New School Year Resolution – Get going with my blog! I’ve been intending to begin a website for a few years now, with only one entry to show for it. There have been many times I’ve written most of a blog in my head, only to not get it onto my website. This week that happened again, however whether it was because of how strongly I was feeling about the topic, or because I could carve out an hour this morning, I actually am putting the words down and sharing some of my thoughts on an emotionally charged subject – the statements made by the conservative party this week regarding changes in the way we teach math.
I am a common ground person. By this I mean I regularly try to listen to what people are saying (whether or not I agree with them) to see if there’s something I can learn and to determine if there is common ground between us; a place where we can start from and build both of our understandings. I don’t feel the media often takes this stance. Every opinion is polarized which results in a very conflictive mentality in this, and many other debates. For awhile I’ve been considering the common ground in the memorization vs conceptual understanding debate that is ongoing. I have a few thoughts on this that I would like to share.
Misunderstood Common Ground 1: Students need to be automatic with their facts. Believe it or not, Ontario educators do believe this! It’s in our curriculum, and it’s foundational for later success in math. However, HOW we do this is likely an area for discussion. Students who build automaticity through rote drill have very little to fall back on if their memory fails them – they have efficiency, without conceptual knowledge. On the other hand, students who have many ways to determine a fact, but without efficiency will spend so much time figuring out 7 x 8 that they forget why they were calculating it in the first place – they have conceptual knowledge without efficiency. So, can we find common ground here? I’d like to think it’s in a place where students are provided lots of opportunities to build conceptual understanding of number relationships (i.e. inquiry problems, number talks and strings, math discourse, etc.), and as they build an understanding of strategies to work with numbers, they also have the opportunity for purposeful practice. This may look like drills, but the key word here is PURPOSEFUL. If students are considering how to use their understanding of 10 times to know their 9 times facts, then they engage in games and drills to practice this UNDERSTOOD STRATEGY. This is very different than a drill to memorize 9x without conceptual understanding.
Misunderstood Common Ground 2: Memorization is one important component of learning. For a number of years, I was not on board with this, until I revisited my definition of memorization. I realized that I was defining memorization as something that must be based on rote practice only. It wasn’t until I had the opportunity to ask Jo Boaler a question about the Black Cab drivers that she has referred to in her talks that this became clear for me. She clarified that yes, the cab drivers have memorized the countless complicated streets and routes in London, but this was based on driving and experiencing them, thereby creating a mental map of the area. This can’t be achieved through rote drill. This was a moment of realization for me that memorization through experience, building conceptual understanding and strategies is critical to creating important pathways in our synapses. As concepts are understood, there can be time for repeated practice – but it is purposeful and helps to build automaticity based on understanding.
It is my deep hope that as we embark on this journey of curriculum reconsideration under a new provincial party that we can keep in mind our common ground and ensure that we are basing important decisions on clear understandings and research. We need to remember that our number one common ground is the goal of supporting the development of strong mathematicians to prepare them for a future that is sure to include problem solving, critical thinking, creativity, and definitely mathematics.