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Beware of “Gaps” in Students’ Fraction Conceptions

Many students have a dominant part-whole conception of fractions. We examine why this is problematic and explore strategies to move students beyond this limitation.

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Building Algebraic Procedures From Concepts: Like Terms

This task sequence for adding and subtracting like terms—grounded in the concepts of equivalence and algebra as generalized arithmetic—helps students see connections between concepts and procedures in algebra.

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Digital Learning Routes: An Example of Mathematical Modeling

An online activity provides instructional strategies that can help students engage in mathematical modeling and autonomous learning.

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Broken Ceiling Lights: Circular Area Without the Radius

A customer walks in to a lighting store with a broken ceiling light, and the solution to finding a replacement glass illuminates an alternative approach to finding the circumference and area of a circle without knowing the circle’s center, radius, or diameter.

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Problems to Ponder

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.

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Using Public Records to Scaffold Joint Sense Making

Teachers can more productively use board work to scaffold joint sense making.

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Construct It! Progressively Precise: Three Levels of Geometric Constructions

This article shares an activity scaffolding the construction of the circumcenter of a triangle, culminating with a Triangle-Ball Championship game.

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Construct It! Triangle Puzzle Challenges

This article presents an original puzzle that supports students’ development of visual thinking and geometry ideas based on the Van Hiele levels of geometric thought.

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Discuss It! Collaborating on the Tortoise and Hare Task

The authors share an online collaborative problem-solving activity that integrates support for students’ developing conceptual understanding, focused engagement, and positive feelings of agency and identity.

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