Week of September 14th – Problem Solving

“I used to think math was useless… but then I realized that decimals have a point!”

– Anonymous

Class Review

This week we spent time examining the math curriculum, specifically taking time to explore the four step problem solving model (See Ontario Math Curriculum Grade 1-8 pages 12-13). Before we discussed this concept, we participated in an activity and discussed how our efforts aligned with the four step model. The problem was called, “the Handshake Problem” and was posed like this:

If you have a room full of people and everyone shakes hands, how many total handshakes are there?

       We were instructed to solve the problem without searching for the answer on Google and were given free use of several manipulatives as well as paper and pens. We were asked to explore the solution in as many ways as possible. My group chose to model this scenario in our small group of 6 students in order to discover the pattern that could give us the solution. We then proceeded to add 29 + 28 + 27…. + 2 + 1 = 435. This is the correct solution. However, we were interested in learning about processes. Each group shared how they explored the question and many groups used a formula, made a table, or added just like we did. After sharing the processes with each other, we were given more time to use the manipulatives to show the answer.
Here, we used a geometry board and elastics to show the solution:
This is our 4 person version of the handshake question.

We also used blocks to show the solution as well:

This is a 5 person model – count the blocks to find the handshakes.
       So what did we learn? Well, this activity allowed us to examine the four step problem solving model (from the curriculum above) using concrete examples that we had experienced. To (1) understand the problem, we had to talk about what we needed to find with our group members. Next, (2) we made a plan and chose one strategy to try and solve the problem. We (3) carried out the plan, then analyzed the results and attempted our model solution on the bigger problem. Finally, (4) we looked back at our solution and explored different methods to arrive at the same answer.

Some reflection..

              There is a negative opinion of math, a society created negative opinion. It is “cool” to complain about how bad one may be at math and is a social “faux-pas” to be a math genius. As an elementary student, I had positive experiences in mathematics. I really excelled. In high school, the abstract concepts and poor teaching changed my opinion. Math became a burden, a course I needed to get into university. In university, math took a new meaning for me.. it became mostly about statistics. One of my favourite courses I took in university was my kinesiology statistics class because it taught me about real, relevant and interesting math applications. Its hard to argue that if we cannot make math meaningful and relevant, the opinions of our students will stay the same.
       In my opinion, a good math teacher will allow students opportunities to learn according to different learning styles. They also must make math more relatable and continue to offer students opportunities to work with multiple manipulatives. They should also consider allowing multiple ways for students to express their knowledge and understand. A good math student needs to drop the stigma at the door. They need to be receptive of the teacher’s efforts to be creative and interesting and just trust in the process. In essence, it is a team effort. The student and teacher need to work well for a beneficial experience.
        I look forward to learning more about mathematic teaching strategies for multiple grade levels and how to assess student’s progress on their abilities.
– A

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