Why are elementary school math scores declining in Ontario?
Ontario’s declining scores on the Education Quality and Accountability Office (EQAO) math assessment have attracted growing concern among parents and policymakers and could hurt young Ontarians’ future job prospects. As the Institute explores in its most recent Working Paper, Teaching for tomorrow: Building the necessary skills today, math is an increasingly important skill needed to thrive in Ontario’s future labour markets. Analysis by the Institute shows that the best channel to improve math scores is to give current and prospective teachers more math training and hire more teachers with stronger math backgrounds, while enabling further study of the impact of teaching methods on scores.
Math skills are increasingly important for Ontario’s labour market
Alongside reading and writing, math is a fundamental skill that is used in many careers either directly, or as a building block for developing other skills. Although math is required for only 53 percent of Ontario’s projected job openings in the next four years, this represents a 6 percentage point increase from the province’s employment mix in 2011—the largest of any skill category (Exhibit 1). Labour market forecasts predict many openings for math-important jobs such as accountants, renovation managers, and retail supervisors. Most jobs that require math only need workers with a low or medium-low level of math, meaning Ontario’s labour force needs a broad distribution of strong math skills, rather than a few specialists. Math is also helpful for developing critical thinking and problem solving skills, the skill category predicted to grow second-most in Ontario.
Exhibit 1: Share of total job openings by level of math required, Ontario, 2011 and 2017-2021 projections
Math scores in decline
While math is increasingly important for economic success, Ontario’s future workforce is demonstrating worsening math skills. According to annual EQAO testing by the Ontario government, the share of grade 3 students meeting the provincial standard in math has fallen from 72 percent in 2006 to 65 percent in 2017. The share of grade 6 students at the provincial standard has dropped even lower to 53 percent, from 65 percent in 2006. The math performance of fifteen-year-old Ontario students in international testing by the Organisation for Economic Cooperation and Development (OECD) has declined since 2000, and Ontario ranks behind three of four other provinces tested (Exhibit 2). This relative performance has raised questions about what Ontario is doing wrong with its math teaching.
Exhibit 2: Average PISA math scores for 15-year-olds, Ontario and Canadian Provinces, 2000-2015
Challenges with math teaching quality, not quantity
The average Ontario grade eight student spends more time learning math—both in and out of school—than students in peer jurisdictions (Exhibit 3). However, Ontario’s teachers have insufficient math knowledge. Only 6 percent of grade 4 students in Ontario are taught by a teacher with a major or specialization in math, the smallest share among the province’s peers and below the Canadian average. Over 80 percent of primary and junior teachers have never taken a post-secondary math course.
Exhibit 3: Time spent learning math, Ontario and peers, 2015
Which factors most determine students’ math scores?
The Institute analyzed the impact that various teaching methods had on students’ overall level of EQAO math achievement, controlling for other possible confounding factors. The evidence is mixed on the impact of instructional methods—including ‘discovery learning’—on math scores, which some argue is the reason for recent declines, and most analyses showed that instructional approaches had little significance on students’ level of math achievement. This was especially true when the impact of teaching methods on math scores was considered alongside the role of teachers’ math knowledge.
Nonetheless, some findings are striking. Students with teachers that reported using collaborative problem solving were 1.27 times more likely to have higher math achievement than those that did not. Grade 3 students taught by a teacher with a post-secondary math minor who used mental math methods or practicing procedures, two direct approaches, were also more likely to score higher. A stronger math background also helped teachers who used discovery learning with older students. Grade 6 students were more likely to score higher when their teachers used open-ended problem solving or guided instruction (an ‘enhanced’ form of discovery learning that more actively involves the teacher), if their teachers had received math training in teachers’ college. This fits arguments that discovery learning is most effective when teachers have a strong background in the subject—for example in language arts, a far more popular post-secondary major for teachers than math.
So what does make a difference for math scores? Across several analyses of grade 3 and 6 student math scores, the factors with a consistently negative effect on math achievement were being female, low reading and writing achievement, being in a larger class, and having a disability. Students with positive attitudes towards math, those that talked to their parents about their school activities, and those that more frequently used teacher-developed learning materials tended to score higher. Students without a teacher with a math major were less likely to score higher, even if their teacher had a minor in math or a major in a related subject such as business, science, or engineering. Students also had a probability of scoring higher if their teacher had taken a specialist-level additional qualification in math.
Interestingly, students whose teachers had attended shorter professional development activities (such as courses, workshops, or conferences) on math instruction had slightly lower odds of having higher math scores. This possibly reflects teachers who already struggle with math teaching attending these sessions for remedial learning. In any case, it does not bode well for the government’s plan to improve math scores by asking school boards to hold a mandatory math-focused professional activity day later this fall.
Policies to improve math scores
These results suggest that some policies to boost math scores will be more effective than others, and that there are no quick fixes. Given the lack of concrete links between teaching methods and math scores, the government should enable further study of these links by expanding the EQAO questionnaire section on teaching methods. If curriculum changes are necessary, then discovery learning should be retained in older grades since it is more effective for students that have sufficient math fundamentals.
The government should focus on improving teachers’ math knowledge to round out their education. Rather than expanding and mandating professional development workshops and conferences, the government should promote more comprehensive forms of math training, like additional qualifications courses, and incentivize enrollment through either reducing the cost of the courses or guaranteeing pay bonuses for completion. The government should also develop math skills in teachers’ college through assessing incoming elementary teachers on their math knowledge and requiring an additional, standardized mathematics foundations course for all elementary teacher candidates without an undergraduate mathematics background. Some of the extra course space now available in teachers’ college programs—which were doubled from one to two years duration in 2015—could be used for optional content and pedagogic specialization in subjects such as math.
Written by Jacob Greenspon
Photo credit: vladwel, istockphoto
 The Institute matched labour market forecasts from the Ontario government with a U.S. Department of Labor database of skill requirements for each occupation to produce a forecast of what skills will be most in-demand across the labour market over the next four years, and how these compare to Ontario’s 2011 employment composition. For a detailed explanation see Institute for Competitiveness & Prosperity Working Paper 33, Teaching for tomorrow: Building the necessary skills today, Appendix 1.
 Institute for Competitiveness & Prosperity analysis based on data from the Trends in International Mathematics and Science Study (TIMSS) 2015 International Results in Mathematics. Summation of share of students taught by teacher with Major in Primary Education and Major (or Specialization) in Mathematics and share of students with teacher with Major in Mathematics but No Major in Primary Education. http://timssandpirls.bc.edu/timss2015/international-results/wp-content/uploads/filebase/full%20pdfs/T15-International-Results-in-Mathematics.pdf.
 The Institute’s analysis used multilevel mixed-effects ordered logistic modelling to control for related math scores among students with the same teacher and at the same school. Depending on the specification, the regression analysis included several explanatory and control variables: gender; class size; whether the student was in a split-grade class; the teacher’s total years teaching; the student’s reading and writing EQAO scores; whether the student had a physical or intellectual disability; giftedness; the student’s previous grade 3 EQAO math score (for grade 6 students); whether the teacher indicated using various math instructional methods; the teacher’s area of study; whether the teacher took math training in teachers’ college’; and the level of the teacher’s additional qualification courses in math.
 Discovery learning introduces students to a problem and has them work their way back to discover the problem-solving method, rather than memorizing facts and algorithms. Evidence suggests it is frequently-used: In 2017, around two-thirds of grade 3 and grade 6 students had teachers that reported using collaborative and open-ended problem solving methods and nearly half had a teacher who used collaborative inquiry approaches.