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Susanne Prediger, Kirstin Erath, Henrike Weinert, and Kim Quabeck

Empirical evidence exists that enhancing students’ language can promote the mathematics learning of multilingual students at risk, whereas other target groups (e.g., monolingual students, successful students, both with diverse academic language proficiency) have hardly been considered. This cluster-randomized controlled trial (N = 589) investigates differential effects for these extended target groups, comparing two language-responsive interventions (with or without vocabulary work) and a control group. The regression analysis reveals that all students significantly deepened their conceptual understanding in both interventions. Unlike what was anticipated, multilingual students’ growth of conceptual understanding had no significant additional benefit from integrated vocabulary work. These findings call for promoting language-responsive mathematics instruction for all students and for using a discursive rather than a vocabulary focus.

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Daniel Frischemeier

Bar graphs are fundamental to display distributions of categorical variables in primary school. Here is an approach using TinkerPlots™ to create bar graphs on different representation levels in small and large data sets.

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Mindy Kalchman

Process-oriented, question-asking techniques provide a framework for approaching modern challenges, including modality pivots and student agency.

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Megan H. Wickstrom

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

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Ming C. Tomayko

A series of activities uses media coverage of a natural disaster to develop quantitative literacy.

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Amanda L. Cullen, Carrie A. Lawton, Crystal S. Patterson, and Craig J. Cullen

In this lesson, third graders were asked how many degrees is a full rotation around a circle. After we gave students time and space to disagree, to make and test conjectures, and to explore, they reasoned about angle as turn and determined a full rotation is 360 degrees.

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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.

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LouAnn H. Lovin

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

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Tracy E. Dobie and Miriam Gamoran Sherin

Language is key to how we understand and describe mathematics teaching and learning. Learning new terms can help us reflect on our practice and grow as teachers, yet may require us to be intentional about where and how we look for opportunities to expand our lexicons.