Bringing the science of learning to maths education

Dr Michael Johnston
NZ Herald
22 March, 2022

Do you fear and loathe mathematics? If so, you are far from alone. Many otherwise well-educated people dislike mathematics and believe that they are poor at it. In fact, it has been estimated that nearly one in six adults suffer from a syndrome known as mathematics anxiety. This is no joke. Mathematics anxiety can kill the motivation of young people to study the subject.

For many years, I taught on a compulsory research methods course for a Master of Education degree programme. Many mid-career teachers took the course to improve their knowledge and upgrade their qualifications. In my part of the course, we covered some elementary statistic concepts and their application to the analysis of research data.

Almost all the students who took the course were nervous about its mathematical content. In some cases, the nervousness bordered on anxiety. A few students were utterly terrified. Sometimes there were even tears.

Anxiety aside, there is a genuine problem with mathematics proficiency in New Zealand and many other countries. PISA is an international test run every three years by the OECD to measure the educational achievement of 15-year-olds. PISA results suggest that a quarter of test takers across the OECD cannot reliably complete certain benchmark tasks.  These include converting prices into different currencies and comparing total distances across alternative routes.

New Zealand’s performance in PISA mathematics has shown a downward trend since testing began in 2003. Still, it remains close to the international average. So, PISA results are indicative of the proportion of New Zealanders who cannot perform everyday numerical tasks.

It seems that education systems are failing to impart mathematical knowledge that could afford wonderful opportunities to young people. And I don’t only mean opportunities in the job market, although mathematical skills are certainly in demand. More generally, mathematical literacy opens a window on the world. It is key to understanding many of the scientific challenges of our times and has made numerous contributions to the visual arts.

Tragically, our education system leaves many people are left feeling incompetent at, and alienated from, mathematics. These feelings often persist throughout life. Of course, not everyone needs to study advanced mathematics – but that’s not the point. Everyone does need to have at least the basic level of proficiency indicated by the PISA benchmark. 

Why do so many young people leave school unable to perform numerical tasks that are important in everyday life, promising themselves never to look at another equation? Is mathematics just too hard for most people to grasp?

My experience in my research methods course suggests not. I can’t claim that I switched all my students onto a statistical career. But a large majority of those who started the course nervously ended up doing well. Some who were probably suffering from full-blown mathematics anxiety did very well indeed.  Many commented to me that the course had been a watershed for them. A few even went on to undertake quantitative projects for their thesis work.

I don’t regard myself as an especially gifted teacher of statistics. I do love the subject (I know, I know, I’m very odd) and my enthusiasm for it certainly didn’t hurt. But I credit whatever success I had to the insights of Australian Educational Psychologist, John Sweller. Sweller applied theories from cognitive psychology, the science of human information processing, to the educational setting, developing what he called ‘cognitive load theory’.

To massively oversimplify, cognitive load theory recognises that we have short-term memory and long-term memory. Short-term memory system is known to cognitive psychologists as ‘working memory’ because it stores information while we are consciously using it.

Working memory has a very limited capacity and requires constant attention to keep its contents in place or we quickly forget it. That’s why, if we’re trying to remember a telephone number, for example, we might repeat it over and over in our heads – doing that keeps the number in working memory.

Some, but by no means all, of the contents of working memory can be transferred to long term memory. Unlike working memory, long-term memory has an essentially infinite capacity and does not require us to attend to the information stored there to maintain it. Once information has been encoded in long-term memory, it can be stored for a very long time. Then, when we want to use that information, we can deliberately recall it into our working memory.

Understanding the basics of cognitive load theory helps enormously when teaching skills like mathematics. When working memory becomes overloaded, people become confused. That happens easily when we’re learning new concepts, especially in subjects like mathematics. Mathematical concepts tend to be hierarchical, meaning that understanding a new concept depends on having learned other, more basic ones.

To prevent working memory from overloading, it’s important to ensure that a student has done enough practice with a concept to solidly encode it in long-term memory before building on it. Otherwise, the student’s working memory will become overloaded, and the student will become confused. If that happens often, confusion will turn to frustration and the student will lose motivation. Eventually they’ll conclude that they’re just no good at mathematics and give up.

Cognitive load theory is just one aspect of a rapidly developing field known as the science of learning. Insights from the science of learning would have much to contribute to many areas of education, if only we would make sure that teachers understand them. But oddly, the science of learning does not typically feature in teacher training courses. This needs to change.

Mathematics anxiety stunts the opportunities and enjoyment offered by one of the oldest cognitive disciplines. Allowing so many young people to fall prey to it when we know how to avoid it is simply unforgiveable.


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