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The Fear of Maths: How to Overcome It
By Steve Chinn
Souvenir PressCopyright © 2011 Steve Chinn
All rights reserved.
Understanding What Can Cause Problems with Learning Maths
If you can't do mathematics it is likely to be for some very good reasons, which probably have little to do with how clever you are. There are many factors which can get in the way of learning mathematics. Some of these are listed below. You may recognise some of these factors as relevant to you. You may be unlucky enough to be affected by all of them, but even then you may have found ways to get round some or most of the difficulties these factors create. If you haven't, this book will help you to find some ways.
You may have reached the stage where you have decided that enough is enough and that you and mathematics can live without each other. I hope to persuade you to have one more try. It is a useful skill in so many aspects of life.
When you meet a problem, a good starting point is to try and understand the causes of the problem. This often helps you understand the problem itself and should make it easier to tackle. This awareness may even help you to avoid or at least reduce the influence of the problem in the future.
So, let's look at these problem factors....
Anxiety can really get in the way of learning.
It is an accumulation, a consequence of all the other factors and difficulties and how they have affected your attempts to succeed in mathematics, and how they have affected your attitude towards carrying on working at this subject.
Anxiety is the last difficulty to occur (because it is a consequence of all the other problems) and the first to overcome if you are to return to using mathematics and numbers. This does not mean, however, that it doesn't occur in young children.
One of the best ways to reduce this anxiety is to find some areas of success. It is important to know that everyone can do some maths. As my colleague, Richard Ashcroft says, mathematics is a subject that builds like a wall, but it is a wall that can still stand and be strong with some gaps, some missing bricks. You do not have to be perfect in all of maths to have success. For example, an ex-student of mine still cannot give an instant answer to "What is 8 × 7?" but he does now have a degree ... in maths.
The work in this book will attempt to use and build on what you know.
To be good, or even just OK at mathematics you have to practise, to gain experience, but if you are anxious about maths you will probably try to avoid doing any practice at all! For you to feel more comfortable and then, hopefully confident, I have to convince you to change your mind and try some practice.
If you do suffer from maths anxiety you are certainly not alone (see for example page 143). There have been whole books written on this subject. My guess is that people who are mathematically anxious are in the majority!
There is a (free) questionnaire on maths anxiety in adults on my website, www.stevechinn.co.uk.
DO TRY THE IDEAS IN THIS BOOK. THEY ARE DESIGNED TO HELP YOU SUCCEED AND START TO OVERCOME SOME OF THAT ANXIETY.
Learning how to do maths successfully will help reduce anxiety. Set your own targets and your own speed of working. Despite many beliefs about having to do maths quickly, there is no rush! Make both of these realistic, and then slowly increase your goals. Above all ... BEGIN.
Long term memory
One of the most common problems in mathematics is remembering the basic facts of numeracy, in particular the times table facts (such as 6 × 7 and 4 × 9). Some people find this task virtually impossible. And since this is one of the first demands from teachers of mathematics (and expectations from parents) it can create an early sense of failure and inadequacy.
YOU DO NOT NEED TO REMEMBER ALL THE 'BASIC' FACTS.
Memory can also let you down when learning addition and subtraction facts (such as 7 + 8 and 13 – 6), but these can often be worked out, quite quickly, on your fingers. These times table and addition facts are the basic building blocks of number work, but if you cannot remember them, all is not lost, there are some ideas to help (see chapter 3). These facts can be accessed by methods which are not just about memorising each fact separately. Many of the ideas in this book try to pull together, inter-link and extend the number facts and methods, so that they become mutually supportive. You practise and learn less of the facts, but use these to access more facts.
Your memory may also let you down when you try to recall a process or method, such as how to work out percentages. I will try to make each process real by relating it to something you know to give you a good understanding and add some meaning to the maths. Understanding can support memory.
If someone asks you to recall a fact from memory, say a times table fact, and your memory is a blank, it is something like looking into a deep black pit. There seems to be no way out and if remembering the fact is your only option, then indeed, there is no way out. I will try to provide some steps to bring you out of the pit.
There is a belief among some education policy makers that doing sums 'in your head' (mental arithmetic) is good for developing maths skills. Quite simply, this is not so for many people. Mental arithmetic can overload your memory, so I have included some suggestions to reduce the possibility of this problem occurring and help you tackle this activity.
Some methods for doing arithmetic are best when written, some are better to use 'in your head.' One of the reasons for memory overload is that people try to use written methods for mental arithmetic and not all written methods transfer successfully to mental arithmetic. I will attempt to suggest which methods are better to use for each case.
Any memory decays or slips away. The brain is designed to forget as well as to remember. What holds things in your mind are frequent reminders.
Then there is the way that you remind your brain. If you can put information into the brain via different experiences, then you should have a better chance of remembering what you want to remember. The more you see, hear, say or feel, that is, putting a memory into the brain by all senses, then the more likely it will be a permanent entry in your mind.
Short term memory and working memory
Short term memory is used for remembering information, usually small quantities such as a phone number, for a short time.
Working memory is used for working with information 'in your head'. Classically used for mental arithmetic. You can check working memory by having someone say a string of digits, at one second intervals, starting with three digits. When they have finished, you have to say them in reverse order. The 'working' bit comes in as you try to hold the numbers in your mind and reverse the order. Move up to 4 digits, then 5 and 6. At some stage you will be unable to remember and reverse the digits. The biggest number of digits you succeeded with indicates how many items you can deal with in your working memory.
A weakness in either or both of these, especially working memory, is very detrimental for the ability to do maths. However, research and experience suggest that many of the problems can be circumvented.
It is a great shame that maths lessons for pupils in English schools begin with mental arithmetic. Those with weak working memories are very likely to experience failure at the start of every lesson. Failure does not motivate!
Words and language
Learning is about receiving effective communication which should then lead to understanding. Unfortunately the vocabulary and language of maths is often like a foreign language.
Sometimes the words people use when talking about arithmetic are confusing. I have a similar problem when a fluent computer expert starts explaining new software to me. It seems to me that they have a language of their own (which, of course, they do!)
One source of possible confusion in our early experience of maths is that we use more than one word for a particular mathematics meaning, for example, to talk about adding we can say, for example, ... 6 more than 3, 17 and 26, 52 plus 39, 15 add 8. Having more than one way to express an idea or concept can challenge our need for consistency.
Another potential problem is that sometimes the words we use have other, non-mathematical meanings, for example 30 take away 12, 18 shared between 3 people.
Sometimes the same words can mean two things, for example; 'What is 5 more than 8?' is addition, but 'Emily has 16 sweets. She has 6 more than Sarah. How many sweets does Sarah have?' This is subtraction.
Then there are words for the more common everyday examples of mathematics ideas that do not fit the normal pattern of other maths vocabulary around those ideas. For example with fractions we have special names for the three most common values, ½, 1/3 and ¼. These we call one half, one third and one quarter rather than one twoth, one threeth and one fourth which would fit better into the subsequent fraction pattern. The other fractions use words that are better related to the numbers in the fractions, such as one seventh (1/7) and one twentieth (1/20).
The teen numbers are another case of a break with the later pattern causing possible confusion. This is especially true for young children as they try to make sense of our number system. The way we say the teen numbers is backwards to the way we say numbers in the twenties, thirties, forties and other two figure numbers. So we say eighteen (eight ten) and write 18, then we say twenty eight, thirty eight and so on which have the figures in the correct word order 28, 38 and so on. This particular situation is exacerbated by the words eleven (which could be 'one ten and one') and twelve (which could be 'one ten and two'). Even the 'backward' words such as thirteen would be better if they were threeten (and didn't sound a lot like thirty). I suppose a small benefit of eleven and twelve is that it saves two more teenage years.
Although these examples may sound insignificant, they can be enough to start an impression in the learner that maths is confusing and inconsistent. Early maths is frequently inconsistent which does not help learners who are looking for patterns.
Also early experiences, the first experiences of trying to learn something new are very dominant in our brains. If we learn incorrectly, it is hard to subsequently unlearn.
School maths and some adult maths courses use word problems. Largely speaking, these are rarely nothing what-so-ever to do with real life and are often worded in a strange, almost non-English language, style. Singapore has the highly effective 'Singapore Model Method' for addressing this issue.
Sequences and patterns
If you can remember and recognise sequences and patterns it will help your memory. For example it is much easier to remember the seven numbers 1234567 than a random set such as 5274318.
Sequences and patterns such as 2, 4, 6, 8, 10, 12 ... or 10, 20, 30, 40, 50, 60 ... are very much a part of maths. You need to be able to remember them, understand them and often adapt them. So 10, 20, 30, 40 ... can be adapted to 13, 23, 33, 43, 53. ... Some people find this adaptation difficult. This particular example is about understanding place value.
This book will show you lots of suggestions and ideas for organising and accessing facts, often by using patterns.
IF YOU CAN'T RECALL A MATHS FACT, YOU CAN USUALLY WORK IT OUT.
I like this aspect of maths. You can use one fact to access other facts. Maths facts usually interlink. Not true for many other subjects. For example, if you know that the capital of France is Paris, you cannot use that information to find out the capital of Greece.
Not only do people expect you to do maths correctly, they often expect you to do it quickly. Both these expectations create anxiety in many people. Trying to work more quickly than you normally do will increase anxiety in you and will almost certainly make you less successful. This is like taking up jogging. You cannot convert yourself from a couch potato to a 5 minute mile runner overnight (and you may never ever reach that 5 minute goal, nor want too!). If you do want to start jogging, or squash, or oil painting or fishing you will need to learn new skills and practise them. As you practise, providing you succeed, you get faster and the task gets easier, or to be precise, because the task stays the same, you find the task easier. But often you have to ask about maths, is there really any need to hurry that much?
You can develop quicker ways with maths, but on the whole this is very much a secondary goal, unless you want to appear on Countdown.
It seems obvious to say that not everyone thinks the same way. We have our own thinking style for all the different things we do in life. This includes having our own thinking style for maths.
It helps us learn if we understand the way we think. In fact there is a word for knowing how we think ... meta-cognition.
Our maths thinking style is the way we work out maths problems. It is possible to simplify this individuality down a little and imagine that our own thinking style lies somewhere along a line or a spectrum. At one end of this spectrum are the inchworms and at the other end are the grasshoppers. It is usual for people to make use of both styles.
An inchworm likes to work with formulas and fixed methods. Inchworms work step by step, preferring to write things down. They see the details of a problem.
They also tend to see numbers exactly as they are written, a sort of numerical equivalent of a literal interpretation. This can be a disadvantage if you have a limited number of facts (and procedures) ready for retrieval from memory.
Estimation is not an inchworm skill
A grasshopper often goes straight to an answer. Grasshoppers rarely write down working. They like to see the whole picture – they overview. They are intuitive, have a strong sense of number and can be confused by formulas (and see no reason to use them). They tend to see a broad value in numbers, inter-relating them to comfortable values, for example 98 is seen as a 'bit less than' 100 or 25 is seen as half and then half again of 100. Grasshoppers are good at estimation ... a great life skill.
If someone tries to explain a grasshopper method to an inchworm, the inchworm learner will probably not relate to the method. And vice-versa. This is a fairly important situation for teachers and learners to understand.
For example, an inchworm will mentally add 340 and 98 step by step, just as if it was being done on paper, starting with the units. So 0 add 8, then 4 add 9 and finally 3 add (the carried) 1 to give an answer of 438. Inchworm workers usually like to use pen and paper to write down their method, probably as
This is a difficult procedure if you have a poor working memory.
Faced with the same question, a grasshopper will look at the 98 and round it up to 100, add 340 and 100 and subtract the 2 (which made 98 into 100), getting an answer of 438 without writing anything down.
It is best if you can learn how to make use of both thinking styles. Generally speaking, grasshoppers are better at mental arithmetic and estimating, while inchworms are good at using formulas and detailed work. So you can see that to be versatile in your maths skills you need to be able to draw on both styles of thinking.
Some people are set at the extremes of the thinking style spectrum and find it very hard to adjust to the other style.
Throughout this book you will see that some methods are more inchworm friendly and some are more grasshopper friendly. It may well be the consequence of your thinking style that makes some methods easier to understand than others.
Remember, both thinking styles have strengths and weaknesses. Ideally, you need to learn to make the best use of both.
This is closely linked to anxiety and is a good final topic for this chapter.
One of the attitudes adopted by people who are not succeeding in maths is the attitude of not caring, not trying. This is usually based on an idea of protecting yourself from being wrong, from failing (any sensible person tries to avoid failure). So if you do not try to answer a question you cannot get it wrong. But this also means that by not allowing yourself to be wrong you are not allowing yourself to learn. I hope to encourage you to take the risk of sometimes being wrong. Even the best mathematicians make mistakes.
One of the key factors for success is a willingness to take a risk. If you look at every number problem and think "I can't even begin that" then you will not learn. You need to take that risk and experience new ideas.
Often in schools children are placed in situations where they meet a question to which they do not know the answer. Rather than be wrong, they do not try to work it out. They are withdrawing from a learning opportunity ... understandably. My recent research suggests that this becomes a significant issue, for too many children, at age 7 years.
Excerpted from The Fear of Maths: How to Overcome It by Steve Chinn. Copyright © 2011 Steve Chinn. Excerpted by permission of Souvenir Press.
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