Well, the EQAO (Ontario's provincial testing) results are out. Although there are a lot of things I could rant about (like how we should scrap it altogether, or decide to keep our children home during the testing, etc.), I just want to address the discouraging trend of our grade 6 math scores getting increasingly lower.
I have been an elementary school teacher for 20 years. My degree is in Music (which will actually be relevant as you read), but I am a classic "left brain" kind of person. I think mathematically. In fact, my career path into teaching was an 11th hour left turn from a career path in engineering, which occurred about mid-way through grade 12. My commentary is not founded upon any research but on my observations. However, if the current approach to math teaching is to be measured in a scientific way, using actual data, ten years of declining math scores should be all the evidence we need in order to suggest that, whatever research the current methodologies are based on, they aren't working.
First, the differences in math and music are not as vast as one might think. I would even suggest that the differences between so-called "right brain" and "left brain" are also not as vast as one might think. If you can't see that a good math solution can involve elegance and creativity, then you are probably not very studied in math. And if you can't see how any of the arts (ie. visual art, music, dance) depend a good deal on patterning, logic, sequence, shape, proportion, and physics, then you're probably not very studied in the arts either.
I was talking to a music teacher colleague of mine about how we learn music. At first, much of it is by rote. We don't have kids figure out through discovery how to read notes on the staff. We teach them by giving them explicit strategies. We don't have kids figure out through discovery how to play a Dm chord on the guitar, or how to play a G on the trumpet. We teach them explicitly. At this point, our students are mostly just parroting the things they have learned by rote. No problem.
And bit by bit, we get less reliant on the rote stuff and we begin to internalize things. We understand it, not merely academically, but intuitively. After a while, we can pick up our instrument, and all that rote learning and technical practice coalesces into something more, and music just begins to "happen" - almost as if it were just a part of us.... as if our hands were guided by the musical impulses in our brains.
But wait! We're talking about math.
First, let me be clear. We absolutely MUST engage our students with genuine problem solving that connects to their real-life experiences. This is not only about making math relevant to our learners, but this is also about bringing students past the rote learning and into actual the actual thinking that is required in order to actually *do* math. Just because you can plunk out Happy Birthday on a piano doesn't mean you know music, and just because you can multiply 3-digit numbers doesn't mean you know math. It just means that you can follow a rote series of steps.
Before asking kids to solve problems, though, we need to give them the tools to do so. Good, reliable, sharp tools. This means being able to recall from memory what 7 x 4 is, or how to divide one number by another - automatically. The current state of teaching puts the cart before the horse. We ask kids to solve problems, and in the course of solving those problems, they discover clumsy methodologies to circumvent their lack of basic tools. And we call that learning.
Let's say we ask two people to build a table. That is the real life problem. It has to be big enough to seat four people comfortably, and sturdy enough to support a weight of 50 kg. Just like in math, there are a lot of possible solutions to this problem. Just like in math, my solution might not be the same as yours, but as long as we achieve a solution that works to the same problem, then we are both right. If your table falls down, no matter how fancy you got with it, it's still a failure of a table - just like in math.
But our current (as in for about the last ten years or so) methodology of math instruction will say to give kids some wood and a variety of found objects and have them use their "existing schema" to go build a table. So, they'll lever pieces of wood with rocks and stuff to try to break the wood into the appropriate sizes and shapes. Maybe they'll gouge away at it with a spoon from their lunch, eventually wearing through something vaguely resembling a cut. They'll glue and tape the corners. And it will be an awful little table on virtually any measure - except it was one that they did themselves without any help. And then we'll de-brief at the end and talk about what strategies they used, what worked and why, and what didn't work and why, and what we might be able to do in order to make a better table as a next step.
I say, give them tools - sharp tools, and precise tools - and teach them how to use those tools. Practice cutting a few scrap boards. Practice drilling. Be by their sides while they do so to make sure that they are doing it right. THEN ask them to build a table. They will make far superior tables in considerably less time. THEN they can talk - knowledgeably - about what strategies they used, what worked and why, and what didn't work and why, and what we might be able to do in order to make a better table as a next step.
As we begin to internalize those rote strategies used in math, we begin to understand it, not merely academically, but intuitively. After a while, we can pick up our pencils or our calculators, and the math - like the music - will just begin to flow out of us in a way that seems natural and intuitive. But it won't happen without developing and practicing the foundational skills first.
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