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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Beware of “Gaps” in Students’ Fraction Conceptions
Patrick L. Sullivan, Joann E. Barnett, and Kurt Killion
Building Algebraic Procedures From Concepts: Like Terms
Leah M. Frazee and Adam R. Scharfenberger
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.
Digital Learning Routes: An Example of Mathematical Modeling
Salomé Martínez, Flavio Guiñez, and Darío González
An online activity provides instructional strategies that can help students engage in mathematical modeling and autonomous learning.
Broken Ceiling Lights: Circular Area Without the Radius
Nicholas J. Gilbertson
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.
Problems to Ponder
Chris Harrow and Justin Johns
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.
Using Public Records to Scaffold Joint Sense Making
Keith R. Leatham, Blake E. Peterson, Ben Freeburn, Sini W. Graff, Laura R. Van Zoest, Shari L. Stockero, and Nitchada Kamlue
Teachers can more productively use board work to scaffold joint sense making.
Construct It! Progressively Precise: Three Levels of Geometric Constructions
Carmen Petrick Smith
This article shares an activity scaffolding the construction of the circumcenter of a triangle, culminating with a Triangle-Ball Championship game.
Construct It! Triangle Puzzle Challenges
Enrique Ortiz
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.
Discuss It! Collaborating on the Tortoise and Hare Task
K. Ann Renninger, Maria Consuelo De Dios, Annie Fetter, Maeve R. Hogan, Moe Htet Kyaw, Ana G. Michels, Marina Nakayama, Richard Tchen, Stephen A. Weimar, Helena Werneck de Souza Dias, and Feven Yared
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.
Imagine It! Choose Your Own Pattern Block Adventure
Anita A. Wager, Brittany Caldwell, and Jamie Vescio
When given the opportunity to play with mathematical materials and ideas, children demonstrate their mathematical understanding in innovative ways.
