Summer and Ideas and Structure (Oh My!)

There’s been a bit of a hiatus on the blog for the past year, but we’re back! Rest assured, we’ve been busy bunnies the whole time. Now that summer has started we’re hopping into high gear with some fresh faces on the team and lots of familiar ones. We’ve hit the ground running and are excited to share the work we’ve been doing. 

Our new main direction for this summer’s work is to direct our focus to the intermediate levels, grade nine and ten. The first problem that we looked at in our group meetings was one involving parabolas and tangent lines, with the idea that we might be able to get it into grade nine classrooms. That specific problem turned out to work with more ideas from the grade ten curriculum, but we’re still interested in getting more of the structures from the problem into other formats more suitable for introduction earlier on. One of our mantras is “start early.”

Some grade nine students may have difficulty with the algebraic concepts surrounding parabolic graphs and their transformations, but are there ways to introduce them geometrically first? The graphs that generally make it into grade nine classes are of straight lines, and parabolas offer a richer understanding of graphical transformations that will be valuable if they can be introduced in a manageable way. 

One of the ideas we’re exploring is that of using what we might call “apps” to enrich the curriculum. These are pieces of mathematical structure that students can work with even when they don’t fully understand how they work. This applies to things like giving students a formula for a tangent line to a curve at any point before they’ve encountered the ideas of calculus that would allow them to derive such a formula for themselves. Introducing concepts this way allows for problems to fit into the “low floor, high ceiling” approach, in which one problem can offer richness and interest for a wide range of skill levels. 

We’ll keep you updated as things progress!

Peter Taylor Quote of the Week: “Be prepared to modify your objectives.”