National Council of Teacher Mathematics Standards Vocab

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Problem Solving
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Engaging in a task force for which the solution method is not known in advance. In order to find a solution, students must developed new mathematical understandings.
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Reasoning and Proof
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Mathematical reasoning and proof offer powerful ways of developing and expressing insights about a wide range of placements. People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those problems are accidential or if they occur for a reason.
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Communication
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Is an essential part of mathematics and mathematics education. It is a way of sharing ideas and clarifying understanding.
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Connections
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When students can connect mathematical ideas, their understanding is deeper and more lasting. They can see mathematical connection in the rich interplay among mathematical topics, in contexts that relate mathematics in other subjects, and in their own interests and experiences.
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Representation
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The ways in which mathematical ideas are represented is fundamental in how people can understand and use these ideas.

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