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It doesn't add up

Out-of-date thinking, not recommended training, behind math difficulties

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So, faculties of education are out to lunch.

Or are they?

In his Free Press editorial Education faculties should disappear (Feb. 3), Michael Zwaagstra makes numerous claims, not all of which can be addressed here. But two of his points demand challenge.

One claim is faculties of education promote faulty teaching methods and the better teaching method is the traditional one of direct instruction and lots of worksheets. Many adults experienced traditional mathematics teaching in their days in school. The reader can decide how personally effective that approach was for encouraging a desire to learn mathematics and for developing an understanding of the mathematics being taught.

Faculties of education recommend a method of teaching mathematics that can be referred to as guided discovery. It involves problem posing, question asking and discussion to help students understand mathematical matters. Practice is needed, and it can occur in the form of worksheets. Sometimes direct instruction is necessary for a short while. But worksheets and direct instruction should not dominate. They are merely add-ons.

Asian students tend to do better at mathematics than their North America counterparts. Why? To answer this, consider a comparison of Japanese and American mathematics teaching from a research study. The Canadian situation is similar to the American one.

Is the reason the amount of time spent on the task? No; American students spend an average of 143 hours per year studying mathematics. In Japan, the figure is 117 hours.

Is it emphasizing skills? No; learning a skill, such as using a standard formula, is the goal of about 60 per cent of American mathematics teachers, compared with 27 per cent of Japanese teachers.

Is it emphasizing mathematical thinking? Yes; exploring and understanding concepts and discovering multiple solutions to problems is the goal of the lesson for 71 per cent of the Japanese teachers, compared with 24 per cent of American teachers.

The Japanese approach to teaching mathematics is similar to what Canadian faculties of education recommend. Each Japanese mathematics lesson is designed around solving a single problem. The typical lesson flow is:

1. The teacher poses a problem. Each student is expected to come up with a solution. (The teacher does not demonstrate how to solve the problem.)

2. The teacher facilitates discussion about the solutions because the goal is to develop students' understanding of the mathematical concepts and skills embedded in the problem.

3. This is followed by practice, usually on a blackboard.

Traditional teaching does occur in Asia. China is an example. Why then do Chinese students outperform their North American counterparts? A good part of the explanation concerns who teaches mathematics and how teachers relate to each other.

As early as Grade 1 in China, specialists teach children, with the teachers moving around to different classrooms. For example, a mathematics specialist might teach mathematics to a total of 50 children in a school day. Lesson preparation is therefore low in volume and so is teacher stress.

As well, Chinese teachers are expected to collaborate on a daily basis in order to learn from each other and to share useful teaching techniques. These circumstances lead to high-quality lesson preparation. Part of the traditional teaching involves variation and an emphasis on mathematical thinking, understanding and explaining. In other words, the typical lesson is not simply about doing worksheets, with the teacher monitoring what students are doing.

Is there any hope of implementing a similar organization of teaching duties in Manitoba? Not as long as the provincial government and the Manitoba Teachers' Society control the matter.

Another claim by Zwaagstra is faculties of education should fold their chalkboards and quietly disappear into the cloakroom because they are isolationist in thinking. Interesting! University has an abundance of isolationist groups. It is the nature of a specialist and university is inhabited by specialists.

One could easily argue instead that faculties of education should divorce themselves from the university because of the traditional teaching (lecturing) that happens in many university classes, because of the irrelevant courses that pre-service teachers have to take in their undergraduate degrees (BA, B.Sc.) and because of the doctrine of "publish or perish" that dominates university life, a doctrine that discourages education professors from focusing on what is important -- namely preparing quality teachers.

Maybe Las Vegas might offer such a divorce.

Jerry Ameis is a faculty member in the faculty of education at the University of Winnipeg.

The Learning Curve is an occasional column written by local academics who are experts in their fields. It is open to any educator from Winnipeg's post-secondary institutions. Send 600-word submissions and a mini bio to

Republished from the Winnipeg Free Press print edition February 25, 2012 J12

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