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.

### Terri L. Kurz

People who lay tile for a living use mathematics every day to decide how much tile, grout, and other supplies are required to complete each job. Measurement and geometry are an integral part of designing tile patterns. Collections of short activities focus on a monthly theme that includes four activities each for grade bands K–2, 3–4, and 5–6 and aims for an inquiry or problem-solving orientation.

### Jennifer M. Tobias and Janet B. Andreasen

Using the context of restaurants and ratios to find equivalent fractions can push students' strategies forward.

### Signe E. Kastberg and R. Scott Frye

How do classroom behavioral expectations support the development of students' mathematical reasoning? A sixth-grade teacher and his students developed this example while discussing a ratio comparison problem.

### Christine C. Benson, Jennifer J. Wall, and Cheryl Malm

Are third graders ready to connect procedures to concepts of area conservation, distribution, and geometric interpretation?

### Pamela Edwards Johnson, Melissa Campet, Kelsey Gaber, and Emma Zuidema

Three preservice teachers used virtual manipulatives during clinical interviews with students of elementary school age. The technology exposed students' problem-solving strategies and mathematical understanding, promoting just-in-time teaching about the target content. The process of completing and reflecting on the interviews contributed to growth of the preservice teachers' technological pedagogical content knowledge.

### Trena L. Wilkerson, Tommy Bryan, and Jane Curry

Using candy bars as models gives students a taste for learning to represent fractions whose denominators are factors of twelve.

### Katie L. Anderson

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.

### Drew Polly and Chandra Orrill

To support mathematics educators as they consider implications of the Common Core State Standards for Mathematics (CCSSM) for instruction and assessment, Teaching Children Mathematics is publishing a series of feature articles. In this fourth installment, authors Polly and Orrill suggest implementation strategies for grades 5 and 6. A final, cohesive article will appear in the August 2012 issue. Authored by Susan Jo Russell, the last piece concentrates on the implementation of the eight Standards of Mathematical Practice (SMP) and the constellations of Practices and Standards.