Observing Student Reasoning and Proof
 Introduction | Completing Patterns #1 | Problem Reflection #1 | Completing Patterns #2 | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Questions and Answers | Your Journal
"Being able to reason is essential to understanding mathematics. By developing ideas, exploring phenomena, justifying results, and using mathematical conjectures in all content areas and -- with different expectations of sophistication -- at all grade levels, students should see and expect that mathematics makes sense. Building on the considerable reasoning skills that children bring to school, teachers can help students learn what mathematical reasoning entails."

## (NCTM, 2000, p. 56)

We begin this session by looking at an activity in which children take note of and describe patterns using "attribute blocks." (Note: If you haven't worked with attribute blocks before, this activity will help you become familiar with them.) Since patterning and classification form the basis of early mathematical reasoning in the primary grades, the student work in this session involves pattern recognition and classification.

Before beginning this type of activity, students should have time to explore the attribute blocks with a partner for several minutes while the teacher informally observes what the students do with the blocks. This provides the teacher with an opportunity to see whether the students are engaging with the attributes of the blocks, which helps the teacher determine how to interact with the students during the activity. Some students may already be able to sort the blocks by the values of a chosen or designated attribute, such as size, shape, or color, and others will need to have their attention called to these aspects of the shapes.

Let's begin by looking at the set of attribute blocks that students will use for this activity:

 Answer the following questions about the blocks (you might ask your students these questions as well): If you were to sort the blocks, how might you choose to do so? How would you describe the pieces by shape? How would you describe the pieces by color? How would you describe the pieces by size? How are the blocks sorted here? How are the blocks sorted here? And how are the blocks sorted here?

These are just some examples of how attribute blocks can be sorted. There are many other characteristics around which sorting and classifying can be done, for example, shapes with straight lines and shapes with curves. Can you think of other examples?

Now that you are familiar with the blocks, let's take a look at some students who are working with this problem.

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