Ontario’s math test results in recent years are adding up to be a real embarrassment for the province. The latest test results show half of Grade 6 students and 42 per cent of Grade 9 students in English-language schools are not meeting the provincial standard. This comes after years of promises and changes from the Doug Ford government meant to boost the province’s dismal math scores.
At a December press conference, Ontario Education Minister Paul Calandra expressed disappointment and vowed to appoint an advisory board to lead a review. Instead of more study, he should act on an example right in front of him (and which he cited in his comments to reporters). Mr. Calandra mentioned two school boards, the District School Board of Niagara and the Niagara Catholic District School Board, that significantly boosted their math scores – without additional funding.
The puzzling problem of low and dropping math scores has confounded education leaders in all provinces in the last two decades, but the answer is simple. The Niagara boards focused on step-by-step instruction, in-depth teacher training, and regular monitoring of students. In short, the boards treated math as a skill that could be practised, honed and mastered. Mr. Calandra and his peers should move quickly to replicate these methods across the country.
Ontario Education Minister Paul Calandra listens in on a Grade 6 math class at Wazoson Public School in Ottawa in December. Mr. Calandra vowed to appoint an advisory board to lead a review after disappointing standardized math test results in the province.Justin Tang/The Canadian Press
The types of methods the Niagara boards uses are sometimes described as “back to basics,” a term its proponents distance themselves from as it evokes images of rigid strict teaching environments from the past. Instead, they prefer terms like “explicit” or “teacher-led” instruction.
Ontario government unveiled its “back to basics” elementary math curriculum meant to address declining scores more than five years ago. It was a fulfillment of Premier Doug Ford’s pledge to get rid of “discovery math” – a newer method of learning that emphasizes problem solving and experimentation instead of rote learning. In education circles, it’s often referred to as “inquiry-based instruction.”
It’s a method that has gained favour due to its focus on boosting student engagement, but as math scores have continued to drop, it has come under growing scrutiny. Critics say it’s a fad that has taken deep root in the education system, and its group-intensive methods and approach that encourages students to “figure out math theories and formulas on their own” have failed. A new framework is needed.
A Grade 6 classroom is arranged for social distancing at a Toronto public school in September, 2020. The decline in Ontario’s math test results in recent years is a systemic problem, rather than a temporary setback caused by the COVID-19 pandemic.Nathan Denette/The Canadian Press
Declining averages
The decline in mathematical ability isn’t just a temporary blip caused by COVID – it’s a systemic problem that’s been happening for decades. The trend is deeply concerning because just like literacy, numeracy opens a path to building knowledge and is the foundation for an important part of adult life.
A lack of math knowledge or fear of numbers hinders individuals doing basic tasks such as shopping, cooking, managing money and doing renovations. Knowing math keeps the doors open to high paying jobs in finance, business, engineering, tech and AI, which are key to growing the economy. Researchers have found that student math scores are strong predictors of future academic outcomes and earnings.
Canada has been dropping in the international assessment Trends in International Mathematics and Science Study (TIMSS). On the chart below showing the latest Grade 4 assessment, you need to look way down the list to find Canada, which lands in the middle of the pack, below Albania, Armenia and the United States.
Results from another math benchmark, the OECD’s Programme for International Student Assessment (PISA), shown in this second chart, reveal that performances of Canadian students dropped significantly between 2003 and 2022, although they are still above the OECD average. (Drops in scores have occurred in every province, although Quebec and Alberta are still ahead of the pack.)
While teachers’ unions are quick to blame the provinces for underfunding, Canada remains ahead of the OECD average for money spent on primary and secondary education. As a recent C.D. Howe report points out, Canada’s per student funding is higher than Japan, which has much better math scores. It’s unlikely that funding is the primary issue.
The math wars
The so-called math wars have been raging for more than 30 years in the U.S and Canada. The advocates of explicit instruction rely on step-by-step instruction, memorization, and testing. With inquiry methods, on the other hand, children receive less instruction, and instead, direct their own learning, working in groups to tackle open-ended problems meant to lead to deeper understanding.
It’s easy to understand the appeal of inquiry-based math. Many educators themselves have weak math skills, and may have negative memories of boring lectures, stressful drills and rote memorization from their youth. A whole industry of highly paid consultants has sprung up offering professional development and educational materials to school boards. Equipped with whiteboards for group work, they promise to make math fun and engaging, and to prevent students from feeling stressed and discouraged.
But like being asked to jam on the guitar before you know chords, or diving into the deep end of a pool before you know any strokes, students without foundational math skills can struggle in these less formal environments. While some high performers do well, and others get by thanks to parental help or tutors, kids without these advantages tend to learn less than with traditional methods.
The rise of inquiry-based learning has correlated with the drop in math scores in the past 20 years. Andreas Schleicher, who oversees the OECD’s PISA test, says that explicit instructional practices tend to better predict student achievement than student-oriented learning. “Some consider this a statistical fluke, but it has been a consistent finding,” he wrote in 2019.
Despite an ever-present emphasis on “STEM” (Science, Technology, Engineering and Mathematics), and the reworking of the Ontario curriculum, inquiry-based training programs for teachers are still used in many schools in the province. School boards and faculties of education, which provide teacher training, often favour these newer methods.
Across the country, some schools have shifted back to explicit instruction, while others are using enquiry-based methods, or a mix of both. University of Winnipeg math professor Anna Stokke points to the fact that Grade 3 students are allowed to use calculators on Ontario’s standardized EQAO tests as proof that basic math skills, like memorizing multiplication tables, aren’t being prioritized.
The decades-long 'math wars' in Canada and the U.S. shows the divide between advocates of explicit instruction, and those who favour inquiry-based methods.Fred Lum/The Globe and Mail
Zeroing in on what works
Returning to explicit instruction doesn’t equate to adapting an antiquated style of rote learning where teachers smack your hand with a ruler if you get a wrong answer. It does mean that teachers need to spend more time ensuring children understand the fundamentals before moving on to high-level problem solving and group work. Because math is hierarchical, it needs to be practised, honed and mastered.
Schools where math scores are high tend to use similar practices. A teacher goes through the concepts clearly and slowly, breaking them into small, manageable steps. There is practice to build mastery, and frequent checks to identify children who need additional help.
The District School Board of Niagara is using these techniques, and now 79 per cent of its Grade 3 students meet the provincial standard, versus the provincial average of 64 per cent. The chart below shows the percentage of Grade 3 and Grade 6 children meeting the standard in Niagara’s schools has risen in recent years.
More than 2,000 teachers at the board took a university-level math course so they could understand the material better themselves. Students in the district take a mid-year test, which serves as a practice to the EQAO and allows teachers to identify students falling behind. Niagara’s Catholic board has employed similar techniques to boost its own math scores.
Quebec is another good model. It has been the national leader in math for decades, and its PISA scores continue to beat other provinces’. The reason, according to education author Paul Bennett, is a greater focus on math in the curriculum, more thorough teacher training and a requirement that students pass a math exam to graduate high school.
While an inquiry-based approach can appear to make math more fun and engaging, students without foundational math skills may struggle in these less formal environments.Fred Lum/The Globe and Mail
Another success story is Jump Math, a nonprofit with a well regarded program used in 500 schools across the country. Calling itself “structured inquiry,” it blends strategies from the two opposing camps in the math wars. The method starts by breaking concepts into manageable chunks and later progresses to problem-based work. The focus is on individual work with ongoing assessment, but there are games and group activities. The method has boosted EQAO scores at some Toronto public schools.
The way forward on math is clear. Education ministers need to hold school boards and individual schools to account, and make sure that explicit instruction is used in classrooms. The provinces can set the stage for success by bringing in regular universal screening programs, such as checks to ensure Grade 4 students know their multiplication tables. Children falling behind should be given extra help.
Instead of eliminating exams, as some schools have done, they should be used to assess progress and prepare children for higher education. Improved standardized tests can also be an important tool for gauging progress. Report cards written in plain language and with clear grading will alert parents if their children need extra support. Teachers also need additional training in math to boost their own competence and confidence.
Much of the rise of inquiry-based learning has been driven by the fear of math. However, the best way for children to get past math anxiety is not to avoid the hard work of learning math, but to learn it properly.