Defining Communication
 Introduction | Developing Mathematical Ideas Through Communication | Analyzing and Evaluating the Thinking of Others | Additional Strategies | Your Journal

Earlier, in Part B, we considered a problem about whether two triangles were the same shape. Now see how this problem was used in a classroom.

Kyle and Ravi are fourth-grade students. Below is Kyle's response to a question that is designed to encourage his reflection about the thinking of others and to reconsider his own understanding. As you read what Kyle says about Ravi's statement, think about the value of such an activity to Kyle.

 Teacher: Why did Ravi say that these two triangles are not the same shape? Kyle: I think they're the same because they're both right triangles and not different, like one triangle and one square are different shapes. But, if Ravi thinks "same shape" means "congruent," like it does sometimes in math, they aren't congruent because one is larger than the other. The larger one looks like it was stretched or put on a copy machine to make a bigger right triangle. To be congruent, they have to match exactly, like two puzzle pieces that have matching sides and matching angles.

It is important for students to have opportunities to share and compare their ideas with others in pairs or small groups as well as in large-group discussion. This helps students reflect and build on their own understanding of the mathematics by contrasting their ideas to the ideas of others. Designing classroom experiences around having students working in groups enables students to verbalize their thoughts, ask one another questions, and clarify their understanding as well as misunderstandings.