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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## Difference Not Deficit: Reconceptualizing Mathematical Learning Disabilities

### Katherine E. Lewis

## 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.

## Early Understanding of Equality

### Aisling Leavy, Mairéad Hourigan, and Áine McMahon

One of the first math symbols introduced=the equals sign=underpins much of the algebraic reasoning a child will use in later years.

## Norms and Mathematical Proficiency

### 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.

## Virtual manipulatives to assess understanding

### 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.

## An Appetite for Fractions

### 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.

## CCSSM: Examining the Critical Areas in Grades 5 and 6

### 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.

## Winning the “Hundred Years' War”

### Luann Voza

Arm your students for victory in the age-old battle to master subtraction with regrouping.

## Fractions and the funky cookie

### Aimee J. Ellington and Joy W. Whitenack

A mathematics specialist has great success using a pattern-block configuration to help a small group of fifth graders understand that fractional parts of a whole unit must be equal in size. That's just the way the funky cookie crumbles.

## Math by the Month: Speedy Gonzales

### Patricia O'Donnell and Amanda Frick

Do you remember clever, energetic Speedy Gonzales, “the fastest mouse in all Mexico,” one of the animated characters in the Warner Brothers Looney Tunes cartoon series? This month our “math by the month” activities, reminiscent of the spirited Speedy, will have your students calling ¡Ándale! ¡Ándale! ¡Arriba! ¡Arriba! (colloquial Spanish for “Come on! Hurry up!”) as they ask for more problem-solving scenarios based on this month's racing theme.