Mathematical Understanding and Multiple Representations

The aspect of the authors argument that convinced me of the importance of mathematical understanding and multiple representations was the point on teaching students “using a combination of instructional practices” (Pape & Tchoshanov, 2001, p.125). This was done by using both analytical and visual means to demonstrate different representations. I agree with this approach, as all students learn differently. So by providing multiple modes of representation it allows for all students to grasp a concept in a way that they feel comfortable with, while also becoming comfortable switching between different modes of representation they are less comfortable with. As well this approach promotes collaboration between students to learn from each other. 

Kinds of mathematical representations included in this article are graphs, tables of data, written symbols, pictures, diagrams, algebraic equations and charts. Kinds of representation that are excluded in this article are virtual representations, videos and graphing software. A type of mathematical representation that was used during my time in Math 11 and 12 to demonstrate graphing different types of functions was graphing software. Although graphing was mentioned in this article as a type of representation, I found graphing software incredibly helpful for my own understanding of what functions looked like. A way I may use this form of representation in my own teaching is to demonstrate again what functions look like. However, I would use it to manipulate functions and show students how changes in the negativity, the power or inputs into the function could significantly change the way it looks and behaves. Using this type of representation also allows students to get involved with the access of technology in classrooms. They can use graphing software's to manipulate and play around with functions to see the outcomes of certain changes as a way to better understand what functions look like.