Canada’s education system entered 2014 on a low note. The Program for International Student Assessment (PISA), released its annual rankings of the world’s education systems based on student’s abilities in math, reading, and science, and it wasn’t pretty. While Canada still ranked above the OECD average, the trend, at least in math, is clear: Canada is slipping. Since 2000, Canada’s ranking has gone from sixth to thirteenth, prompting calls for reform across the country.
The rankings have given impetus to the growing discontent with the way math is taught in Canada. A gradual shift in K-8 from fundamentals to ‘discovery learning’—which uses problem-solving and personal strategies to learn concepts—has coincided with the decline in rankings, even as parents routinely complain that their children’s math homework has become incomprehensible. While Canada was once a world leader, changes to the way math is taught are destroying students’ abilities.
Proponents of discovery learning argue that it is more important for students to understand the concepts behind math than the algorithms needed for calculations. This is a false dichotomy; proper education teaches both. Adding by columns is an algorithm that works for all equations, but when taught well also explains the fundamental concepts of addition and place value. Knowing what addition is doesn’t mean sacrificing the ability to add.
Fractions, the operation that most plagues elementary math teachers, exemplify discovery learning’s failures. Modern teaching focuses on understanding the question, making students ask “How many halves are there in one-fourth?” and giving them time to figure out the answer, often using pictures to represent it. Understanding then attained, the algorithm has been made redundant, according to recent trends in teaching.
Or has it? Textbooks in this style stick with simple equations. Having been taught in this manner, children only feel able to solve those equations they can visualize. Teaching algorithms is not meaningless memorization of strategies. It is memorization, yes, often with endless repetition, but even the master pianist started by doing drills. Start with intuition, but use it to build understanding of the abstract. Otherwise, we set students up for failure.
Math, like reading, builds on itself. As such, students are very vulnerable to failure at a low level: fall behind in grade two, and catching up becomes nigh-impossible. This hurts the country, as we lessen our ability to lead the world in technological and scientific advances, but it also hurts every student who loses access to the many rewarding (and well-paying) careers requiring math. One year of poor math teaching can quite literally have lifelong implications.
Canada faces many challenges in teaching math. We spent too little time teaching our teachers. We don’t expect—or demand—excellence from all our students, and when we see excellence we don’t challenge it. And we accept the corrosive idea that some people “aren’t math people”, excusing students from working harder and schools from teaching them better. But the worst by far is the idea that teaching and practice have no place in math. Students need real instruction to build real skills, and when we fail to teach students, we only teach them to fail.