CAN EVERYONE LEARN MATHEMATICS?

My strong belief is that everyone has a basic ability to learn mathematics. It’s like learning a language. If you heard an unfamiliar language, say Slovenian for example, you might at first think it sounds very difficult. However, in Slovenia everybody starts to learn Slovenian from an early age, everybody realises that they have to learn it, and everybody uses it a little every day. And, hey presto, everybody turns out being able to speak Slovenian.

It’s the same with maths. Start off by making sure you have your basic vocabulary (addition bonds and times tables). Then you need to practise sentence construction (basic methods like column addition and short multiplication). As you go on, be careful about punctuation (use of the equals sign) and grammar (correct working out). Practise a little bit each day so that you grow in confidence. Eventually, you will become fluent in the LANGUAGE OF MATHEMATICS.

WHICH IS MORE IMPORTANT, MEANING OR METHOD?

For most schoolchildren and their parents, method tends to be foremost on their minds. “Show me how I can do what I need to do to get top marks in my exams.” And what’s wrong with that? Getting good exam results ultimately means more options in your future, being able to go to whichever university you like to study whatever subject you like and follow whatever career you like. And to get good exam results, it helps to use simple clear-cut reliable methods that can give the answers quickly and accurately. Perhaps this is why there has been a marked growth in practice-oriented worksheet-based schemes in recent years, all emphasising systematic learning and the importance of good method.

Ultimately, however, there are limitations in any pure ‘rote learning’ system. In order to apply mathematics, one has to have a feeling for the circumstances when one would apply one method instead of another. For instance, when do you get the answer by multiplying the two numbers in the question, instead of adding them? To do this, it is important to get a feeling for what the answer to any given calculation ‘means’, even if you never learn the deeper significance of every single step of the calculation.

In short, my preferred balance is a drop of meaning to provide inspiration, followed by plenty of practice to reinforce good method. Just remember,

SUCCESS IN MATHS = 1% INSPIRATION + 99% PERSPIRATION

HOW IMPORTANT IS COMPLETION TIME?

Working with students leads me to say that the time taken to complete work CAN be a basic indicator of fluency. When a student starts a topic for the first time, I always tell them to concentrate on reading the examples and thinking about what methods to use, even if the work takes a little longer than normal. With practice, their completion times invariably come down. For example, let's say they were doing five similar sheets of the same work on five consecutive days, one sheet per day: they might take 15 minutes the first day, then a minute less on each subsequent day. This shows a steady improvement made by the student, which is exactly what we want to achieve.

However, there can be all sorts of problems if we over-state the importance of time. We should NEVER ask a student to prioritise time over accuracy - students gain nothing by rushing through work and getting lots of answers wrong. Also, it can be very harmful to emphasise absolute targets - “This work you should be doing in 10 minutes”. Even if the student eventually reaches such a standard, they will feel most of their work has been a failure. On the contrary, relative targets (for example, improving completion time by one minute each day, on similar work) can be a highly achievable and motivating target for a student, given a properly-designed maths programme.

In short: take your time at first on new topics; then aim for high accuracy and a STEADY IMPROVEMENT in times through further practice of that topic.

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