterns, 9, 51, 97
handwriting, 126
hanging gardens, 87
heart attack, 8
honey bees, 71
humour, 112
illumination, 81
imagination, 119, 142
improvement, 7, 12, 29, 31,
33, 37, 131, 132, 134, 145
incubation, 33, 81, 93, 134,
induction, 90, 91, 93, 134,
information, 21, 40, 42, 67,
73, 81, 95, 112, 116, 118,
124, 125
Innocentive, 80, 141
innovation, 6, 69, 97, 101,
115, 117, 133, 134, 142
intelligence, 39, 137, 143
interaction, 67
internet, 11, 71
intimation, 81
invention, 56, 83, 97, 112,
journaling groups, 35
language, 28
last lecture, 26
lateral thinking, 93, 103,
104, 134, 139
Latin, 14, 145
learning, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 19, 23, 26,
28, 31, 32, 33, 34, 35, 37,
40, 41, 42, 44, 46, 47, 49,
50, 51, 52, 55, 57, 61, 62,
63, 64, 66, 67, 68, 69, 70,
95, 96, 97, 104, 112, 118,
121, 124, 129, 133, 134,
139, 142, 143, 144, 145
line tracing, 16
linkages, 61, 84
liquid nitrogen, 113
long-term consequences, 85
long-term memory, 40, 41
love, 10, 64, 139
management, 137
master, 50, 67
materials, 93
Mathematics, 58, 95, 140
matrix of contradictions,
means end analysis, 93, 134
memory, 31, 41, 85, 112, 137,
Menlo Park, 97
mentors, 19, 25, 67
metacognition, 146
metaphors, 16, 59, 60, 61,
69, 95, 133
mimic, 6, 39
mind, 19, 28, 33, 42, 81, 83,
84, 85, 97, 119, 125, 131,
mindfulness, 15, 16, 18, 69,
106, 133
modality principle, 125
money, 105
mood, 121
motion, 97
motivation, 7, 37, 67
muscles, 13, 16, 49
music, 48, 101, 121, 122, 125
narration, 125
neural network, 9
neurons, 145
novelty, 112
novice, 40, 42, 44, 62, 66,
69, 129, 131, 132
nurture, 66, 67, 97, 99, 100,
115, 131, 133
oxytocin, 9, 10, 99
parents, 10, 25, 32, 100
peers, 24, 25, 35, 67, 106,
perfectionism, 20
PhD, 11, 29, 35, 46, 50, 55,
56, 59, 63, 141
photograph, 105
physical exercise, 16, 68, 69,
95, 133
Physics, 58
politician, 26
postdoctoral studies, 19
Power Point, 124
practice, 16, 44, 47, 49, 51,
85, 94, 95, 97, 99, 100,
102, 111, 112, 115, 119, 129,
131, 132
preparation, 28, 81, 137
pressure, 83, 116
prior experience, 40
prior knowledge, 39
problem solving, 5, 12, 36,
39, 40, 44, 58, 69, 70, 71,
76, 80, 81, 82, 87, 93, 94,
95, 96, 101, 102, 112, 116,
133, 134, 139, 142, 145
production blocking, 80,
provocation, 105, 116, 134
Psychology, 15, 58, 67, 138,
139, 140, 142, 143, 145
public speaking, 16
Quicksort algorithm, 75
quiver, 96
random entry, 106, 109, 116,
reading groups, 63
reasoning, 16, 121, 122, 141,
reciprocal teaching, 63
reflection, 11, 15, 20, 26, 28,
29, 33, 35, 36, 37, 38, 69,
83, 85, 94, 95, 133, 138
reflective journal, 35
rehabilitation, 8, 10
relevance, 41, 134
research laboratories, 97
risk-aversion, 20
robust, 9
role models, 23, 61, 67, 131
root causes, 37, 85
rote memorisation, 16, 112
Royal Mint, 51
Royal Society, 51
sand, 113
scanning, 84, 95
schemas, 40, 42, 44
seekers, 81
segmentation principle, 125
self-sabotage, 19, 20
signalling principle, 124
social loafing, 80, 109
solvers, 81, 95
speech, 8
speed, 71, 114
sport, 48, 85
statistical, 46
steam engine, 83
stories, 131
stress, 121
stroke, 7, 8
substitution code, 91
sugarcane workers, 37
summaries, 60
summarizing, 62
surface heating, 113
surprise, 46, 106
swimming, 85
task variation, 46, 51
teachers, 25, 69, 129, 131,
132, 140
telephone, 41
TERISSA, 36, 138
training, 6, 7, 9, 13, 16, 106,
129, 137, 141, 143, 144
transfer, 13, 14, 15, 41, 50,
51, 137, 140, 143, 144
trial and error, 73, 76, 93,
trick, 6
TRIZ, 5, 56, 71, 93, 112, 115,
116, 134, 145
TV, 106
undergraduate students, 19,
84, 106
underlying principles, 15,
40, 42, 55, 57, 69, 71, 133
vehicles, 71
universal gravitation, 51
vacuum, 83
velocity, 71, 114
venture capitalists, 21
verification, 81
video, 26, 62, 106, 129, 131
vision, 6, 7, 8, 9, 12, 15, 16,
19, 20, 21, 23, 48, 51, 69,
95, 106, 131, 132, 133, 134
visual, 93, 125, 134
weight, 13, 16, 33
whiteboards, 126
whole person, 95
wonder, 51, 61
worked example effect, 43
working backwards, 87, 93,
writing block, 29
You-tube, 26