I’ve noticed recently that I’ve been doing something almost subconsciously, and I want to start doing it some more intent.
I’ve been doing this long enough that I’ve got an idea of where kids will get hung up, get frustrated, and quit. I haven’t found a way to force them through that in situ, but what I’ve learned to do is give them a particular tool a couple of days or maybe a week earlier (but never a month before) that gets them through. An early example of this is the two step helper, but even that smacks too much of actual process and math.
Here’s one I did a couple of months ago. I know that these kids would have difficulty translating slope and rise and run to graphs, or from graphs. They could tell it’s a line, but they wouldn’t be able to pick out what makes the rise, or the run.
So, before I even start with two variable equations, I had a day of drawing triangles on graph paper. They got to pick two numbers (which I conveniently decided to call the rise and the run), and had to use those numbers for the rest of the day.
I had them draw repeated triangles.
I had them draw scaled triangles.
And I had them draw flipped over triangles.
At the end of the day, they had a piece of graph paper that had a lot of parallel lines – and in particular parallel lines that were not going the same direction as their neighbors parallel lines. They learned that the rise and the run do indeed determine a unique angle, and more importantly, they learned to identify a triangle shape as being related to rise and run.
On its own, this lesson sucked. The graphs were messy, the kids thought it was stupid, and there was nothing concrete that this would ever be applicable to.
But when I taught them to graph lines a week and a half later, just about every kid could figure out the rise and run of a line drawn on a piece of graph paper, or make a line with the appropriate rise and run.