This weeks Math Pod podcast with Cathy Fosnot was about teaching math in context – making it relevant to students and teaching it as something they will need to use, rather than a bunch of skills they might find helpful in certain jobs or when they have to balance a chequebook or figure out their discount at the clothing store sale, and thank goodness for fractions if we want to double our cookie recipe!
In August of this year I was at a Summer Institute session put on by leaders in my board. Someone (I want to say it was the Director, but I might be wrong) said, “If kids want to know why and the only answer you have for this is ‘Because I said so.’, then you are not prepared enough.” Or something like that anyway – that’s not necessarily the exact quote. I’ve thought a lot about this since and was thinking about it again while I was listening to this podcast. I’m noticing more and more how important it is to have a “why” attached to every single thing we teach. In my first real classroom teaching assignment (in 2000), I taught grade 5. I was the math teacher on a rotary team, which meant I taught math 3 times each day. It was a great experience. I can picture a boy in my first class so clearly saying to me, “But why do I need to learn to ‘Guess and Check’ to solve problems? I hate that strategy! I don’t like writing down guesses that are wrong and having to start again. I want to figure it out in my brain and then write down the correct answer.” That is a direct quote. He inspired me to go looking for the “why” of Guess and Check, which was a favourite problem solving strategy for the math textbook publisher whose books we used. Because I needed to give him a why (and thank goodness I realized I needed to!) I spent time figuring out this strategy, and realized it was more of an estimation strategy than a real guess. That changed my teaching of this strategy because I realized what it meant, and how and when to use it. Can you believe I was a teacher before I ever learned this? Well, I was. (I’m putting the blame for that on my math teachers, who are all probably enjoying a lovely pension cheque right about now, and congratulating themselves on a fabulous career.) Later in the year, I was teaching multiplication of fractions. Before multiplying, we would “cross reduce” the fractions so we didn’t have to reduce big numbers in the end. The same boy wanted to know why this works. I couldn’t tell him. It was a big school and there were 13 other math teachers in the building, including one working on her doctorate in math education, and not one of them could tell me why this works. There we all were, university educated teachers, teaching this “strategy” (or is it a trick?) to hundreds of kids year after year, and nobody could actually explain it. Weird, right? But those two experiences, and a few others that year, and the year before when I was on a short term assignment in grade 7 and grade 8 math classes, showed me how important it is to know the math deeply before teaching it, or at least be willing to learn it along the way.
Early on I found that, especially when teaching math, I really had to consider what my students already knew, or already needed to know, before we could launch into an activity. I taught grade 5 for a while, with a really nice textbook to follow, and I taught kindergarten for one super long year. But most of my career has been in grade 3/4 split classes. Every year I’d find myself thinking, “Why don’t they know this? Why do I feel like I am starting from scratch?” Then I taught a grade 2/3 split for the first time and really looked carefully at the grade 2 curriculum for the first time. I realized my grade 3 students didn’t know certain things because I was the first person teaching it to them. I knew that was true about multiplication and division. However, I didn’t realize how true this was when I was teaching fractions, or making graphs. The
amount depth of work in these two subjects in grade 3 compared to grade 2 is huge. This seems so obvious now, and maybe a bit embarrassing to admit, but I spent so much time looking at my own curriculum requirements that I didn’t have time to look at a different grade. That’s what learning the Landscape of Learning has done for me. I’ve stopped thinking only about what the curriculum is asking, and looking more at what the students are doing, what skills they have and which strategies they use, and then going from there. I know that I need to pay attention to curriculum. I know that! And I do that. But I don’t feel constrained by that. Are they meeting those standards? This is a question I have to ask as I prepare report cards. Have I covered that material? Of course I have to look at that. But as with reading and writing, I feel like I am moving students toward their personal next steps more and more, and we are doing this along a nice trajectory instead of trying to jump to a level that we are not ready for, and then floundering.
My biggest take-away from the last round of VoiceEd podcasts with Cathy Fosnot is that I don’t need to pre-teach skills before starting a unit. I will admit to having thought that before. But I am not doing that at all this year, and I find it so interesting to see students really build the strategy for themselves. I think this gives them a purpose for using the strategy. They have seen it work, they have used it to solve a big problem so it makes sense to them. This shift has really changed how I am approaching the Math in Context units. I love how Cathy says that our math teaching shouldn’t be about some rich tasks, but rather a series of tasks that build one upon the other to help students progress in their understanding of math concepts.
I also love how Cathy Fosnot keeps talking about opening students up to the aesthetic of math, rather than just teaching them some useful skills. The useful skills are important, but we have to go a bit further than that.
I’m reaching the end here and want to have a really good summary paragraph that pulls all of my points together. But this is more of a rambly kind of brain-purge. Hopefully not in an “Oh, dear. It’s Sunday night and this woman has to be in charge of 22 little people tomorrow. Someone do something!!” kind of way, but more of a “She’s experiencing some cognitive dissonance. Excellent!” kind of way.