Recently, Andrea Sands of the Edmonton Journal published an article outlining the current debate in Alberta around math curriculum. It was well-balanced and well researched. It presented both sides nicely. I sent her a short email pointing out my only concern with the article. She quotes University of Alberta Math Professor Gerda de Vries, who I have met and respect. de Vries says,
Alarm bells have been going off for a while. The students, in theory, are supposed to be better problem-solvers and that’s not what we’re seeing. And I’m getting that message from my colleagues in physics and chemistry is that the students just are not as well-prepared to solve problems.
Nowhere in Andrea’s article does she mention that de Vries and the rest of her colleagues at U of A have seen exactly one term’s worth of students who were taught using the new curriculum. Last September’s 12th grade students were the first batch of high school graduates to have any exposure at all to the revised curriculum, and they only had it for three years. If alarm bells have been going off for a while, then they were going off under our old curriculum.
Andrea replied quickly and assured me that de Vries was careful to say that she wasn’t sure whether the curriculum was the problem or whether there might be other factors at play. Unfortunately, the article fails to mention that. Andrea then asked about blending the approaches. Here’s what I sent her (slightly edited).
You’re bang on. This whole debate is a little silly. One camp thinks if we only teach algorithms, understanding will be lost. The other camp seems to think that if we only focus on understanding, proficiency will be lost. Why would we consider doing one without the other? Why is there the perception in the public that we are doing one without the other?
Bumpy is a great way to describe curriculum implementation, mostly from the teacher perspective. It takes a while to figure out what the new standards are. This curriculum was new, not so much in content, but in how we were being asked to teach. Older curriculums focused on algorithms (procedures) and hoped understanding would come along for the ride. This one flipped it so that we were to start with understanding, and have students build algorithms with that foundation of understanding. This is where things got bumpy for some of us (teachers).
The debate seems to center on two main things.
- At what point to we give students the algorithm if they are unable to develop it on their own?
- Do students have to do it one way that makes sense to them, show it to me in multiple ways regardless of their preferred method, or do it the one traditional way that many of us were taught?
The classes I taught (at the secondary level) were always based on the idea that I had to help my students get at the understanding in addition to the proficiency. I did this because when I went to University, I struggled with math at first despite doing quite well in high school. I was a great imitator. I didn’t have great understanding. My teacher would show a problem and then put the same one with different numbers on the test, which I would ace. When I hit university and had to think, I was in trouble. In addition, I had never struggled with math before, and didn’t know how to get out of trouble. This was in 1988, which is why I can say with some personal experience that this notion of students struggling in university math is not a new thing.
So when I became a teacher, I tried hard to make sure my students knew not only what to do to solve questions, but WHY that method worked. I wanted them to avoid a struggle at University like I had. Instead of starting with the algorithm, I tried hard to start with the understanding, and build the algorithm out of that understanding. In the end, whether the understanding was there or not, I had to give my kids an algorithm so they could do certain things. I just flipped it so that instead of starting with the algorithm, I started with understanding and built (or gave out) an algorithm from that understanding. To me, that’s the more effective way to teach math. I agree with your assertion that it’s not one or the other.
This may oversimply things but this debate is about proficiency (ability to DO math) and understanding (knowing WHY they are doing what they are doing and WHEN to do what they are doing). We can arrange those two things four ways.
Proficiency with understanding – I think we would all agree that this is what we are shooting for. If every kid got there, we’d be doing a great job.
Lack of proficiency with lack of understanding – Clearly, none of us want our students ending up here.
This whole debate seems to come down to how to rank the other two permutations of those two states, which is a little silly. Very few kids end up with one without some of the other.
Lack of understanding with proficiency – These kids would be able to multiply numbers quickly and efficiently. They’d struggle with why it worked, and would struggle with when to use multiplication. This was me. I could take complicated derivatives with the best of them. I had no idea at that time what a derivative represented. People who think this is the better of the other two states are happy kids can multiply without a calculator (and make change – It always seems to be about making change).
Lack of proficiency with understanding – These kids would struggle to multiply numbers quickly and efficiently on paper. They’d know what multiplication represents, and when to use it. People who think this is the better of the other two states think that kids can use a calculator for mundane calculations, and knowing why and when to multiply is the important skill.
That got long. That wasn’t my intention. Thanks for following up.