Observing Student Reasoning and Proof
 Introduction | Sums of Numbers | Problem Reflection #1 | Products of Numbers | Problem Reflection #2 | Classroom Practice | Observe a Classroom | 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)

Reasoning is a fundamental human activity and certainly an important aspect of developing mathematical abilities. Students should be presented with challenging problems that encourage them to pose questions, formulate conjectures, justify conclusions, and make logical arguments. Reasoning and proof are closely connected to problem solving and communication.

Following are two examples of student work for you to consider. As you observe these problems, identify examples of students making and investigating conjectures, refining their thinking, and attempting to make convincing arguments.

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