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Jennifer Throndsen

This simple dice game supports students' development of flexibility with numbers, the properties of the four operations (+, −, ×, ÷), and the order of operations. It requires only dice and a game board for each player.

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Shiv Karunakaran, Ben Freeburn, Nursen Konuk and Fran Arbaugh

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

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Sharon A. Edwards, Robert W. Maloy and Gordon Anderson

Learning mathematical problem solving is as easy as 1, 2, 3 when teachers use flexible instructional strategies.

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Lisa Englard

Easy-to-design puzzles that encourage mathematical reasoning and promote numerical fluency, arithmogon puzzles are simple: Add the numbers in two circles to get the number in the square. Every month, this final page of the journal highlights a quick game, puzzle, activity, or instructional strategy and suggestions for teachers of different grade bands to use the idea in the classroom.

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Allison B. Hintz

Teachers can foster strategy sharing by attending to the cognitive demands that students experience while talking, listening, and making mistakes.

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Cristina Gomez and Dani Novak

Consider using these problems to help students develop number and operation sense in a simple and fun way.

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Martha Hildebrandt

This article shares ideas for using the calendar date to increase students' mental mathematics and problem-solving skills. Postscript items are designed as rich grab-and-go resources that any teacher could quickly incorporate into his or her classroom repertoire with little effort and maximum impact.

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Lisa M. Buchholz

Several detours prompted me to find time in an overcrowded school day to incorporate important, powerful, daily, whole-class application of fact strategies.

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Jonathan N. Thomas and Pamela D. Tabor

Use these descriptions of diagnostic and instructional tools to help young learners move beyond reliance on physical materials to negotiate arithmetic tasks.

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Gina Kling

Applying known facts to derive unknown facts results in efficiency, flexibility, and an understanding of number combinations for young students.