Since I have much more class time available for students to engage in learning material, I have been playing around with various types of tasks. One of which is getting students to generate examples of questions they may be asked. Any teacher who has developed their own questions knows that doing this is more difficult that it seems. A lot of knowledge is required to make a question to which a solution may be found using prerequisite knowledge. I was teaching a unit on using properties of exponents to simplify exponential expressions. I asked students to generate a question in groups and give the question to another group to solve. I also asked them to create a potential unit test in order to build study skills. I was afraid that students would choose to create extremely simple examples and that they wouldn’t learn enough from the task. However, I didn’t realize how difficult it can be for a student to create a “simple” example. In order to know that it will be simple to solve, they need to be fluent with their knowledge. In my class, all the students decided to try to make the most difficult problem they could think of! I was shocked. It led to a lot of good discussion and I was able to clarify several key points to them through analyzing how they would solve the problem. For example, a lot of them threw in addition signs but didn’t realize how much more difficult it is to simplify rational exponential expressions with several terms in the numerator and the denominator! This stemmed from the fact that they were still unsure of the difference between multiplying exponential variables and adding exponential variables. Other nuggets came out as well. This task was so useful that I ended up putting a question on their unit test to create an example and solve it. The fact that they had to solve it themselves forced them to try to stick to using properties they understood.
I’d like to share my favorite student generated example from the group work activity:
This is truly brilliant. Is it not?