As a teacher, sometimes I was pretty good at showing students lots of different ways to solve a problem. I often wasn’t so good at asking them to make sense of *when* to use these strategies, hence Idea #4: Choose your own strategy.

Once students have developed some understanding of different ways to approach a particular type of problem, we need to have them make sense of when to use which of these strategies. My favorite way to do this is to just make this the whole task. For example, instead of having students graph the following lines or lines containing the given points,

I would instead ask them to:

Choose the strategy (calculator, determining two points and connecting them, using the slope and y-intercept, mental math*, etc.) you would use to graph each of the problems and explain your thinking.

*mental math means you can do it in your brain without showing work. Students should still explain what their brain is doing.

Notice, I didn’t ask them to actually graph the lines; they’ve already practiced that. Instead, I asked them to think about *how* they would graph the lines. The difference is subtle, but important. When we say our students aren’t making sense of the math, it’s often because they never had to do so. If we design tasks where this is the entire goal, they will grapple with choosing a strategy and, consequently, get better at it. As a bonus, you can also have students share their choices. If students choose different strategies for the same problem you can have an interesting discussion about the different reasons behind those choices. Having students realize that different strategies just make for different adventures en route to solving a problem is just another great benefit of this idea!

If you want another example of lesson that uses this idea, a few years ago my friend and frequent collaborator Sam Otten and his brother Andrew (who is a math teacher) created a lesson on systems of linear equations that was published in the Mathematics Teacher.