This article was originally published in April 2016
Anna Stokke is an associate professor of mathematics at the University of Winnipeg, co-founder and president of the non-profit organization Archimedes Math Schools, and author of a C.D. Howe Report, "What to do about Canada's declining math scores."
-----------------------------
Ontario Education Minister Liz Sandals has announced a $60-million plan to improve math training in elementary schools.
The move comes in response to declining scores in standardized math tests, which showed that the portion of Grade 6 students meeting provincial standards fell to 54 per cent from 61 per cent over a five-year period. In that same period, scores in reading and writing increased, suggesting that policies specific to math education caused the decline.
The Ontario government is to be commended for addressing the problem, but it is important to consider carefully what might be contributing to the decline and how it is best corrected. For example, what resources were used over the period of decline? How has math instruction changed in recent years? Is the province using a sound curriculum? Is increased spending required to improve outcomes?
It is possible to invest money in so-called educational solutions that actually hinder math performance. This may already be happening in classrooms across Canada.
For example, it is difficult to understand why the poorly written, expensive and confusing math texts published by Pearson and Nelson are the predominant resources used in Ontario classrooms from kindergarten to Grade 8, when the much more rigorous, and less expensive, JUMP Math program is available (and is published by a Toronto-based charity).
Central to the minister's announcement is that, starting next fall, 60 minutes of daily classroom time will be devoted to math. More instructional time in mathematics is necessary, but this initiative is unlikely to have a positive impact if the extra time is not spent on evidence-based practices and if the underlying math curriculum and student resources are flawed.
Important concepts are missing or introduced too late in the Ontario curriculum.
Memorization of the multiplication tables is optional. Fraction arithmetic, which is extremely important for later math success and requires time and practice to master, is not introduced until Grades 7 and 8. In high-performing jurisdictions elsewhere in the world, such as Singapore, and in previous Canadian curriculums, fraction arithmetic is introduced in Grades 4 and 5.
Both the curriculum and commonly used texts place too much emphasis on open-ended problems, multiple strategies and hands-on materials (such as blocks, fraction strips and algebra tiles). Rigorous student practice, which is essential to success in math, is often played down.
It is claimed that current teaching techniques – rooted in an educational philosophy often referred to as inquiry- or discovery-based instruction – help children become strong problem solvers and creative thinkers. Educational stakeholders are often presented with a false dichotomy that claims basic skills interfere with deep understanding.
There is a problem with this thinking.
Research in cognitive science points to the importance for students of mastering basic skills, such as times tables, because this frees up working memory to be used for other tasks. If the mathematical foundation is neglected, students will struggle with more complex problems.
When new learners are presented with multiple strategies and open-ended problems, working memory is overloaded, which hampers learning. This may be most harmful to struggling students, who need a great deal of structure, practice and guidance from an experienced teacher.
A successful math student should both understand the meaning of mathematical procedures and be able to perform them quickly and efficiently – without the use of a calculator.
There is nothing wrong with introducing concepts using hands-on materials, but too often students do not move past these clunky techniques and on to using standard procedures such as column addition and long division.
The Ontario tests, run by the provincial Education Quality and Accountability Office, also raise red flags: Grade 6 students were permitted to use calculators and materials such as blocks throughout the test, confirming the province's apparent reluctance to ensure that students are fluent in basic skills. There is a clear desire to produce students who are strong problem solvers, but this requires having a well-stocked toolbox to draw from, which includes fluency with basic skills.
The Ontario government's move to improve math training in grade schools has positive aspects, but it is unlikely to have a positive effect if the problems with the curriculum and student resources are not addressed.