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Reasoning and ProofSession 04 Overviewtab atab bTab ctab dtab eReference
Part C

Defining Reasoning and Proof
  The Reasoning and Proof Standard | Inductive and Deductive Reasoning | Thinking About Reasoning in the Classroom | Questions and Answers | Connecting to the Other Process Standards | Summary | Your Journal
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One of the major goals of mathematics education is to help students learn to think and reason. Middle school students should begin to move from reasoning and proof based on observations to reasoning and proof based on combining facts in a logical way.


Reasoning and proof is not an isolated topic to be taught on specific days; rather, it should be integrated into all aspects of the middle school mathematics curriculum. Here is what a middle school mathematics classroom that incorporates reasoning and proof into a lesson might look like: First, students are engaged in a rich mathematical task that not only develops a mathematical concept, but also encourages students to extend their findings to more general situations. Students may begin the task individually or in groups. However, an essential part of the class is for students to have the opportunity to share and justify their reasoning to other students or to the teacher. A variety of materials and tools are available for students to use as they complete the task. The teacher is actively involved in asking questions that support students and move them forward without taking over the process of thinking for them. There are many opportunities for students to share different strategies that encourage diverse thinking. Through these classroom interactions, students are expected to reason mathematically, justify their ideas, and evaluate their own and others' thinking.


video_alt: "Mathematics as reasoning is a focus on providing the why, the explanation, the clarity to what we're doing in mathematics. Not trying to learn things to be done just in isolation without any other way to validate than using the student's answer key or the teacher's authority. In this way, we're trying to have student say, "I can show you why it's true." (Henry Kepner, Reasoning Standard video)


next  Questions you might ask students about the Frosted Cube Cake problem

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