Math Education

This past week in class we had a lesson instructed to us by two of our peers. They each chose a different activity to teach a lesson from the same grade and strand of math. This pair chose to present on Grade 9 and 10 Academic math. During their presentation, I was introduced to a website provided by the National Council of Teachers of Mathematics (https://www.nctm.org/classroom-resources/illuminations/interactives/algebra-tiles/) where students could use algebra tiles to model and solve equations. This technology blew me away! I was originally introduced to algebra tiles in the fall when a partner and I prepared a lesson on Polynomials to teach to our cohort class as part of an assignment. We had never heard of or used this manipulative before, but we quickly taught ourselves how they worked and were able to use them with ease. Our lesson went very well and I found that students who were unfamiliar with the mathematical concept of adding and subtracting polynomials, or who were not ...

When I was in high school it was common for us to use graphing calculators when we needed a quick way to visualize functions. I found it fairly simple to plot a function on the calculator, but there were a lot of commands required and it was difficult to memorize all of them. I found that we needed to have a re-introduction to them every time we needed to use them. While it was fun to have an unfamiliar piece of technology to use in the classroom, it was also frustrating at times. In class we had the opportunity to use graphing calculators combined with motion censors to simulate position-time graphs. Many of my classmates had never used a graphing calculator, so it was something that was new and a change from our regular methods of problem solving and modelling. Despite our excitement, my group discovered that the technology could not connect or did not work properly once it was connected. We tried many different combinations of calculators and motion censors before we disper...

In class we were introduced to a type of activity for problem solving called the Japanese Bansho Method. Ottawa Bansho defines Bansho as "a method of teaching developed in Japan that focuses on teaching math through problem solving. It allows students to see connections and progressions of the thinking involved when developing strategies to solve a problem" (https://ottawabansho.wordpress.com/bansho-in-the-class/). At first glance, this method seemed the same as the gallery walk activity that we had used in a previous class. However, this method takes solutions one step further by having students group and categorize solutions based on level of difficulty. We began the activity by solving a problem about a class with a certain number of boys and girls in it. This appeared to be a fairly simple problem, however we were again challenged to create multiple solutions. Each different solution was written on a separate piece of paper and posted on the board. Once all of the solut...

This class built off of our previous discussion of looking to find multiple solving methods for one problem. We began by watching a TEDTalk in which a math teacher gave examples of problems and the various ways in which her students conceptualized and understood them. She mainly discussed series and how students observed patterns of growth by connecting them to other ideas. For example, one student saw the terms of a geometric series that took the shape of a triangle to be a visual representation of sand being poured into a pile. As more sand was added to the height of the pile, more sand spilled over the edges and made the base wider. I am a very mathematical thinker, so when I look at a series like the one above, I don't often think of it in an abstract way when it comes to explaining the changes. I immediately jump to the algebraic expression that is used express the series. It was very interesting for me to see into the minds of various students to understand the ways in wh...

During class, we were given a fairly simple problem involving solving for maximum area of a box. We were asked to solve the problem among our desk groups. Fairly quickly, we were able to find a solution using algebraic methods. Based on our group's advanced background in mathematics, this problem appeared trivial and was not difficult to solve. We were then asked to come up with at least one other method of solving the same problem. This should have been easy - right? Wrong. Thinking outside of what we knew proved to be more difficult than I thought. I was stumped when it came to figuring out another way of solving. One of my group members suggested using a table of values and more of a trial-and-error method to come up with a solution. This seemed so tedious and unnecessary to me, given that I already solved the problem much quicker using my own method. However, we went ahead and used the new method and came up with an identical answer. This made me think - why would anyone so...