In the past year there has been a pretty big battle around the future of mathematics education in Canada. People who actively engage in the debate have dug in their heels and carved out a good old fashioned Us Vs. Them fight. In Ontario the fight has most visibly polarized people around the strand of Number Sense and Numeration (pg 9). On one side there’s a group that wants a return to arithmetic basics. On the other side there’s a group that wants a focus on discovery math.
Both groups want students to have a good sense of numbers, but I’m not sure either group is right. After spending the better part of last week at an inservice with one of our math resource teachers, Bart Vanslack, I’m starting to think that our biggest need (within the Number Sense strand) is a new way of looking at numbers. We need to start seeing numbers as being flexible. //giphy.com/embed/JW31Daaaegqgo
The way Bart explained it (forgive me Bart if I got this wrong) is that some basic memorization is needed when it comes to number sense. This might be akin to high frequency words that primary readers memorize to help build their reading fluency. Students need those initial math building blocks to help them build speed and fluency. Having said that, if fluency is ever to grow into comprehension (a deep understanding of math), students have to be able to see how they can break numbers apart and how they can rebuild numbers. Young mathematicians need to understand (as Bart said) that “numbers are flexible and we can play with them to make them work for us”.
I would argue that when we look at numbers in this way, not only do we empower our students to ditch the calculators, fingers and other manipulatives that infuriate back-to-basic-ers, but we also build their overall numeracy.