Activating Students as Learning Resources for one another.

Whilst Jones (2021) Wiliam & Leahy’s Five Formative Assessment Strategies in Action focuses on Peer Assessment as the primary pedagogical method for using this strategy in the classroom; my department and I have interpreted it in different ways.

Inspired by Watson and Mason (2005) Mathematics as a Constructive Activity, we have been looking at how learners’ mathematical powers can be exploited in lessons as a source that can help the lesson progress.

One way we have most commonly used this method is as an extension task where learners can be challenged to make up their own question related to what they have just been doing. This question can then be shared on the board for others in the class to attempt.

This can lead to considerable discussion:

• is it harder or easier?
• is it solvable? Why? Why not?
• how does it relate to what we’ve just been doing? How is it different?
• can you think of alternative ways to solve it?

Learners can also be asked to exemplify a general concept that they have been learning about. Additional restrictions can be added to make it more challenging. These examples can be shared without comment for others in the class to check. Do they satisfy the properties? How do you know?

Learners generating examples can expose learners to aspects of the concept that they may not have considered before; it is a way for learners to expand and refine what Watson and Mason refer to as their Example Space. This is the group of mathematical examples that learners associate with a certain concept. Expanding would include learners realising that certain things they did not consider can be included, Refining would include learners having their non-examples challenged.

I recently used this with my Year 10 class as outlined here. Asking the class to generate integer points on the circumference of circles that weren’t horizontally or vertically aligned with the centre led to discussions of vectors, Pythagoras, the distance formula and how to decide whether or not an integer point was possible. Students were asked to share their points and justify that they were on the circles — points that had been verified and agreed upon by the class were then used as points from which to calculate tangents.

Using student generated examples definitely felt like a motivator for students. It was novel and led to engagement as students tried to verify their peers’ work.

I will certainly be using this more in the future and trying to embed student examples into future tasks.