When we came to the end of two weeks learning all about index laws, I was struggling to come up with an activity that would get my students to really think about all the misconceptions and common mistakes related to the topic. Eventually, I decided to have them each write an end of topic test.
The test had to include 10 multiple choice questions and 5 questions that required working. The catch was that the four solutions provided for each multiple choice question must be solutions that arise from misconceptions or mistakes that are commonly made (and of course students must indicate the correct answer). This meant that students had to think about all the things that they (and their friends) didn’t understand straight away, and those silly mistakes that they just keep making.
For the last 5 questions, students were required to provide solutions, explicitly showing all steps, each with a brief explanation of what had been done, and why. I found the best way to describe this to students was to tell them to imagine teaching their little brother or sister about indices, and write down everything that they would have said.
Students had some time to start working on their test in class, which meant that (after showing some examples of what I was expecting on the board) I could walk around and clarify exactly what they needed to do for those students who were still unsure.
There were grumbles. There were complaints. There were comments that “this is stupid”.
But did they learn from it? Yes. Absolutely.
I’m not saying that every student recognised every mistake they’d ever made, and because they have identified them, will never make those mistakes again, but I definitely heard a lot of aha! moments as students discussed which answer was correct, and why.
And that’s what this was all about.
As with most tasks, the crucial component is feedback. Sitting down with students after looking through their tests and discussing any errors ensures that there are no lingering misunderstandings.
When it came time for this topic to be formally tested, students were given questions that their classmates had written, and maybe even one of their own!