When I was in eleventh grade, my high school put forth an initiative to make peer tutoring more widely available. A classmate of mine had volunteered to instruct ninth and tenth graders in math, and his outlook wasn’t optimistic. He was frustrated with the students, who often struggled with the basics.
“She couldn’t add double digits in their head,” he reported about one ninth grader. “She had to use her calculator.”
This would not be a pressing issue if it weren’t for the overall pattern. The national standard in math has been falling against that of other countries in the OECD survey. In Ontario, the quality of mathematical education in elementary schools was seriously called into question in 2016 with the release of the EQAO results: only half of the sixth graders writing the test were able to meet the provincial average; falling 8% short of the previous year’s pass rate, and further disproving the notion that 75% of students can pass the ‘Level 3’ benchmark. The 2016 results weren’t an anomaly, either: The pass rate dropped to 49% in 2018, and again to 48% in 2019.
The resulting bout of tirades was almost unanimous in casting the blame — the culprit was the Ontario curriculum. Having relegated classical methods, it pushed for more progressive methods of teaching which ultimately failed.
This might seem counterintuitive at first. The new “problem-based”, creative approach to learning math appears logical: it aims to make students understand, rather than blindly memorise the material. Under this curriculum students would use practical approaches to solve problems on their own. It seems correct to teach critical thinking at the elementary level, and it is; the problem isn’t in the ideology but in its application.
By neglecting the traditional building blocks of mathematics, the curriculum strays from what we know from the study of cognitive development to be the best method of instruction for children. In order for students to effectively learn math, they need to practice and master the essentials. Memorization, in this case, prepares students for higher-level learning: reciting times tables isn’t an unnecessary vestige from the days of old but a requirement for the thorough understanding of the basic mathematical concepts. Elementary school students do not have a sufficient background to be able to learn on their own through inquiry-based activities. It is a pointless exercise in putting the cart before the horse. As said by New York Times columnist David Bornstein, “Asking children to make their own discoveries before they solidify the basics is like asking them to compose songs on guitar before they can form a C chord.”
This approach leads to poor results when solving more advanced problems is hindered by a weak grasp of the basics. If you do not understand the foundations of math well enough, anything beyond requires sheer memorization and suspension of disbelief; the opposite of the values one would hope this method of instruction would promote. In middle school, I myself was a peer tutor; I helped a seventh grader with science and math homework. Halfway through the semester, I discovered she didn’t know that the order in which you multiply numbers is irrelevant, that the product will remain the same. In class, she was learning pre-algebra. How could she begin to justify order of operations to herself when this is what she believed? Memorization of key concepts such as times tables doesn’t just give kids the ability to rattle off six by four or two by three. It teaches them necessary and invaluable mathematical concepts.
Curiously, critiques of the curriculum seldom mention the flip side of memorization: by knowing the material, students are able to find its patterns, often without the guidance of a teacher. As a second grader, I avidly described my method of remembering my nine-times-tables to a friend, who looked at me strangely. “I just multiply by ten, then take away what the first number was,” she said. What she described bears a close resemblance to the method taught under the problem-based curriculum, which outlines how to break apart numbers to multiply them more easily. The difference was that by learning the times tables the hard way, she figured this out for herself. Conversely, starting with this sort of approach leads to confusion and does not build the base knowledge needed in later grades. Children are capable of learning the tricks of the trade. But you must first teach them the trade.
It is impossible to criticize this system, and to analyze its shortcomings, without considering the countries whose systems of education outrank that of Canada. The high math performance of Singaporean students, for example, is often cited in articles as an ideal which we should aim to replicate. The same applies for South Korea and Japan, which scored higher on the OCED PISA for mathematics than Canada but lower than Singapore. The academic prowess of these countries is widely admired; their context (at least in tirades against our own system) is often ignored.
Even if a more meritocratic system was proven to be the best solution to Canada’s faulty system of mathematical education, could we really adapt to it culturally? Sources are divided as to whether the “Asian Model” could be replicated elsewhere. Some ascribe the system in Korea to the Civil Service Examinations of the Choson dynasty, implying that it is the natural outcome of a particular sort of a particular set of historical circumstances that may not be replicable. Furthermore, statistics show that Asian immigrants to Western countries are more likely to invest above-average amounts of money into their children’s education, and that their children are more likely to academically succeed. Conversely, some studies found that investment in tutors was determined mostly by wealth, and by ethnicity and culture only insofar that it affected wealth.
This last point is crucial because the positive effect of wealth on quality of education is undeniable even in Ontario. A Toronto Star survey revealed that 77% of respondents believe economic status affects education, and they would be correct: standardized test scores are higher in high-income neighbourhoods. Alarmingly, the disparity between the highest and the lowest ranking students in Ontario (the mathematical bell curve) has been increasing as well. All the while, the rate of families paying for private tutoring services has been on the rise. If Canada — whose system of education is significantly less demanding and less oriented towards standardized testing than that of other countries — already requires investment to succeed academically in the most elementary level, how much more privatized could it get if it were a meritocracy?
Leave a Reply