## Response to article on Multiple Representations

July 13, 2010The article I read discussed an experimental curriculum put into place by middle school teachers that involved multiple representations.

Multiple representations in math classes refers to the fact that algebraic problems can be solved using different methods. For example, a problem may be solved using an equation, a graph, or a table. The emphasis on computational skills does not help students make the conceptual shift to the meaning and use of variables. This hinders their development of algebraic thinking. The idea posed in this paper is that by focusing less on the rote procedures and more on the conceptual representations of algebraic problems students will become more capable problem solvers. (Moseley; Brenner 5)

Research has shown (Mayer, 1989)that the process of solving a word problem can be broken up into four parts: Problem representation, solution planning, solution execution, and solution monitoring.

The authors used an experimental curriculum on the focus group that was based on real life problems that might come up in the running of a pizzeria. The control group was taught in a teacher centered approach while the focus group was encouraged to work cooperatively to problem solve the situations. They were guided towards multiple representations by the teachers when needed but were left to their own devices most of the time. Through their experiment, the authors found the students with the experimental curriculum that was based on the ideas of multiple representations for the same situations had a much higher success rate when trying to solve word problems that could be modeled algebraically. Not only were they more successful in solving the problems but they correctly represented the problems with variable expressions.

Multiple representations are a great way for students to begin their understanding of the important idea of variables and how they impact algebraic thinking. For the past two years I have been teaching a program that we get through Carnegie Learning that is based on the idea of multiple representations. In every section we are using real life scenarios and writing equations, graphing results and creating tables. I also teach a “regular” algebra 1 and I do not have the same focus on multiple representations that the Carnegie Learning text does. I have noticed that my Carnegie students have a much higher success rate on open ended questions that require students to create their own equation or expression.

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