.boxed { border: 1px solid green ; }

Solving the Math Teaching Problem

Chris Meyer

How should we improve math instruction in our province? Pundits and politicians are worked up about the recent, discouraging math scores from the provincial standardized EQAO tests. Luckily, our premier, Kathleen Wynne, is coming to the rescue with an announcement of “sweeping changes”, or maybe a “refresh”, for education in our province. But how will we know if any new changes are going in the right direction? The field of education is littered with the wreckage of pedagogical fads driven by experts who have little connection to functioning classrooms. To navigate this debris, the best maps are those that have been informed by the science of learning and the effective practices of our most successful teachers. These maps will help answer the questions we should be asking as we try to solve the math teaching problem.

How do people use math?
Take a moment to think about how capable people, or experts, productively use math in their daily lives. Consider, for example, successful people in business, science, and skilled trades. The science of learning reveals that these people possess certain common traits. First, they have a strong number sense, meaning that when they see numbers or symbols at a glance, a rich web of associations is activated in their minds: the figures mean something to them. Second, their math skills are very fluent and can be used with little effort. Third, they have the ability to see through messy situations and find the right math ideas to use. These traits — number sense, mathematical fluency, and seeing deep into problems — should become the goals for new math instruction.

How do people best learn math?
Over the past decade, several streams of science have joined together to create an exciting new science of learning. As a result, we now have a good and growing understanding not only of how our brains learn, but what meaningful learning looks like. When people learn outside of school, it is often with a clear purpose. Students in class need to feel a similar sense of purpose, and they must also develop an early understanding for how mathematical ideas can be useful to them. Traditionally, purpose and usefulness are often explored only near the end of a topic or grade, leaving students wondering “why am I learning this?” The science of learning shows that teachers cannot simply “transmit” their expert understanding to students. Deep understanding develops slowly and only when students build a personal understanding of new ideas atop what they already know. This is a profound and well-supported insight from the science of learning that goes against the instincts of most well-meaning teachers and parents. Students need to test their growing skills with more and more varied but meaningful tasks. Most importantly, all students need to experience success throughout their learning process. A true feeling of success comes not from receiving inflated grades, participation ribbons, or passing scores on standardized tests. Instead, it comes from the student recognizing on her own that she was able to use her new math skills to solve a tough, engaging problem. This is the most reliable way to help students to develop an intrinsic interest in math – recognizing that they are good at math, and that math does interesting and useful things.

What about the great “math debate”?
Readers familiar with the math debates might have recognized in the previous passages hints of direct instruction (efficient, fluent, highly practiced skills) and discovery learning (students building their own understanding). The battle between these two approaches is a false one: both are crucial for the development of expert-level skills. Learning should begin through carefully guided discovery (often misrepresented as students haphazardly making things up for themselves). Learning should be honed through repeated, careful practice (often misrepresented as mindless drills). Finally, learning should be tested and refined using rich, nuanced applications. Problem solving falls short when basic skills are not fluent; basic skills fall idle without the understanding needed to penetrate a problem.

How do we improve the educational system?
“Fixing the system” is a fetish of politicians and bureaucrats. Hastily conceived top-down approaches, often announced with fanfare, seldom work. What does work is starting small with well-tested ideas. Politicians typically don’t have the patience for this kind of approach, but we need to insist on it on behalf of Ontario’s young people. Teachers need time, resources, and credible coaches to help them understand the science of learning and how to use it in their classrooms to teach math. Teachers need repeated opportunities to learn how students of a particular age tackle a certain math idea, instead of being shuffled around to teach a new grade every year. With their needs met, these teachers will become the next group of credible coaches. The successful solution to the math teaching problem will grow from within the system. Will our Premier find this solution?
©Ontario Association of Physics Teachers Contact the Newsletter