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The Questions We Don't Ask About Math Education

24 May 2017
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Meeting the incredible range of students’ needs in diverse Canadian schools is a daunting task. In every classroom, there will be students who easily grasp new concepts and others who need more time, more support or a completely different approach to help them learn. Simultaneously meeting these differing and often competing needs is what makes good teaching and learning so challenging. One approach used in teaching math, Discovery Learning, has become a flashpoint for anyone concerned with math education in Canada. 

Discovery Learning can be traced back to the writings of American philosopher and educator John Dewey over a century and a half ago, but the modern Discovery Learning movement is generally attributed to educational psychologist Jerome Bruner in the 1960s. Discovery Learning differs from traditional education in that rather than using direct instruction, students are encouraged to solve complex, “real life” problems, and through that process develop understanding.

When Ontario’s math curriculum was last revised in 2005, one of the stated key fundamental principles was “...the belief that students learn mathematics most effectively when they are given opportunities to investigate ideas and concepts through problem solving.” A clear indicator of a shift towards Discovery Learning.

Concerns about the effectiveness of Discovery Learning began to be raised in 2011 when math test scores began to drop. Parents became concerned that their children weren’t developing the math skills they expected. Gone were the familiar days of flash cards, times tables and algorithms, replaced instead with open questions that allowed for a variety of “right answers”.

Concerns about Discovery Learning have fueled a robust public discussion about math education methods. However, the discussion is sometimes superficial and ignores key issues. As advocates of “back to basics” math become ever more critical of Discovery Learning educators are increasingly asked to defend new methods of learning math.

It’s a well-worn cliché that in education, there is no silver bullet. In a classroom with differing and diverse needs, the notion that any single instructional approach can help all students succeed is misguided. The Discovery Math vs back-to-basics debate is dominated by “armchair educators”- people who rarely have the responsibility of helping a group of students understand a math concept. Teachers don’t have the luxury of discounting any approach that might help a student learn more effectively.

I’ve yet to see a classroom that uses Discovery Math or back-to-basics rote learning exclusively, or met a teacher who advocates a single approach. Every student is different and good teaching employs a variety of methods. The most effective approach will change depending on the concepts being taught and the students who are learning. In the classroom, there’s no room for ideologues. 

This public math debate also reveals how limited our thinking is about math education. We commonly think of math as adding, subtracting, multiplying and dividing and not much else. Most teachers have been accosted by a disgruntled friend, family member or neighbour who’s upset because someone working at a store couldn’t accurately calculate how much change they were owed when the cash register wasn’t working. These are computation skills.

But the math curriculum is much broader than computation. Understanding numbers and operations is just one of five areas of math that students learn about. In the Grade 5 math curriculum there are 77 separate learning expectations but only seven, barely 10%, refer to computation skills. What about the other 90%? 

The simple story that math test scores are dropping is superficial and misleading. Are test scores dropping across the board, or are there some areas (geometry, data management, measurement) where students are improving? What about student ability to solve complex problems? To think about math? Our collective ability to teach math to over two million students can’t be properly assessed with a simple thumbs up or thumbs down response. 

One of the non-computational math skills students learn is data analysis. They learn about bias in data collection and how to collect information to ensure that any conclusions drawn are accurate and representative. They’re taught to critically analyze the data used to avoid drawing inaccurate conclusions. It’s a skill that’s underutilized when we use test scores to assess our effectiveness in teaching math.

When test scores are released, we immediately begin drawing conclusions without considering whether the scores are, in fact, accurate. When collaborative problem solving is one of the main methods of math instruction in Ontario schools, why is math learning assessed through an entirely independent pen and paper test?

Students learn math from Junior Kindergarten into high school by sharing ideas and they communicate that understanding in a variety of ways (writing, speaking, drawing diagrams, etc). But on standardized tests, there’s only one way to represent your understanding, only one right answer, and students can’t ask questions. It isn't surprising that some students struggle to make that transition. Why don’t we ever stop to consider that maybe the test might be the problem?

Our unwillingness to critically question our testing methods is just another indicator of a superficial public debate about math instruction. Rather than entering into a nuanced and informed exchange, parents, advocates and pundits retreat to their respective camps and defend their corners. And as the debate rages, teachers continue working hard – using the best methods available – to ensure students are learning the math curriculum in the most effective way possible. 

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