# Another Lovely Learning Day, Part Two

The other day I wrote about my morning session for the summer conference of PCTM (The Pennsylvania Council of Teachers of Mathematics) and today I will write about a session I attended. Unfortunately, child care considerations meant I had to leave at lunch time on Friday but I did have the pleasure of attending a session led by Dr. Daniel Ilaria of West Chester University in Pennsylvania. Professor Ilaria had one of his students, Kaitlin Nora Silard, along with him. She is about to begin her student teaching in the fall. The presentation was titled Learning to Persevere in Problem Solving and its description sort of sang out to me as something that would be of interest to me personally and that might be a great talking point for my department this year. They did not disappoint.

One of the highlights of the discussion – as it should be at a valuable PD event – was the opportunity to share ideas with other educators. There were about a dozen of us in the room and Prof Ilaria was terrific at allowing space for us to discuss and debate. His student Ms Silard was excellent as well. At one point after presenting a problem on the projector Ms Silard walked by and saw I had a solution and I had put my pen down. She looked at my work and simply said ‘Why don’t you try to find another way to solve this?’ Awesome for her and an important reminder for me. I should not let myself get away with a ‘Do what I say, not what I do’ type of attitude. Below is the problem we were working on at the time:

My original approach to this problem is what I would call an additive approach. In figure 2 I saw a row of 3 on top of a rectangle that was 2 by 3 and then 2 left over on the bottom row. In figure 3 I saw a row of 4 on top of a rectangle that was 3 by 4 with 2 left over on the bottom row. In figure 4 I saw a row of 5 on top of a rectangle that was 4 by 5 and then I saw 2 left over on the bottom row. I generalized this as (n+1) + (n(n+1)) + 2 which simplifies as n^2 + 2n + 3