My Weekly Report and Reflection 4 (Week 6)

The content for this week was very stimulating and it sparked a lot of discussion amongst the class! Although there were no reading, phot word problems, or professional reading circle discussion this week, it was still very valuable pertaining to my knowledge regarding teaching mathematics. In particular, I enjoyed learning how to plan and create the “Structure Problem-Solving 3-part Lesson”. It was interesting to investigate our own experiences as students in math classes. I noticed that, although Brock University strictly enforces teacher candidates and graduates to create a meticulous 3-part lesson before every class, very few, if any, of my past teachers seemed to do this. I was surprised to see how much emphasis is supposed to be put on the final “Consolidation and Practice” and “Follow Up” stage. I do not recall either of these phases being areas of focus as a student. Similar to how the Entry and Reflect stages are often underplayed by students while solving a problem, the beginning (“Getting Started”) and final (“Consolidation and Practice”) stages seem to be ignored by teachers while planning the lesson. Therefore, I now know just how important each of these phases are when creating a lesson, which I will use to guide my future lesson planning as a mathematical educator.

Joyce also had us learn about, and personally practice, what is known as the “Gallery Walk” strategy. This is a method of mathematical problem-solving in which the students complete their work, then they can either post their solutions or leave them on the desk for viewing. The name suggests the next part of this strategy, during which students walk around the “gallery” and view and reflect each other’s work. We practiced this using the “Open Box Problem”, which we solved in groups of 3, then walked around and used the RUBRIC writing to reflect on our classmates’ problem-solving methods with the same question. Finally, we had a group wide discussion on what worked and what didn’t, as well as how we could facilitate an understanding of and implement this method in our own classrooms in the future. It was very insightful to listen to and observe my classmates’ reasoning behind their methods, and to explain my own techniques when solving the “Open Box Problem”. It was also useful to hear how my colleagues would plan and implement their own 3-part lesson using this problem. This not only supported my knowledge and understanding on the topic, but also provided me with a realistic way to apply this thinking into my professional practices. The small groups were also beneficial as they allowed every member to provide input into potential solutions and each one of us felt like a significant member. Our individual ideas and thoughts could be brought up to the group and considered in a collaborative effort with the others. Additionally, I found it especially interesting to see that every group thought of similar, but unique, solutions to the problem at hand. Not only did this allow us to see that there are multiple ways to figure out a solution, but also that every individual has different ways of thinking and learning. This is crucial knowledge for our careers, since we will encounter hundreds of students, no one having the same learning style. There are numerous different ways to solve mathematical problems, and there is no single “correct” strategy; so teachers must be weary of this and encourage diversity in the classroom by using differentiated instructional methods.