Maths phobia and how to beat it From the Skills Team, University of Hull This guide aims to discuss the problems people have with learning and using mathematics, and explain strategies to counteract them. There are often different ways of doing things in Mathematics and the methods suggested in the worksheets may not be the ones you were taught. If you are successful and happy with the methods you use it may not be necessary for you to change them. If you have problems or need help in any part of the work then there are a number of ways you can get help. For students at the University of Hull Ask your lecturers. You can contact a Mathematics Tutor from the Skills Team on the email shown below. Access more Maths Skills Guides and resources at the website below. The fear of maths Many people have a deep-seated fear of mathematics, and maths tutors see a lot of scared students. There is not a ‘type’ of student that has a problem with maths; it could be anyone. They could be college leavers or mature students, first years or PhD students, local students or international students. There seems to me to be no discernible pattern to the students with this problem. The fear of maths may not seem as scary as a fear of snakes or tarantulas; but think about it - when was the last time you encountered a snake in the checkout queue at the supermarket, on your phone bill, or in your homework (biologists excepted from the latter). People who fear maths have to deal with that fear on a daily basis. Clearly it can be a major problem, and can seriously affect people’s lives. Maths phobia affects people’s lives by making them: lose confidence in themselves and in their academic abilities trust blindly any bills they receive, because they daren’t question the figures shy away from helping their kids with their homework avoid courses in case they contain maths leave courses when they encounter the maths element run up credit card bills as they can’t keep track of how much they’ve spent Web: www.hull.ac.uk/skills Email: [email protected] The main problem seems to be understanding that, for the most part, it is fear that stops people, and not a lack of mathematical skills. There are many reasons why people develop a fear of maths. These range from bad school experiences, to suddenly having to use maths for the first time in years. Sadly, as the world becomes more automated, the everyday use of maths is decreasing. Now that you can pay for goods and services on your credit or debit card, it is no longer as important to add up the cost of your shopping as you go around the supermarket. You have some idea of the total cost - whether you’ve gone mad or been very frugal - but probably couldn’t estimate the cost of your trolley load to the nearest £5. In this way, our basic arithmetical skills, the very core of maths, are largely ignored, and we lose our confidence in using them. This lack of confidence leads to a general lack of confidence in all maths, and may continue on into maths phobia. My job is to help people who are struggling with the maths on their course or who want to improve their skills in mathematics. However, the majority of the people that I see have no real problem with the mathematics involved, but instead believe that what they are doing is wrong because they doubt their ability. They think they may have answered a question correctly, but require a second opinion to boost their confidence. Maths isn’t like riding a bike, where you never forget how to do it. It is more like a sport. You may be the fastest sprinter in the county, but if you don’t run for five years, you will slow down and find it harder. The only way to get faster is to practice. In the following sections various causes of maths phobia will be identified possible solutions discussed. You may find that your problem stems from more than one, or several of these causes. Even if you think that an issue doesn’t affect you, look at the solutions anyway, as they may still help you. Possible cause 1: speed of delivery of university material Think back to when you were at school. Whenever you tackled a new mathematical concept, it was introduced slowly with lots of examples. Sometimes you did exercises that led you to the result, so you discovered rules and theorems for yourself. By learning topics in this way, you knew where the mathematics had come from, what it was used for and how to use it. Because you had done so many examples, you felt confident with it, and using the method you had been taught became second nature. You may even have had pictures and rhymes to help you remember formulae and methods. Most students find the jump to university mathematics difficult. No longer is there a great deal of one-to-one contact with your teacher. Because of the sheer number of students in the lecture theatre, you may feel too scared to ask questions in case you look foolish in front of the other students. And then, just as you begin to understand the topic, the lecturer moves on to a different one, and you are lost. At this point many students may panic, or decide that they will not be able to complete their course successfully. 2 Possible solutions The thing to realise is that at university, there is less time to go over topics in detail. This means that you are learning mathematics in a different way. Once you get used to this change, you will find that the maths is not as hard as you first thought. There are many ways to tackle this problem: 1. Read the recommended texts These will often go through the work in similar detail to that which you experienced at school. They will also explain where this branch of maths has come from, and possibly, its uses. It is always best to look at more than one textbook as different explanations work best for different people. Note - If possible try to stick to texts that use the same notation as that used by your lecturer. 2. Ask questions You may not feel confident enough to ask a question during a lecture, so ask questions in tutorials instead. The aim of tutorials is to reinforce the information given to you in lectures, so your tutor will expect to be asked questions. Remember, if you have put the work in and still don’t understand a concept - ‘there is no such thing as a stupid question’. 3. Ask your friends Very few people on your course will have the same mathematical background, so it is likely that someone you know may have seen the topic before, or learned something similar. Sometimes all it needs is a couple of minutes to ‘get your head round’ a difficult topic. 4. Work on exercises with friends You and your friends may have understood different parts of the topic, so you can help them, and they can help you. Having someone nearby answering the same question can also provide a confidence boost as you can check if you both have the same answer. 5. Use tutorials and problem sheets wisely Whenever you have a problem sheet, attempt every question. You may surprise yourself by getting through a question you were sure you couldn’t answer. Any attempt, no matter how short, at a question will provide lecturers and tutors with an idea of what you know, and where you are not sure. Tutorials are normally taken by either a lecturer or a postgraduate student, all of whom will be able to answer any questions you have. As tutorial groups tend to be smaller than lecture groups, this makes it easier to ask your questions. If you are provided with a solution sheet, read it. It will show you how best to answer all the questions that were set the week before and show you how the answers should be set out. Problem sheets and answer sheets make valuable revision materials. 6. Rewrite your notes Chances are you’ll have made notes of everything your lecturer said and written them in the exact ways he/she said and wrote them. Is there another way of saying what they said, but which makes more sense to you? If so, make alternative notes to refer to when doing exercises. 7. Repetition When you understand a concept or method - use it. Make up some examples that are similar to those encountered in lectures or exercises and try to solve them. You could also swap these examples with colleagues to get even more practice. It is worth noting 3 that examples given in lectures are often very similar to those used in the exam, so the more practice you have of these, the better. 8. Read between the lines Often in maths lectures (whatever your course), the lecturer will skip lines in their working in order to save time. If you just look at the lines of working on the page, it may not be clear how the final answer was reached. In these cases it is good practice to work through these examples yourself and convince yourself of where all these lines of working came from. In time you will find that you can produce ‘shortened workings out’ yourself. 9. Organise a deputation If you find that all the previous ideas have not sorted out your problem, and there are a few of you with the same problem, go to see your lecturer. Your lecturer wants their students to pass their course and if there is anything which is preventing students from doing so they will want to know about it. If it is a small problem, they may be able to sort it out for you then and there, if it is a larger problem you may be able to arrange for a help session on the topic. Remember, lecturers are very busy people, so the sooner you let them know about the problem the better. Possible cause 2: Information overload Too much information on a page can create a knee-jerk ‘I can’t do this’ reaction, especially with algebra exercises. Mathematics involves a lot of repetition to get the facts cemented in place, so exercises tend to be quite lengthy. Here is an example taken from Algebra 1, one of the Skills team’s mathematics help leaflets: Simplify where possible. If it is not possible say so 1. 4s 2s 10s 2 8s 3. 3x 2 y 4 x 3 y 8 z x 6 y 5. xy 7 xy 3x 5 y 2 xy 2. 2 p 2 1 p 3 p p 2 2 4. 2abcd 3acbd 12dcba 6. 3x 2 2 x x 2 x 4 On first glance, this exercise looks quite complicated. This is most likely because, when you first see it; your brain tries to read it like a book. Possible Solutions 1. Self-talk Try to convince yourself of the following (true) statement: Yes there is an awful lot of algebra in the box, but it is not one huge impossible question. There are 6 questions, which together look bad, but I only need to do one bit at a time. I will imagine that the other questions are not there and focus on the question I am answering. 2. Remove the other questions from sight If you are working on question 1, write the question out on your answer sheet, then put the exercise out of sight. If you are faced with a sheet of paper that is blank except for one question, you are less likely to be panicked by it. Removing the whole exercise from your line of vision will help you to concentrate on the question at hand. 4 3. Revise If you have tried the 2 options above and the question is still bothering you, then it is time to look back over the topic and ensure that you understand it fully before proceeding. Possible cause 3: reliance on technology There are many labour-saving devices around that can do your maths for you. There are calculators than can manipulate algebra, draw graphs and perform calculus. There are computer packages that do similar things. We rely very heavily on technology. Over time, the brain realises that we don’t need to store all the number facts any more and we find it hard to work without a calculator. A lot of mature students face mathematical problems in their first year at university, purely because they haven’t needed to work anything out in their head or on paper for a long time due to the universal dependence on calculators. Calculators are wondrous little machines that you put sums into and always get the right answer, and so are ideal for those who are not confident with their mathematics. Why should I have to know the theory behind the formulae when my calculator can solve equations and integrate functions? Why you shouldn’t rely on a calculator for exams 1. Your batteries might run out during the exam and you’ll be stuck. 2. Calculators that can manipulate algebra and perform calculus will certainly not be allowed in exams where they can be used instead of the methods taught in lectures. 3. Most exams give method marks for answers, which are very valuable, especially if your answer is wrong. If you use a calculator you cannot get any method marks as you’ll only produce an answer. 4. Calculators do give the right answer if they are given the right instructions in the right order. If you don’t understand the theory, you won’t be able to produce an estimate for the answer, and so won’t know if your answer is sensible or if you have pressed the wrong button. 5. Sometimes it is not clear which part of a function is done first, such as for . If you were unaware of how this function works, you would be unable to put this into your calculator correctly. Possible Solution Calculators are no replacement for learning mathematical methods and theories. The best solution to calculator reliance problems is to learn how to estimate. You can use calculators to produce your final answer to a question, but before you can do this, you need an estimate for the answer. If you have not produced an estimate, you will have no way of knowing if your answer is sensible. Ask yourself, are any of the numbers in the question close to numbers that are easy to work with? e.g. if you were working out , you could estimate that the answer will be around that of (the real answer is 1323). Care should be taken here though. If you round both numbers up, your estimate will definitely be larger than the true answer, whereas if they were both rounded down, you can expect the true answer to be larger than your estimate. 5 In order to make estimates, you need to know the theory. In lectures and problem sheets you may find that certain types of calculations produce certain values, such as probabilities always being between 0 and 1 inclusive. You can use this information to check your answers. Often the question will give you a clue as to whether your answer is sensible. If you are asked for a length or distance, you should expect a positive answer, as you cannot have a negative distance. If the question involves things like a person’s age, it is clear that the answer will be positive and, at most, 3 figures. If you are looking for an average from a list or table of data, your average will always be within the range of that data e.g. if your data values went from 3 to 27, an average of 30 would be impossible. Remember: it is very easy to press the right buttons on a calculator, but it is equally easy to press the wrong ones. Possible cause 4: mathematical notation When you were at school, new formulae or equations will have been spelled out explicitly in words when you first met them: i.e. Mean = Sum of all values number of values Once you get to university it is assumed that you no longer need to be gently introduced to new formulae and you can meet things like: 1 x n n x i 1 Now although this looks very different from the first definition, they both say the same thing. In the second case, standard mathematical notation has been used. This notation is used because it allows the equation to be presented unambiguously and in as short a form as possible. Further work on statistics will continue to use the same notation, thus making it easier in the end. The problem with this change in notation is that, for many, what was once a familiar concept is now unrecognisable. Possible Solution The temptation when faced with complicated looking mathematics is to immediately think ‘I can’t do that’. This is not an easy habit to break; in fact I sometimes get these feelings myself and I’m a maths specialist. Examine the question. Look at the equation and ask yourself some questions: 6 Have I seen any of this notation before? Were any of the letters in the equation defined earlier in the lecture/week/course? Do any of the letters have a logical connection with the text above it, such as P occurring when you have been looking at numbers of People? If you still aren’t sure, you need to ask someone. It is possible that you missed a verbal explanation in the lecture, or missed a line of notes. Remember, if your course is modular, all the maths you do will normally be taken one topic at a time, giving you a fair idea of what your equation might mean. You may find it helps you, once you’ve ‘translated’ the equation so that you know what it means, to write it out in your own words. However, still learn the original form of the equation as it will be the form that you will be expected to produce in the exam, and future courses may assume that you know it. Possible cause 5: maths is something only geniuses can do In this country maths has a similar image to that of cabbages and sprouts, in that you are not supposed to like it and if you do, people think you are strange. We are taught directly or indirectly by relatives and the media that maths is hard, maths is pointless, no-one can do maths well, no-one likes maths. We get this kind of information from an early age and it is constantly reinforced. Because of all this, maths has been put on a pedestal as ‘very hard’, if you can’t do it, it’s accepted, it’s the norm. If you can, you are revered as some kind of genius. This problem is probably the most common. You may have come across a couple of problem topics and now you are convinced you know nothing at all about anything. Possible Solutions 1. Ground maths in reality, your reality Higher mathematics can be very difficult to understand or even visualise, but the majority of school and college level maths can be contextualised in every day life. For example, one vital part of mathematics is arithmetic. Without arithmetic, formulae and equations could not be solved and so a lot of maths would not exist. However, arithmetic is simply the four main operations, add, subtract, multiply and divide. These are all operations that can be practised as you do the shopping, for instance. 2. Find the root of the problem If you find you are having problems with, say, equations involving fractions, go back a step. Think about whether it is the fractions holding you back or solving equations in general. Once you know what the problem is you can revert back to earlier work on the topic and work on that until it gets easier. Maths is a subject which builds upon itself, much like a wall, so it is vital that you are happy with one level, before you try to lay the next set of bricks. 7 3. It’s never too late If your expectation of failing maths at school caused you to fail, it is never too late to learn the basics. There are many sources of help, and the majority are aimed at people in your situation. Possible cause 6: ‘I haven’t done maths for years’ In a way, building maths confidence and knowledge is like body-building. It takes a lot of work to produce the muscles, and if you don’t use them, they slowly waste away. It is very easy to forget mathematics that you haven’t used for years, but luckily, like muscles, you can get it all back with a bit of work. Luckily maths is a subject that changes very little. Although the courses taught at secondary schools today will contain different material to that which you studied, the core of maths, the rules and techniques always stay the same. Also over time, a lot of the harder topics have been taken out of school and are taught at college, so the chances are that you already have some A-level knowledge of maths. Possible Solutions 1. Get hold of a school maths textbook. You may think that you’ve forgotten most of your course, but it may be that you can remember, but are not confident enough to use your maths. This is where the school textbook is ideal. They introduce each topic slowly and in detail and follow up with copious amounts of similar exercises in which to build confidence. Most also have answers at the back, so you can be sure you’ve got them all right. The best (and free) sources of these texts are the University’s libraries. 2. Grab a leaflet or two The Skills team have a collection of mathematics help leaflets which can be downloaded from the Skills website (www.hull.ac.uk/skills). These cover various topics including basic algebra and calculus. A full list of the topics available is on the website. 3. Ask a child If you are a parent, you have a fantastic opportunity to have a look at your child’s textbook, and to learn alongside them. Ask them to explain to you what they are working on; to the child it may seem like you are just taking an interest in their work or that you are testing them on the topic. One important fact about this is that the person explaining the concept gets as much out of it as the person having it explained to them. This is because the ‘explainer’ has to put their concept of the topic into words, and possibly find a few different ways of explaining it. Overall this leaves them with a greater understanding of how the topic works. So if you ask your child to explain something, you both learn from the experience. 4. Tell people what you know If you have a partner or friend who also has a problem/fear with maths try to explain to them one of the topics of which you have a good grasp. As stated before you’ll benefit as much as they do. You could also involve a child in this process. If a child is struggling with a certain topic, study it yourself and then explain it to them in your own words. You help someone, you become more confident, and as a bonus, less likely to forget that topic in the future. 8 5. Take a course If you took maths but didn’t get the result you wanted, there is nothing to stop you from re-sitting. This can involve anything from taking a full year’s course, to just taking the exam. Many schools, colleges and adult education centres now offer GCSE maths courses in the evenings. These courses will usually take up two or three hours a week, they are inexpensive, and there are many concessions available. If you would rather study at home and then take the exams, you can. Many institutions will allow you to come in just for the exam session, as long as you pay for the exam paper, and register in good time. It is best to call a few institutions beforehand to find out which offer this service. It may be worth approaching: Wyke 6th Form College, Hull; Web: http://www.wyke.ac.uk/ Tel: 01482 346 347 Hull College, Hull; Web: http://www.hull-college.ac.uk/ Tel: 01482 329943 Scarborough 6th Form College, Scarborough; Web: http://www.scarb-6-form.ac.uk Tel: 01723 380745 6. See a private tutor Private tutors are a good idea if you don’t have much time for study. You can arrange for a private tutor to come to your house for an hour or two, which is handy if you have young children. Again, you are the one in charge, and they will cover the topics you need to cover. The one drawback with a private tutor is the expense. 7. Websites for school and college students There are many great websites out there for students about to take GCSE and A-level examinations. They provide you with quick run-throughs of a topic and then interactive exercises. These are ideal if you just need a quick recap. The one I’d recommend would be http://www.bbc.co.uk/schools/. 8. Revision Texts Many companies now produce guides for examinations. They normally come in two forms; a full revision of the topic with exercises, and a past papers book which contains past papers and small chunks of revision. If you understand the topic but want more practise, then choose the past papers. If it is the theory that is the problem, choose the full revision guide. Written by Lynn Ireland, edited by Jacqui Bartram The information in this leaflet can be made available in an alternative format on request – email [email protected] 9

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