It's about the maths, not the test scores

There has been a lot of talk of late about maths education due to New Zealand’s poor results in international testing. We can certainly improve maths learning experiences in our classrooms, and outcomes. However, I’m concerned that the desire to get better test results might lead to undesirable curriculum changes and unwanted consequences.

At the heart of the issue is the question of why we teach maths, which isn’t to get bragging rights for high marks in international tests, or at least, shouldn’t be.

We teach maths because we want a numerate society. We want adults in our country to be confident with numbers and able to problem solve, to deal with the numeracy requirements of their jobs, and to understand the sort of finances (mortgages, budgets, credit card debts) and statistics (in advertising, media) that we often need in daily life.

We also want to equip people who want to advance their careers in roles that require advanced mathematical knowledge, like scientists, technologists, engineers, statisticians, and medical professionals.

We don’t know what the future holds in any of these jobs, but it remains likely they will still need maths to get entry into those professions.In primary school, we can’t distinguish those who will simply need to be numerate from those who will grow up to have a career involving mathematics, so we must teach all of them for both situations.

Maths lessons need to thoroughly cover the basics as well as foster an interest in the subject itself.Ideally, maths lessons should develop children’s curiosity and interest in maths and their motivation to persevere with tricky problems; to make sure those who do carry on to maths-related fields reflect the diversity of our population.

Good maths teaching requires four different facets. First, teaching must be intentional, and it must make learning explicit. Intentional teaching includes teachers having high expectations of their students and holding classroom discussions in which children can argue and justify their ideas.

Second, students must practise what they’ve learned so they become fluent and confident with maths. They need to be able to quickly recall key facts and concepts as a solid base for future learning.

Third, students need to solve problems that are contextual and relevant to their lives, that are, for example, related to their communities and cultures. This helps them to see maths as useful to them. This facet addresses the ‘When am I ever going to use this?’ question, that is so often heard in classes that don’t include the students’ own contexts in learning. This might be designing a skatepark for their local community, which could involve maths-based tasks such as surveying stakeholders (data collection), calculating measurements, creating geometrical design features and estimating building costs.

Finally, maths teaching needs a creative, investigative element where children learn that maths can be joyful and fun. Here is their chance to experience the beauty of maths in a playful manner.In Aotearoa New Zealand, there is certainly room for improvement in each of these four areas of intentional teaching, practice, problem-solving, and creative exploration – but the classrooms that are missing even one or two of these facets leave students bereft.

Globally we’re seeing increased calls to follow the ‘science’ of learning, which refers here to cognitive psychology, arguing for explicit instruction that considers working memory and cognitive load, as recently outlined here on Newsroom by a colleague at the University.

Such calls also argue for the importance of drill and practice for instant recall of facts. In other words, the first two facets of good teaching, which are indeed important – but they’re only half the picture.

The field of maths education (in which I work) focuses research on the implementation of a rich, problem-solving approach; contextual problems, and those that do not have obvious solutions.

Children may not know how to get the right answer immediately, but they learn how to cope with this uncertainty and to persevere. It’s important to note that maths education doesn’t advocate this approach because it is the only method for teaching but because it’s an approach so often missing in classrooms, especially in those classrooms constrained by intensive testing regimes where teachers must prepare their students for exams. In other words, the emphasis is placed on the other two facets of good teaching, while the creative and the contextual, are typically missed.

The research from cognitive psychology and mathematics education are not incompatible. In fact, all four facets are important for quality teaching. We should draw on all the research for the best of both worlds.

My deep concern is that recent talk and handwringing around poor international testing results and too much emphasis on findings in cognitive psychology will lead to redeveloping our curriculum to prioritise the end-goal of test improvement, with the result being the exclusion of some (possibly many) students. Classrooms in Aotearoa today rightly represent the full range of human diversity found in our school communities and wider society.

Maths learning is for everyone, and it will be relevant and meaningful for every child when teachers are able to draw on a broad range of evidence-based learning experiences that build on the strengths and interests of every child.

This broader maths learning experience addresses society’s need for a curriculum that recognises problem solving as a useful and creative approach to teaching maths and which may, in the future, help our students to address critical issues that require innovative solutions.

The worst-case scenario is that we improve our students’ ability to take tests, but along the way, we lose their interest in mathematics altogether.

Unfortunately, such a consequence will not be seen until long after any curriculum change, when it will be too late.