**Engagement and creativity through online inquiry**

*Brian Ridpath reports on how the inquiry developed:*

My hope for that day was that the students would try to find a way to combine the objects they were looking at and then eventually discover how to add and subtract a matrix. I started with the whole class looking at the prompt and asked them to write comments about what they noticed. Of course, many asked what they should do with all those numbers. I said nothing. But a few said they saw that 1 + 3 = 4 and 1 - 3 = -2. Immediately after this insight I gave the students three **r****egulatory cards**: **Work in a group to continue.****Ask questions for two minutes then work in a group.****Continue to work as whole class.**

They voted roughly 20 - 1 to work in a small group (we have a polling tool that is easy to set up and have students choose). I am able to cruise through groups and ask questions or spur them on or just watch and head to a group that is struggling to start. I had six groups of four that day and four groups were able to come up with a reasonable conclusion while two were on their way at time stop. One of the groups had started labelling entries as A1 + B1 = C1 and so on, while another group had colour coded the pairs.

We came together and I had one group explain their results, and then I showed results from other groups especially the A1 notation and colour coding and asked them why they were doing that. A student-led discussion with my questions ensued and we worked from labelling and colours to spreadsheets until a student said we could always use numbers and write A(1,1) to refer to a specific number. Eventually, to wrap up, I summarised their main points for addition of matrices, the labelling of elements and the relationship between the two. I sent them on their way with a few practice problems at that point.

The students' self-assessment of the activity was positive and in general I have found more participation in class. *They did well and I was completely surprised by their creativity and questions, which were much more to the point. They were definitely more willing to attempt things.* I would like to extend the time the students think and work. I see that I have to train them to develop their sense of adventure and inquisitiveness further.