Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Exploring Representation
 Introduction | Scaling Area | Problem Reflection | Summary | Your Journal
 As we think about how to encourage students to use representations in their mathematical work, we should consider the processes we use to show our own thinking. We begin by creating a representation from the given information -- whether geometric or numeric -- to model the problem. We then decide whether we are going to draw a picture, make a table or graph, or use technology. This can be challenging, as problems often require more than one representation. In the Scaling Area problem, we used the power of the computer technology, but we also used drawings and tables to represent our thinking. Using multiple representations to break down a problem into smaller, more meaningful steps is often helpful. While using the technology and your own drawings, you had to generate many examples and then look for patterns, perhaps with the help of a table. This allowed you to reason about the problem before you could make a generalization that would apply to all rectangles or all triangles. The use of representations made these steps manageable and meaningful. Moreover, our representations gave us a way to communicate our new mathematical knowledge to others, if needed. Remember, young students will develop their own, sometimes wonderful, forms of representation to gain a deeper understanding of the mathematics they are studying and to help them problem-solve. Through questioning, you can get a better understanding of the ideas underlying these non-traditional representations. Good questions will help you determine whether students' strategies, as shown in their representations, are appropriate.
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