My grade 8 students just spent 40 minutes working on this problem:
A circle with a area = pi is tangent to the x and y axes of a grid. What is the distance from the centre of the circle to the origin?
Other than defining “tangent” for them, I didn’t give them any other hints. They were able to solve the problem using the knowledge that they have just acquired about Pythagorean Theorem, along with their prior knowledge of x-y co-ordinates and the area of circles. The class is a mixed-ability class (as all math classes are at my school), but I had grouped students in similar-ability groups for this activity. As a watched students working on the problem, I was impressed with a few things…
- The level of engagement was high for all students, regardless of ability level. They seem to be much more motivated to persist with difficult tasks when they can work collaboratively.
- All groups were challenged by the problem. While I had expected one group in particular to breeze through it, they didn’t solve it as quickly as I thought they might. Instead, they took their time, engaging in a rich (and lively) debate about whether the assumptions they made were valid.
- All groups were able to solve the problem. A few groups needed a prompt or correction at some point along the way, but even the students who generally struggle with math experienced success.
I am becoming increasingly convinced that students to their best work when they work together. What does that mean for assessment?