About a month ago a colleague of mine Kyle Pearce wrote a post “Does memorizing multiplication facts hurt more than help.” It was a very interesting read and I happen to agree with Kyle’s point of view. As many of my frequent readers of this blog know, I prescribe to the constructivist approach to learning mathematics. I believe that students through discovery and proper guidance will be able to understand a wide load of big ideas and theories. Not only do I believe this but I have witnessed this first hand with my students in every grade that I have taught.
However, this is not so for many people. In fact it was a discussion on Kyle’s blog post (feel free to read the thread) that has me thinking more and more about this topic. And not only thinking about it but trying to fix and insight thoughtful discussion around the ways in which we are teaching math.
Maybe a little background first. Math has been a hot topic for the past year, if not for the last century. For many countries, provinces, and states, math curriculum has undergone a significant change from what we grew up with as children. Some. like myself, believe that these changes are for the better, some have not. I was recently at the OAME and listening to Brent Davis a professor at University of Calgary. In his lecture he shared that the reason math curriculum was introduced was so we could have a work force to crunch numbers, nothing more and nothing less. As we have evolved beyond that (not saying fact crunching is not important) our skills have also changed and I think this is what we need to remember; we have evolved.
For this reason I and many others are proposing a more balanced approach to mathematics. Lets stop this war and needless debates and get to teaching good mathematical practises. One in which our students will push their thinking and really think about the numbers.
If it was up to me this is what I would include:
1) Math should be linked to Big Mathematical Ideas:
I think this is the first step to thinking about our students as mathematicians. Catherine Fosnot (2002) has some very interesting work around making our students mathematicians. One of the most interesting facts is there was a study done with so many mathematicians and they were asked to solve a problem. Not one of those mathematicians solved it the same way. I found this interesting because that is what I see math. Math is about the mathematics and there is not one way of doing things. We have to teach our students the understanding, the flexibility and the patience to be mathematicians.
2) Math is about real numbers:
Students need authentic experiences to learn. Let’s think about ourselves and how we learn. Now some do learn through reading and replication but if you honestly think about how you learn a concept the best; it is through trail and error and than guidance from a mentor. This is the same for our students. They need real experiences so that they can play and discover the mathematical concepts. In my personal experience both in tutoring high school students and teaching mathematics in the primary and junior divisions it’s the contexts that allow students to really understand what they are doing. It’s the context that helps them build models of representation. In my classroom, these are often done through social justice problems and real life contexts.
3) Students need time to explore:
This goes hand in hand with the above comment. As much as we need instruction, we also need exploration. Students need time to make mistakes, reflect, debate and discuss. These experiences allow students to make connections between concrete and abstract thinking. I was reminded at the OAME that every mistake makes a new synapse in the brain. We need these mistakes I order to solidify our learning.
4) Students need Mentors:
They have never been taught fractions from me before this and in fact as a class we haven’t even started the unit. However, that being said think about their learning and the role they play and the role that I play as a teacher. Where do my questions come from? Why did I ask them at the time I did?
6) Repeated Practise:
What are your thoughts? Don’t you think it is better to discuss and fix our problems rather than lay blame about which is better? Shouldn’t we think about our students first and their needs in their 21st century world? Love to here your thoughts.