Calling for a truce in the classroom math wars

For years, Canadian parents and educators have engaged in passionate debate over how kids learn math. The math wars, especially contentious in Alberta, have pitted "old" math versus "new," or "discovery," math. But Daniel Ansari, of the University of Western Ontario, says it's time to end the wars.

The researcher says the evidence shows that the best way to teach math is with elements from both methods. He refers to the two schools as  "procedural learning" and "conceptual learning," and says they can complement each other when taught together.

Ansari says he understands why the topic is so contentious, but adds that it doesn't need to be that way. He offers his solutions for educators, and for parents too. 

The full interview is available in the audio player above. The following portions have been edited for clarity and length.

You study how children learn math. From your research, what is the best way to teach math? 

I think from my research, and also from the research of many other people, it's very clear that this is a false dichotomy between procedural learning on one hand and conceptual based learning on the other hand. So, a good teaching approach integrates both of those, and there is peer-reviewed, empirical literature, showing that integration of procedural learning — developing your fluency — but also of course understanding what you're doing, integrating those two leads to the best learning outcomes. 

So if the answer lies somewhere in the middle, why is it that the curriculum tends to swing like a pendulum between old math and new math? 

So I think that (there are) a number of reasons. First are these strong emotional associations and alliances between certain approaches, so that people are more likely to teach in one way. I've talked to a lot of advocates for the new math, teachers in school boards who feel very passionate about developing students' conceptual understanding, and I can see a lot of their arguments -- you know, they say that it really develops childrens' thinking skills, it helps them to explain what they're doing, it helps them to be more creative in their problem solving rather than just focusing on solutions. And I agree with all of that, I see a lot of merit in that, but what I would say to them is that you also need the procedural fluency, and the procedural fluency will increase and improve the way you think conceptually about math. So, for example, when you're doing a long division problem, if you can retrieve part of the answer, then that buys your working memory resources that you can devote to taking a more conceptual approach. So both go hand in hand.

What would you recommend concerned parents do? 

I think concerned parents should talk to their school boards, and talk to their teachers, and find ways in which they can perhaps motivate a more balanced approach. They can also do things in the home, so if the curriculum is very heavily focused on conceptual understanding, maybe they can do some work on the procedural skills by using certain programs that allow them to help children develop greater fluency in their skills. So parents, instead of signing petitions that want to refocus the curriculum entirely away from one approach to another approach, they should try to act as mediators to try to find a balanced approach. 

Click the blue button above to listen to the full interview.