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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.

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Eight Unproductive Practices in Developing Fact Fluency

Gina Kling and Jennifer M. Bay-Williams

Basic fact fluency has always been of interest to elementary school teachers and is particularly relevant because a wide variety of supplementary materials of varying quality exist for this topic. This article unpacks eight common unproductive practices with basic facts instruction and assessment.

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Early Mathematics Fluency with CCSSM

Gabriel T. Matney

To develop second-grade students' confidence and ease, use these three specific types of tasks that align with Common Core State Standards for Mathematics expectations.

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Assessing Basic Facts Fluency

Gina Kling and Jennifer M. Bay-Williams

Have you had it with timed tests, which present a number of concerns and limitations? Try a variety of alternative assessments from this sampling that allows teachers to accurately and appropriately measure childre's fact fluency.

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Pattern-Block Puzzlers

Cathery Yeh

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. The current article shares ideas for using Pattern Blocks to increase students' creativity and problem solving skills while extending their understanding of geometric reasoning and number sense.

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Digital Date Equations

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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Improving Preservice Secondary Mathematics Teachers' Capability With Generic Example Proofs

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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Picture it: Flashcards that Encourage Reasoning

Wendy Bray

Flashcards incorporating visual models are presented as a strategy to support mastery of addition, subtraction, and multiplication facts. Postscript items are designed as rich “grab-and-go” resources that any teacher can quickly incorporate into their classroom repertoire with little effort and maximum impact.

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Using KenKen to Build Reasoning Skills

Harold B. Reiter, John Thornton, and G. Patrick Vennebush

Through KenKen puzzles, students can explore parity, counting, subsets, and various problem-solving strategies.

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Mastering Fact Fluency: Are They Game?

Connie J. Godfrey and Jamalee Stone

Take-home binders and daily math talks help a second-grade class ease through Baroody's (2006) stages.