Problem Solving in the Mathematics Classroom

This past week, I was introduced to the activity 'skyscrapers' which is demonstrated in the picture below. Our facilitator asked us to get into groups of about four individuals, handed out some math-link cubes, and briefly explained how this activity worked. 

At first, we were all very confused and could not seem to understand the instructions. We could not figure out how this activity worked and even began saying things like “this is impossible”. I found myself feeling discouraged because I could not figure out how to complete the activity. Instead of giving up, we pushed through the phase of being discouraged and we began thinking of other ways that this activity may be solved. Without realizing it at the time, we used many strategies to try to find the answer. For example, we discussed other possible options, tried to make connections to our prior knowledge, reasoned with each other, and used representations to show our peers our ideas. I realize now that we were all using the mathematical processes in order to solve this problem. 

Earlier in the class, we discussed the seven mathematical processes. As outlined in the Ontario Mathematics Curriculum, the mathematical processes are problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representation, and communication. After completing this activity, it is evident that most, if not all, of these processes allowed our group to find the correct way to solve this problem. Since we had found the answer ourselves, we were excited to complete the activity and moved onto the more difficult problems. As I reflect on this experience, I can see the importance of allowing students to work through problems without providing them with step by step instructions. For example, if we were told exactly how to solve this activity, I believe we would not have been as excited to find the correct way to solve the problem.

This activity reminded me of using inquiry-based learning in classrooms. Inquiry-based learning begins with posing a question or problem to the class, rather than providing the students with all of the knowledge about a specific subject. This type of learning encourages the students to think beyond what they know in order to be critical and creative thinkers. It also encourages them to use the mathematical processes to solve the problem. I plan to use inquiry-based learning in my classroom because it allows students to solve problems in their own way. For example, some students may use manipulatives, whereas, some students may reason through the problem orally. As a future mathematics teacher, I know that my students may arrive at the same answer in different ways. I plan on celebrating those differences and encouraging my students to think outside the box when trying to solve a problem.