# Browse

### Manouchehri Azita, Ozturk Ayse, and Sanjari Azin

In this article we illustrate how one teacher used PhET cannonball simulation as an instructional tool to improve students' algebraic reasoning in a fifth grade classroom. Three instructional phases effective to implementation of simulation included: Free play, Structured inquiry and, Synthesizing ideas.

### Anna F. DeJarnette and Gloriana González

Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We examined the patterns of positioning that students demonstrated during group work and how students' positioning moves related to the ways they established the resources, operations, and product of a task. Students who frequently repositioned themselves created opportunities for mathematical reasoning by attending to the resources and operations necessary for completing the task. The findings of this study suggest how students' positioning and mathematical reasoning are intertwined and jointly support collaborative learning through work on novel tasks.

### Sandra L. Laursen, Marja-Liisa Hassi, Marina Kogan, and Timothy J. Weston

Slow faculty uptake of research-based, student-centered teaching and learning approaches limits the advancement of U.S. undergraduate mathematics education. A study of inquiry-based learning (IBL) as implemented in over 100 course sections at 4 universities provides an example of such multicourse, multi-institution uptake. The study suggests the real-world promise of broad uptake of student-centered teaching methods that improve learning outcomes and, ultimately, student retention in college mathematics.

### 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.

The Connecting Research to Teaching department of *MT* invites classroom teachers to explore research findings in relation to their practice. We also invite education researchers to demonstrate how results from their studies shape classroom practice. Findings from collaborative action research projects are also encouraged. Evidence of connections from research to practice commonly includes student work and brief transcripts from interviews or classroom videos.

### 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.

### Allison B. Hintz

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

### Patricia F. Campbell and Nathaniel N. Malkus

A three-year study found that those responsible for coaching math teachers positively affected student academic progress in grades 3, 4, and 5. Read why this effect took time to emerge.

### Gayle Millsaps

Preservice elementary school teachers (PSTs) often have difficulty understanding hierarchical (i.e., class inclusion) relationships between geometric shapes. In particular, PSTs' predisposition to place squares and rectangles in separate categories can be attributed to their concept images. Although the larger mathematics community prefers the hierarchical definitions of special quadrilaterals, the concept images of special quadrilaterals such as squares and rectangles that PSTs develop in their early experiences contribute to a preference for partitional definitions. This study examines the benefits and limitations of using the Shape Makers curriculum unit to modify preservice teachers' concept images and their definitions of special quadrilaterals.