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Katherine E. Lewis

Mathematical learning disability (MLD) research often conflates low achievement with disabilities and focuses exclusively on deficits of students with MLDs. In this study, the author adopts an alternative approach using a response-to-intervention MLD classification model to identify the resources students draw on rather than the skills they lack. Detailed diagnostic analyses of the sessions revealed that the students understood mathematical representations in atypical ways and that this directly contributed to the persistent difficulties they experienced. Implications for screening and remediation approaches are discussed.

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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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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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Heidi L. Fleharty and Carolyn Pope-Edwards

Sixty-three teachers in a K–3 mathematics specialist certificate program conducted family projects in order to improve their skills in partnering with families around mathematics. Past studies have indicated that family involvement in children's education has many positive influences on academic achievement; however, parents' discomfort with math, and teachers' discomfort with working with parents, may be obstacles. The purpose of the present study was to examine 2 years of teachers' mathematical family projects and describe the types of projects chosen, the risks and benefits of these projects, and the quality of the parent–child interaction. It was found that the teachers implemented a variety of projects that promoted parent participation in mathematics. Teachers were also able to utilize a cycle of inquiry to examine the progress of their project. The results showed that teachers were able to create a strong connection between the math classroom and the home environment of the child, as shown, for example, by findings related to the themes of home–school connections and mathematics curriculum of the home.

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Lynn M. McGarvey

A child's decision-making photo activity about pattern identification presents implications for teaching and learning patterns in the early years.

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Jennifer Noll and J. Michael Shaughnessy

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.

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Johnnie Wilson

Observe a first-grade teacher's use of gesture as a mathematics teaching and learning tool in his classroom.

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Jon R. Star, Martina Kenyon, Rebecca M. Joiner and Bethany Rittle-Johnson

The ability to estimate is not only a valuable math skill but also an essential life skill. Many adults use estimation daily: when tipping a waitress, determining the cost of a sale item, or converting units. Within mathematics, the ability to estimate is linked to deep understanding of place value, mathematical operations, and general number sense (Beishuizen, van Putten, and van Mulken 1997) and allows students to check the reasonableness of their answers to mathematics problems in a variety of contexts.

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Tad Watanabe

“A mile wide and an inch deep” is an oftenrepeated criticism of U.S. mathematics curriculum. In 2006, NCTM published Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence to suggest important areas of emphasis for instruction. Many states produced new standards that were informed by the book. However, Charles (2008/2009) argues that we must address not only the mile-wide issue, by reducing the number of skill-focused standards, but also the inch-deep issue, by making essential understanding more explicit. Charles suggests that many useful resources are available to deal with the latter.