Observing Student Representation
 Introduction | Estimating Blocks | Problem Reflection #1 | Counting Blocks | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Reflection Questions | Your Journal

Take some time to reflect on the questions below. Select "Show Answer" to see our comments or if you need help thinking about the questions.

 Question: How do the physical and written representations in this problem help students show their thinking? Show Answer
 Sample Answer: When students group the beans into tens and represent the groups on paper, they are beginning to put together notions of place value. Some students will have a deeper understanding and will begin to realize that counting by 10 is a more efficient way to represent their thinking. This is a nice example of differentiation and will require teachers to probe student thinking by asking such questions as, "Why did you group the blocks by tens?"
 Question: How does the use of representation help students reinforce the connection between place value and counting? Show Answer
 Sample Answer: Grouping by tens makes counting larger quantities more manageable. Recording the groups and connecting the idea of, for example, 12 groups of 10 to the quantity 120 supports and reinforces the meaning of place value in the number system.
 Question: How do representations provide a context for developing strategies for making good estimates? Show Answer
 Sample Answer: Students often think of estimating as making a "wild" guess. By using representations of a quantity as a basis of comparison, students begin to develop a strategy for making reasonable estimates. The more experience students have with this type of activity, the more adept they become with making estimates.
 Question: What role does communication play in supporting the development of mathematical thinking using representations? Show Answer
 Sample Answer: The representations themselves are a form of communication. Students communicate their thinking by writing, drawing pictures, and using models. When students explain their representations, they reinforce their understanding as they communicate with their classmates and teacher.

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