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New Zealand Initiative: Bringing the Science of Learning to Mathematics Education


Ensuring children have time to understand the concepts will ensure they retain the love of math. Photo / 123RF


Do you fear and hate math? If so, you are far from alone.

Many otherwise well-educated people dislike math and think it is mediocre. In fact, it’s been estimated that almost one in six adults suffer from a syndrome known as math anxiety. This is not a joke.

Math anxiety can kill young people’s motivation to study the subject.

For many years, I taught a required research methods course in a Masters of Education program. Many mid-career teachers have taken the course to enhance their knowledge and improve their qualifications. In my part of the course, we covered basic statistical concepts and their application to the analysis of research data.

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

Beyond anxiety, there is a real problem with math fluency in New Zealand and many other countries.

Pisa is an international test organized every three years by the OECD to measure the educational level of 15-year-olds. The Pisa results suggest that a quarter of test takers across the OECD cannot reliably perform some benchmark tasks. These include converting prices in different currencies and comparing total distances on alternative routes.

New Zealand’s performance in Pisa mathematics has shown a downward trend since testing began in 2003. Yet it remains close to the international average. Thus, the results from Pisa are indicative of the proportion of New Zealanders who cannot perform daily digital tasks.

It seems that education systems are failing to impart mathematical knowledge that could provide wonderful opportunities for young people. And I’m not just talking about opportunities in the job market, although math skills are certainly in demand.

More generally, mathematical culture opens a window on the world. It is essential to understanding many scientific challenges of our time and has made many contributions to the visual arts.

Tragically, our education system leaves many people feeling incompetent and alienated from mathematics. These feelings often persist throughout life. Of course, not everyone needs to study advanced math, but that’s besides the point. Everyone must have at least the basic skill level indicated by the Pisa benchmark.

Ensuring children have time to understand the concepts will ensure they retain the love of math.  Photo / 123RF
Ensuring children have time to understand the concepts will ensure they retain the love of math. Photo / 123RF

Why are so many young people leaving school unable to perform important digital tasks in everyday life, promising themselves never to look at another equation? Is math too difficult for most people to understand?

My experience in my research methods course suggests not. I cannot claim that I steered all my students towards a career in statistics. But a large majority of those who started the course nervously ended up doing well. Some who probably suffered from genuine math anxiety did very well. Many have told me that the course was a turning point for them. A few have even undertaken quantitative projects for their thesis work.

I don’t consider myself a particularly gifted professor of statistics. I love the subject – I know, I know, I’m very weird – and my enthusiasm for it certainly didn’t hurt. But I attribute any success I’ve had to the insights of Australian school psychologist, John Sweller. He applied theories of cognitive psychology, the science of human information processing, to the educational setting, developing what he called “cognitive load theory”.

To oversimplify, cognitive load theory recognizes that we have short-term memory and long-term memory. The short-term memory system is known to cognitive psychologists as “working memory” because it stores information while we consciously use it.

Working memory has a very limited capacity and requires constant attention to keep its contents in place or it will quickly be forgotten. That’s why if we try to remember a phone number, for example, we can repeat it over and over in our head – this keeps the number in working memory.

Some, but not 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 in it to retain it. Once information is 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 tremendously when teaching skills such as math. When working memory is overloaded, people become confused. This easily happens when we learn new concepts, especially in subjects like math. Math concepts tend to be hierarchical, which means that understanding a new concept depends on learning other, more fundamental concepts.

To prevent working memory from being overloaded, it is important to ensure that a student has practiced enough with a concept to encode it securely in long-term memory before developing it. Otherwise, the student’s working memory will be overloaded and the student will become confused. If this happens often, the confusion will turn into frustration and the student will lose motivation. Eventually, they will conclude that they are just not good at math 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 ensured that teachers understood them. But curiously, the science of learning is usually not included in teacher training courses. This must change.

Math anxiety stifles 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 unforgivable.

• Dr. Michael Johnston is Principal Investigator at The New Zealand Initiative.