Friday, 22 September 2017
This summer, at the CEMC Math Teacher's Conference, Michael Jacob's talk, Mind the Gaps, was also very enlightening. He showed us incorrect answers, and had us work out how students came about those answers to determine the misconceptions behind those answers. It was enlightening to take the time to discern where seemingly random answers had a basis in logical, if faulty, reasoning.
The idea that it is OK and expected to make mistakes, and that doing so can be beneficial in the learning process, is reflected in the growth mindset work of Carol Dweck and the mathematical mindset work of Jo Boaler. When students never or rarely make mistakes, it may also mean that they are not being appropriately challenged.
And I thought, why not combine these ideas, and create "Forensic Fridays".
Using one or more of the following sources: incorrect student work or correct student work that uses a unique approach (either one that will work consistently, or one in which the answer is coincidentally the same but the strategy is faulty), old EQAO test examples, and CEMC math contests, I search for problems that match misconceptions associated with underlying concepts of the math we are doing in class.
On Friday, students work in pairs or small groups on the question I have posted. They must determine several things:
- is the answer correct?
- how did the person go about solving this?
- what was their train of thought for each step?
- what (if anything) is faulty about their reasoning?
- how can I prove this is correct/incorrect?
Then they must solve the problem correctly in a way that shows their strategy. As students get more comfortable, we will begin to discuss what constitutes a mathematical proof and how to use this to support their thinking.
As a class, we can create a flow chart to demonstrate how to go about these tasks together, in order to break it down for those who struggle with "just knowing" that something is right or wrong, as well as for those who might need extra support.
Since I do not currently have my own class, I have not had the opportunity to try this out. I'd love to hear your feedback if you have done something like this in your classroom.