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Page 1
The CPM Educational Program Newsletter
Keynote Session: Dr. Jo Boaler
The Mindset Revolution:
Teaching Mathematics for a Growth Mindset
March 2015
Peggy Ratner, Teacher Reporter, Chula Vista, CA
Jo Boaler’s keynote session at the CPM National
Conference exposed those of us in attendance to the
elephant in the room: the fixed mindset that only
some kids are good at math and are born with the
ability to do math. Dr. Boaler debunked this myth
and provided strong evidence that the brain is actually quite flexible and changeable as long as we continue to get our synapses firing. In other words, we
need to embrace the growth mindset.
Why has the elephant been in the room for so
long? Media messages in movies and television have
played into the math ability myth by portraying math,
especially algebra, as some mysterious algorithm that
is only accessible to a small percentage of “smart” or
“nerdy” individuals. This fixed mindset is especially
damaging to girls and students of color. Parents often encourage a fixed mindset by either stating they
themselves were never good at math or by constantly
praising their children for being smart. A child who
considers herself smart may believe the opposite
once she encounters a task she cannot immediately
master. This may lead her to think that maybe she
is not so smart after all. Teachers also contribute to
fixed mindsets by how they grade and group students.
Ability grouping gives students on both sides of the
spectrum a fixed mindset. Teachers grading tasks as
either right or wrong also contribute to a fixed math
mind set.
A growth mindset, on the other hand, sees the
brain as flexible and changeable. Synapses need to
be fired to make deep connections. Boaler made the
analogy that synapses in our brain will wash away
like footprints in the sand unless we learn deeply. She
shared a study about drivers for the Black Cab company in London who must learn thousands of routes
and pass a rigorous exam to qualify as Black Cab driv-
ers. Brain scans show that the hippocampus in these
drivers grew as they studied deeply and prepared for
this exam.
The pedagogy in the United States has often made
mathematics a “performance” subject rather than
a “learning” subject. We tend to favor kids who are
procedurally fast rather than those who think slowly
and deeply about ideas. Math should not be about the
speed in which one can complete “drill and kill” problems because when we face stress, working memory
is blocked. It has been found that the lowest achievers
are those that use memorization strategies for formulas and procedures whereas the highest achievers
are those that think about big ideas and can make
connections between these ideas. Boaler shared results of a three-year New York study that compared
“tracked” versus “untracked” students. At the end of
the three years, the untracked students had the highest achievement rates.
It is the ideas that teachers and students hold
about themselves as math learners that can affect the
depth of their learning. We need to believe that we
can learn anything and every child can excel at math
with the right messages. Teachers need to provide
math tasks that are open ended, with multiple entry
points and approaches to problem solving. Student
discourse is vital and making mistakes needs to be
encouraged as that is when we get our synapses firing. They fire because the brain is challenged when a
mistake is made, resulting in brain growth. We need
to give our students the message: “When you make a
mistake in math, your brain grows.”
Providing constructive feedback when students
do make errors is extremely important. This single
sentence: “I am giving you this feedback because I
believe in you” positively changed the way students
achieved. Boaler even shared a video in the session of
(Continued on page 3)
Page 2
CPM Directors and Coordinators
Everyone listed below can be contacted via email by using
[email protected] The Directors will receive mail and
faxes sent to the CPM Business Office c/o Debbie Jacobs. We look
forward to hearing from you.
Elizabeth Coyner
(916) 391-3301
Karen Wootton
(443) 396-4010
Judy Kysh (SFSU)
(510) 526-1619
Tom Sallee (UCD)
(530) 574-0346
Administration: Debbie Jacobs
(209) 745-2055
fax (916) 226-2427
Research Coordinator: Leslie Dietiker (Boston Univ.)
(781) 281-4443
Curriculum Coordinator: Michael Kassarjian
(949) 422-3497
Professional Development Coordinator: Chris Mikles
(888) 808-4CPM
Assessment Coordinator: Karen Wootton
(410) 672-6474
Technology Coordinator: Carol Cho
(925) 229-5091
CPM Business Office
General transactions with the Business Office
[email protected]
(to send purchase orders)
[email protected]
(to check status of current orders)
[email protected]
(to submit timesheets)
[email protected]
(to submit AP invoices)
Debbie Jacobs
Administration and Accounts Payable
[email protected]
Workshop and Conference Registration
Anna Poehlmann
[email protected]
Jill George
Ordering, Accounts Receivable, Quotes, eBooks
[email protected]
General Information and database records
Lorrayne Graham
[email protected]
Phone: (209) 745-2055
Fax: (209) 251-7529
AK, AL, ID, LA, MT, OK, TN, TX, WY, New York City & Long
Island, International Sites
Chris Mikles
(888) 808-4CPM
fax (208) 777-8605
Central/Midwest/Southwest (AZ, IN, MI, NV, NM, OH, MO)
Lonnie Bellman
(559) 799-5866
Arkansas and Mississippi
Gerry Long
(901) 828-8221
Scott Blatnick
(719) 684-6943
Mike Long
(808) 224-4178
Cheryl Krafka
(402) 660-0160
Amy Rybaczuk
(630) 709-7109
Erin Schneider
(502) 641-4797
Mid-Atlantic (DC, DE, FL, GA, MD, NC, NJ, PA, SC, VA, WV)
Tim Scripko
(717) 434-8190
Lisa Fisher-Comfort
(651) 226-1729
New England (CT, MA, ME, NH, RI, Upstate NY, VT)
Barb West
(802) 362-3329
North Dakota, South Dakota
Sharon Rendon
(605) 431-0216
Oregon, Washington
Darrell Trussell
(503) 393-8024
Utah and Southern Idaho
Lisa Jasumback
(801) 884-2153
Bruce Brusoe
(608) 256-1207
Central Valley (Modesto to Bakersfield)
Karen Arth
(559) 999-0927
Sacramento/Chico/Sonoma/North Coast
Pat King
(530) 219-9458
Southern California
Glenda Wilkins
(909) 794-1567
San Francisco Bay Area
Gail Standiford
(707) 688-8559
Santa Barbara/Ventura/San Luis Obispo
Jerry Chiu
(805) 403-3225
Page 3
Keynote Session (from page 1)
her own daughter negatively reacting to a paragraph
at the end of each CPM chapter that is written in such
a way that might make a student see themselves as
less than smart. She asked for suggestions on how
this paragraph might be changed. These suggestions
were collected to be considered for revisions to the
CPM texts.
Boaler stressed that we need to provide tasks that
give students the “space to learn.” In a five week
summer course that Boaler conducted with Stanford
graduate students, underachieving 7th and 8th grade
students learned to use algebra as a problem solving
tool. Students were asked to think visually about a
task involving patterns. They were not asked what
the nth pattern would look like nor to count tiles
and make a T-table and then come up with an equation. Instead, students discussed about seven different ways that the pattern visually changed for them.
The ensuing discussion opened the eyes of students
about different ways to approach a problem. These
low achieving students remained engaged and discussed math for 40 minutes without interruption. By
changing the questioning from “what is the pattern”
to “how do you see the pattern,” deeper learning occurred.
Boaler ended her session by encouraging teachers
to watch the Stanford videos on mathematics learning
on as well as taking the student on-line class How To Learn Math for Students. These are powerful six to ten minute sessions for students ages ten and up. Students who do not believe
in themselves as capable in mathematics, come away
feeling empowered to do math after viewing these
videos. These videos are also helpful for teachers.
Session 2: Erica Warren, Incorporating the Growth
Mindset in Your Classroom
This session was a great and engaging follow up to
Dr. Jo Boaler’s keynote address. Erica shared several
strategies she has implemented to incorporate the
growth mindset in her classroom as well as had us
read research that shows the brain can be developed
like a muscle.
Erica’s handout and activities followed a lesson
plan she has used with her students to help them
adopt a growth mind set in all areas of their lives.
She had us out of our seats touching two walls, three
tables, and the floor to get us to find new partners to
interact with. We shared things we are currently not
good at but would like to improve, and then saw a
Sesame Street video with singer Janelle Monae called
“The Power of Yet.” This was followed by us restating
our area of improvement with the word “yet” so that
my initial statement: “I can’t do Zumba steps” (a fixed
mind set) was changed to a growth mind set statement of “I can’t do Zumba steps, yet.”
Students continue developing a growth mind set
in Erica’s classroom by watching a Khan Academy video: “You Can Learn Anything” and Erica also shared
various posters and slogans that teachers can have in
their classrooms to promote the growth mindset:
• Each wrong answer makes your brain stronger.
• Your brain is a muscle. Math class is your daily
• I’ve learned so much from my mistakes I’m
thinking of making a few more.
Ideally students will create their own slogans.
Session 12: Erica Warren, Bringing Technology
Into Your Classroom
This session stressed that technology is a tool, not
a learning outcome. Learning objectives are always
math based, but we also need to incorporate strategies for reading, writing, and 21st century skills.
Strategies/applications that Erica used included
one of her favorites, Poll Everywhere, in which students can answer a question posed by the teacher
upon entering the classroom by using their own
hand held devices to submit their answer. Students’
responses are displayed live in Keynote, PowerPoint
or on the web. The teacher can quickly check for understanding during class time as well as use it as an
exit slip.
Another app Erica had us download was a QR
reader. This was an exciting way to do math problems since students would take their device to one of
several QR cards posted around the classroom. Their
device would “read” the problem and students would
(Continued on page 11)
Page 4
Fine Tune your Student Study Teams
Beth Baker, Eureka, CA
It is easy to put students in teams of four, but it
can be hard to get math out of them.
My first training as a new, larval CPM teacher was
in 1991. I am pretty sure the formal team roles of
Facilitator, Task Manager, Resource Manager and Recorder/Reporter had not been invented yet. Or maybe
I was so involved implementing all the other aspects
of the training that I overlooked it. For many years
I would half-heartedly start team roles and then give
them up in favor of a more general set of expectations
that, in my defense, actually did result in good team
work. I really learned about the team roles when I
trained to be a teacher leader, and diligently included
their use in my trainings. I still did not use them myself though. I stayed a caterpillar for many seasons.
In the summer of 2014, CPM hosted a Teaching
Redesign Corps (TRC) and my team chose team roles
as our area of study. My metamorphosis has yielded
the best student teamwork results of my teaching experience. Finally, butterfly mode has been achieved!
This year for the first time my students have been
trained with fidelity in the team roles and my teams
are soaring.
This brings us to the do we get
optimal learning out of our student study teams?
As the grade levels increase, so does the likely gap
between most and least competent ability levels in
our students. The following list is a compilation of
what I have developed to help all students engage
in the team learning structure. I learned the techniques listed below as a participant in CPM’s TRC and
through CPM’s coaching system.
My teaching demographic is 150 eighth graders,
with 65% free and reduced lunch.
Nothing is effective for 100% of students, but the
following set of guidelines is effective for 95% of my
students. For the other 5% I modify as much as I can,
not always successfully. Sometimes I use an isolated
“Safety Zone” desk and an alternative or a shortened
assignment. When possible I have them work with an
aide or tutor. The goal is always to re-integrate the
5% to teams as soon as we both think it is feasible.
Norms. Set the class norms for optimal respect
and responsibility within teams, and reward the desired behavior when you see it. Schools that have a
campus-wide norm system can tap into that for math
class. If not, the TEAMS acronym found in the Teacher’s Edition under Team Support is a good place to
Motivation. See any list of “Top Ten” skills required of college graduates. The internet is full of
them and everyone lists the importance of teams,
even in a non-math context. When they see the large
poster* I have in my room listing all the skills students need to acquire by the time they are adults, my
students and parents believe that team work in math
class is a great idea.
Appropriate use of technology. Do not let fact
fluency be a problem. Remove any stigma from slow
fact recall by making sure everyone has and can use a
calculator for even the simplest computations. Make
graphing sites like readily available. The
CCSSM calls for appropriate application of technology and by middle school students who are not fast in
fact fluency can still fully participate in the lessons if
they do not have to struggle with arithmetic as well
as grappling with new concepts.
Leadership. Emphasize the need for leadership in
effective groups and point out that the most mathematically proficient or the speediest student is not
necessarily the person with the best leadership skills.
Students and parents both appreciate the opportunity for students to contribute more than just their
math skills to the math learning experience.
Student Study Team Roles. All CPM texts start
with the roles. Take the time for students to learn
them and use them all year. Train the teams diligently
on what each role does. A study team role provides a
starting place for each team member so the dominant
students are less likely to run the whole discussion,
and the shyer or more reluctant students have suggestions of how to begin. Team roles contribute both
to classroom management and to the development
of math content. Once you have invested the time
to make team roles second-nature, your well-trained
classes can run at an impressive level of autonomy.
(Continued on page 5)
Page 5
How I Became a Better Teacher at the CPM Conference
Leah Gaines, Teacher Reporter, Westerville, OH
When first arriving at the CPM conference I was
excited to have some time to collaborate with other
teachers and learn something new; little did I know it
would be so much more than that and my experience
at the conference has already had a positive impact on
me professionally.
Beginning with Jo Boaler, the keynote speaker, I
was instantly inspired—she is so passionate about her
work and research. She specifically spoke to issues
that have been brought up on numerous occasions
by our district’s parents and students as we have transitioned to CPM: ability grouping, students thinking
they are “not good at math,” and the research behind
the benefits of a growth mindset. Everything she
shared with us made me a bigger believer in the fact
that we are doing what is best for students and will
continue to see huge growth in their learning.
Next it was on to the individual sessions. The
amount of information I soaked up during these
sessions was astounding. I was amazed by the scope
of what can be done with Desmos, I heard of fellow
teachers’ experience with a standards-based grading
Student Study Teams (from page 4)
Accountability. Use a team points sheet*, participation quiz*, or tap into a school wide reward system
if you have one. Make it explicit that following the
team roles and doing math within the team is why
teams are together, and that the grade book will reflect effective teamwork. Distractible or overly social
teams can be pulled apart into pairs to enforce the
message that we expect teams to be effective.
Positive Feedback. Make sure to praise specific
examples of exemplary work during circulation time.
Circle great work with a highlighter to bring it to
the attention of the team. Do a participation quiz*.
Give teams feedback based on your observation of the
whole class. Students are more receptive when they
realize how many times the teacher notices that the
team is engaged in the work.
Easy access. Make sure team tasks have a “low
floor” or easy access point. If they do not, create a
system, I was introduced to tech tools I can incorporate into my everyday lessons, I learned how to grade
with a rubric, and how to make my grading practices
fair and equitable. I could go on and on about the
invaluable learning that took place. But what really
solidified it for me was the chance to discuss these
topics with my peers.
For the entirety of the two days I was constantly
collaborating with teachers from all over America,
from schools of all types and backgrounds. In true
CPM fashion, this is where the true learning happened. I had the chance to internalize all of the information I had heard, was able to learn what others had
learned in different sessions, and was able to compare
notes and come away with so many ideas for my own
classroom and school.
For me, being a teacher is summed up perfectly
in the saying “you can’t see the forest for the trees.”
As any teacher knows, the day-to-day grind of planning, grading, emails, and meetings makes it hard to
take time out to focus on your teaching practice as a
whole. I know for me personally, taking time to come
to the CPM conference helped me see the forest and
remember why I am a teacher.
resource page or other aide that scaffolds the beginning of the task. As you circulate at the beginning
of a lesson, check in with students and make sure all
students are able to grasp the problem. Students of
all ability levels will get off to a stronger start if the
beginning of the task is easy to understand and has a
low first step. Once started, most students can take
the next steps.
For CPM teachers, student study teams are simultaneously the gold standard of learning and the
most challenging aspect of our day. As I embark on
my 26th year of teaching and my first year of TRC I
am re-examining how to get the best learning from
my student study teams. The above list has become
my touchstone for improving student learning. I am
happy to report that this year’s crop of caterpillars is
developing into some really impressive butterflies!
*The sample forms mentioned can be seen at my
website, under the “For Educators” tab.
Page 6
Staying Afloat in the Storm of Technology
Blendspace is a possible life raft. SAMR Model is the tugboat.
Sara Good, Parma, OH
Just try it and see where it takes me.
That is my new motto for deciding which new
technology tools to use in my practice. I used to
work under the assumption that if I researched and
planned, I could be an expert in the latest information portal, from email to Moodle to the best apps to
try. I preferred positioning myself ahead of the professional curve, feeling confident with sharing ideas
in formal settings. Nowadays, I have come to realize that there is and never was one single curve on
which to position myself. It is more like a turbulent
sea of swells and sometimes crashing waves of ideas
on which we are challenged to stay afloat. And these
waves will not wait for me to organize a formal setting for rolling out ideas to teachers. So on CPM Day
7 training day, I just tried something and let the participants help me consider its potential.
SAMR Model steers me in the right direction.
I am not the type to sail deep, unchartered waters teeming with man-eating sharks! I prefer to
know what will keep me buoyant, where I am headed,
and how to steer
myself back on
course if I find
The SAMR Model, created by Dr.
Ruben Puentedura, helps me
with all of this.
It provides me
the framework
from which to reflect on my improved use of technology.
My goal is to move from Enhancement to Transformation practices; that is, to use technology in
ways that not simply replace older technology, such
as an overhead projector or paper and pencil, but to
create impactful learning opportunities for students
that were not possible before its use. I am not there
yet, but at least I have an idea of where I am headed.
It is all word of mouth.
Like most anything, I learn the best ideas from
trusted friends and colleagues. When I heard of Blendspace from colleague and CPM Teacher Leader Jen McCalla, I tried it out to see where it could take me.
Blendspace is a free collaboration platform created with teachers in mind. It allows teachers to quickly organize lessons that include mixed media from
the most popular sources such as YouTube, Flickr,
Educreations and Google Drive. Teachers can create
classes, assign lessons to classes, and include simple
formative quizzes. Students can collaborate on ideas
and even rate the lesson.
If Blendspace were a life raft amidst a sea of changing information, it is worth grabbing ahold of its line.
Blendspace provides an efficient way to organize
and display content. How the Blendspace lesson is
set up and the type of content displayed determines
the level of its effective use according to the SAMR
I decided to organize content with Blendspace
for CC2 Day 7 Training instead of using a traditional
PowerPoint. I had only used Blendspace a handful
of times with my own district teachers, so I was by
no means an expert (a concept I believe no longer
exists). In my stubborn pursuit to “just try it and
see,” I learned something new from the trusted CC2
colleagues that day.
I moved from Substitution to Augmentation.
Blendspace allows for the simplest implementation. I originally intended to use it as a slideshow,
such as PowerPoint, to keep me focused on the day’s
agenda. I typed up simple content in each Blendspace tile, like a PowerPoint slide, and was able to
easily change the order. A novel tool, but nothing
novel about its use. In the SAMR model, this is Substitution at its best.
I then asked Reporter/Recorders to join me in a
Huddle with their devices. I made them collaborators
(Continued on page 8)
Page 7
Six Degrees of Separation – CPM Style
Mark Cote’, CPM Project Manager
Every so often the phone rings and, instead of an
insurance salesperson or a scammer calling to transfer a large sum of money into your bank account
(just send him the pin and the account number), it is
someone you actually want to talk to. I received such
a call last fall.
“Hi Uncle Mark! It’s Angelina,” said my niece
with a very upbeat and joyful tone of voice.
“Hi Angelina! Wonderful to hear from you. How
are you doing?” I replied.
“I’m fine. You
know what? They
handed out our new
books in math class
today, and your
name is in it! I told
my teacher that
you’re my uncle and
she said you should
come visit our class
as a guest speaker!”
truly excited about
this occurrence, but
you could also hear
the adolescent voice
of doubt in her head
wondering ‘Uh oh. Is
this going to be embarrassing?’
“Wow, what a coincidence!” I replied. “And how
nice of your teacher to invite me.” Having worked
with adolescents for the better part of thirty years, I
added, “We’ll do something fun and I promise not to
be embarrassing.”
This delightful conversation happened because
Angelina is currently a student at Herman Intermediate School in San Jose, CA. The Oak Grove School
District is piloting the Core Connections Middle
Grades Program. By happenstance, I would soon be
traveling from Washington state to San Jose for a
family celebration.
After exchanging several emails in December with
Barbara Maguire, Angelina’s energetic and gracious
teacher at Herman, and Principal Laura Meusel, a visitation date was set. We continued to talk during the
next several weeks about course objectives, class progress, and possible lesson ideas. I was also contacted
by Shannon Anido-Bui, the Oak Grove Educational
Services Coordinator about the possibility of visiting
other classes and meeting with several teachers from
the other middle schools at the end of the teaching
day. This sounded like a wonderful opportunity to
offer additional support. Shannon gave rave reviews
for the initial training provided by Gail Standiford,
CPM Regional Coordinator for the San
Francisco Bay Area
and Teacher Leaders
Gabrielle Baumgartner and Jan CarlsonWilliams.
What a superb
visit to Herman Intermediate! Barbara
and I enjoyed the
opportunity to team
teach a lesson that
helped the students
understand the connection
relationships, lines, and
linear equations. We also employed several study
team strategies to promote discussions and help consolidate the learning. The final bell of the day came
very quickly. After bus duty, Barbara and I debriefed
as teachers from the other intermediate schools in
the district arrived. Over the next hour we had a
stimulating discussion about grouping, pacing, and a
number of other topics. As I packed up and prepared
to leave, Shannon remarked, “Thank you so much for
your time! I have loved learning about CPM during
this pilot year!”
How did I get to help work on the textbook? I
have been fortunate to participate in numerous
(Continued on page 10)
Page 8
Bridging Practices in Argumentation
Jocelyn Dunnack, Mansfield Middle School, Storrs, CT
CPM problems are ripe for teachers to promote
the Standards for Mathematical Practice (SMPs), but
as I have been repeatedly reminded this year, SMPs
(like a lot of other things) take time, effort, and practice. I have been part of a research collaboration called
Bridging Practices among Connecticut Mathematics
Educators (BPCME), which brought together UConn
researchers, graduate students, and teachers from
urban, suburban and rural districts to learn about
the third SMP: Students will construct viable arguments and critique the reasoning of others. We have
developed resources to support teachers and students
in the process of mathematical argumentation. Here
are a few things I have learned:
1. Arguments are not describing your steps or
showing your work. Arguments consist of
claims, warrants, and evidence. You have to
state a claim, and provide enough explicit
evidence to prove you are right. It is more
like those fun problems that have multiple
strategies or solutions, the ones where students have to prove their solution was actually mathematically sound. Argument is about
why you are right, mathematically speaking.
SAMR Model (from page 6)
of the Blendspace lesson so that they could edit and
add content. Each team was able to take and upload
pictures of their STTS concept map, write a description for it and even attempt to make comments on
each other’s maps. Instead of a Gallery Walk, Blendspace allowed for a Bansho analysis in which all ideas
are accepted, analyzed and stored for future reflection.
If CPM were not such a transformative, interactive program compared to traditional classrooms, I
might be able to rate these uses at the Modification
I admit that no Modification or Redefinition took
place on Day 7, but we certainly discussed potential
• Ask teams to work Core problems and create
Educreations videos of their solutions. Post
2. At first, students needed to learn how to provide enough evidence. Then, they had to learn
how to explain the reasoning as to why their
evidence even mattered. That was much harder to do, and much more important.
3. The CPM teachers in BPCME had no trouble
implementing argumentation (and seeing
growth in our students’ work). Great tasks
were already part of our lessons! However, we
did have to devote extra time for these tasks.
By digging into a good argument question
and skipping a few of the other questions in
the lesson, we found deeper understanding
than we previously got. It was definitely worth
the investment and the sacrifice.
Our work will be compiled and submitted for publication approval by NCTM this summer. Even though
I had already been doing argument tasks that existed
in CPM, it was very powerful for me to see what happened when I made a conscious choice to explicitly
teach a math practice, rather than just knowing it
was embedded. Guess what? My kids could not really
do it at first, but now they can! I am sure you are not
videos to Blendspace and require classmates
to post comments and questions.
• Encourage students to find other online content or create videos to add to Blendspace lessons that will help classmates construct understanding for the lesson’s learning targets.
• Create Blendspace lessons for Learning Logs
submissions and Chapter Closures.
• Share Blendspace lessons with parents to improve communication as well as their content
What ideas do you have?
Add them to the Blendspace! Create a free account, join the class with code uepk and add your
comments to the first tile. (The last tile takes you to
Padlet…another technology life raft.) Just try it and
see where it takes you!
Page 9
Find: The Problem
Karen Wootton, Director of Assessment
My new mission, along with changing the perception of mathematics and math teaching in the U.S.
within my lifetime, is to eradicate the use of the word
“find” from mathematics. This mission formulated
slowly; in fact, I spent the first 20 years of my career
using the term freely. “Find x” was definitely part of
my lexicon as was “Find the width,” “Find the area,”
“Find the distance”. I used it all the time.
Maybe it was the well-circulated comic that had
me questioning my practice and pushed me towards
this mission. At first
I just made it a personal goal to not
use the “F” word in
math problems that
I wrote, but now
I have formulated
my opinion on why
I must rid the math
world of “find.”
Some people might
dismiss the comic
as just the response
of a smart aleck student, and not worthy of extra clarification. I strongly
disagree with that
and will now explain
why we must be more clear with our language.
This is a bigger problem than thwarting smart alecks. Let’s remind ourselves of one of our Standards
of Mathematical Practice: attend to precision. Is it really precise to say “Find x”? What does that ask the
student to do? In particular, what does that tell the
struggling student to do?
The definition of “find” is “to discover or perceive
by chance.” Is that how you want your students to
think that is how we do math? Do you want them
to think of solving math problems as random, or by
chance? For many students, and in particular, struggling students, most of their confusion stems from
not seeing the connections, and think that most of
math is random. To many struggling students, math
is for the lucky who are good guessers of what to do
next, or for those people with the elusive math gene
that enabled them to be “math people.”
Let us explicitly ask students what it is we want or
expect. Rather than “Find the intercepts” which implies that there is some way to just have them appear
before you, change this to “What are the intercepts?”
Asking the question at least implies there is something for the reader to do rather than rely on chance.
Better yet, “Calculate the intercepts” or “Determine
the intercepts.” If
we ask “Find the intercepts” we must
give full credit to
the student that
draws arrows pointing to the intercepts
on the graph because the student
has accomplished
exactly what was
asked. But, if that
is what you want
students to do, why
not say “Point to the
intercepts on the
graph”? If we expect
our students to attend to precision,
we must model
what that looks like. Even if we are asking something
that might have an element of luck, we can do better
than “find.” “Find a strategy” can be replaced with
“Develop a strategy” or “Create a strategy” which implies there could be creative work, but work none the
So here is your challenge: whenever you are writing a math problem and are about to type the “F”
word, reconsider. Can you turn a find-statement into
a more precise question? Can you write the question
as precisely as possible, to be sure your expectations
are clear? Let us stop the perception that math is
done by chance.
Page 10
Chris’s Corner
Chris Mikles, Director of Teacher Education
I am thrilled to report that the 2015 CPM National Conference was a success, bringing 340 attendees
together for 51 sessions. We had far more interest
than we had space, so please make your plans early
for next year’s conference that will be held again in
San Francisco on Feb 26-27, 2016.
It took a lot of great people to enable us to successfully pull off this conference. I want to thank all
of our speakers. Many of them offered to repeat their
session so that we could open up the numbers of attendees. We had 51 sessions, with 45 speakers and cospeakers. And, I want to individually thank our keynote speaker, Jo Boaler for her thought provoking,
inspiring talk.
We had a lot of great support during the conference. Thank you to the Regional Coordinators who
served as Proctors, worked as AV techs, answered
questions, handled check-in at the registration tables,
set up the session rooms, stuffed the swag bags, and
mostly just pitched in and did whatever was needed.
There was a lot of work leading up to the conference, and I’d like to point out many who helped set
us up for success. Thanks also to Elizabeth Coyner
who took care of all the logistics. She took care of
details none of us would think of. Thanks to Karen
Wootton who was my sounding board for everything.
She read all the submissions and grants and helped
to make difficult choices. She, Elizabeth and Matt at
Six Degrees of Separation (from page 7)
outstanding professional development opportunities with CPM. One of the very best was assisting in
the creation of the Connections Series and the Core
Connections Series as a contributing author on several writing teams. For 26 years, CPM has relied on
scores of classroom teachers just like you and me to
make the textbooks. After responding to a request
for writers and submitting several sample problems, I
was asked by Senior Managing Editor Leslie Dietiker
to join the team. A year of hard work lead to one of
TC put together the program booklet to make it look
very professional. Thanks to Bob Petersen for getting all the supplies and handouts for the conference.
Thanks to Jill George, Lorrayne Graham, and Susan
Hoffmier for all their work on registration, signs, set
up and check in. Karla Chandler is a name most of
you know as the person who took care of registration
and the wait list. Anna Poehlman took care of the
hotel rooms and some of the flights. Thanks to Danny
Orasco for all his help. Thank you to our sponsors for
supporting us. Thank you to those people I forgot to
I especially want to thank Mark Cote, the cochairperson of this conference. He was definitely my
right hand man. And among many other contributions, he got our sponsors and the swag bag, with all
the goodies that went inside.
I thank everyone again for your interest in this
conference, whether or not you were able to attend.
Without your desire to attend, the conference would
have never happened. As you can see, this conference
was a team effort, and all of you are a part of the CPM
Note: The conference url, http://conf2015.cpm.
org/, will remain active where you can download
speaker handouts. If you did not fill out your feedback forms from the program, you can still submit
feedback at this url. We would love to hear your suggestions for next year’s conference!
the proudest moments in my professional life, holding a copy of the finished text while reflecting on the
dedication of dozens of CPM teachers who committed
an enormous number of hours to the project. And
now, our manual for learning mathematics was in the
hands of my niece, one of ten million students who
have participated in a CPM course.
I am fairly certain that Angelina was not too embarrassed to have her uncle visit school because she
was willing to be in the picture. Here we are, two
members of the CPM family, at zero degrees of separation!
Page 11
News Bytes
Core Connections Courses are available in Spanish!
In order to make mathematics more accessible for
more students and their families a Spanish translation of the CPM Core Connections series is available.
The Spanish versions are identical to the English versions and can be obtained as two-volume softbound
set with an accompanying eBook. The complete
middle school series, Core Connections Courses 1-3
is available now. The translating of the high school
curriculum is currently in production. The first volume of all six Core Connections courses, Core Connections Algebra, Core Connections Geometry, Core
Connections Algebra 2, Core Connections Integrated
I, Core Connections Integrated II, and Core Connections Integrated III, will be available in July 2015.
Volume Two will follow by the end of the year. The
Parent Guides with Extra Practice in Spanish will be
available as downloads on our website. The sample
chapter tests from the assessment materials for these
courses will also be made available in Spanish. Thank
you for making this request. CPM is proud to be able
to offer this service.
formation about their learning and understanding
as well as give information to the teacher. Typically
these lessons provide a problem difficult enough for
students to grapple with and discuss with teammates.
It should be relatively easy to understand (low entry
level) but allow students to go to great heights in
what they can do with it (high ceiling.) You can see
samples of FALs at the webpage for the Mathematics Assessment Project,
materials/lessons.php. FALs could provide a different
approach to a topic of mathematics from what students might have already seen, or allow students to
use what they know in a new context to deepen their
If you enjoy writing lessons and believe you would
be able to produce quality lessons, please apply by filling in the form at
Note: you will need to submit a sample of a formative assessment lesson that you created yourself.
The deadline for applying and submitting is April 10,
2015. For more information contact Karen Wootton,
Assessment Director, at [email protected]
Formative Assessment Lesson Writing Project
Summer Camp for New Teachers
CPM is forming a team to meet for one week, July
20 - 24, 2015 to write Formative Assessment Lessons.
The location is yet to be determined.
Check the CPM website for information about a
possible camp this summer 2015 for teachers who
are new to the teaching profession. We hope to have
more information posted by April 1, 2015.
An FAL is designed to give students real-time in-
Keynote Session (from page 3)
solve this one problem with a partner, and once solved
would go to another QR card posted in the classroom
and repeat the process. This seemed to be a very engaging way to get students to work on word problems
by only having to tackle one problem at a time and
having the opportunity to get out of their seats to
“read” their next problem.
Many other apps along with helpful directions
and tips were included in the thorough handout Erica provided. Included were step by step directions and
links for using the CPM eTools, Explain Everything,
Google Drive/Google Docs and Tiny URL.
A Fortune Cookie activity was incorporated into
the session in which participants could read slips of
papers with technology fears and concerns listed on
them as well as helpful tips. Erica encouraged us to
try just one or two new technology applications and
incorporate them daily until we and our students are
comfortable using them. She also reminded us to always have a back up plan if we plan to use technology for the times that there are “glitches” with the
Note: The conference url, http://conf2015.cpm.
org/, will remain active; you can download speaker’s
handouts such as Erica Warren’s.
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In this issue...
Recap of CPM’s National
Session Highlights
STTS, SAMR Model and more
Future projects
The assessment site has been updated. Visit the new
assessment site at the same url,
Your tests are now editable online and can be downloaded as a pdf, Word, or Open Office documents. At
the links below you can get support for the new features at the assessment site. Also, watch for a new
CPM website coming soon!
Is the number for which I pine
So if you hear me loudly sigh
Don’t give me cake; just give me PI!
How did you celebrate Pi Day?