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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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Madelyn W. Colonnese

A teacher implements this type of personal prose in the classroom to help students make sense of fractions and communicate ideas.

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Sandra Vorensky

Design projects to encourage your students’ self-efficacy and motivate mathematics learning by helping them apply their prior knowledge from real-world experiences.

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Jenna R. O’Dell, Cynthia W. Langrall, and Amanda L. Cullen

An unsolved problem gets elementary and middle school students thinking and doing mathematics like mathematicians.

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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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Heidi Fee

This article shows how to empower students in their own learning by their own creation of instructional videos and assessment.

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Corinne Thatcher Day

This hands-on task, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around NCTM’s eight teaching practices from Principles to Actions, this article describes the task’s setup and implementation.

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Katherine Baker, Scott A. Morrison, and Alyssa Herrmann

This article features a third-grade multiplication exploration that integrates materials from nature and outside spaces. Teaching and learning mathematics with and in nature foster connections—mathematical, interpersonal, and with the natural world.

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Rick Anderson and Peter Wiles

Recognizing the complex nature of students’ geometric reasoning, we present guidelines and suggestions for implementing a Guess My Shape minilesson that focuses students’ attention on properties and attributes of geometric shapes.

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Corey Webel and Sheunghyun Yeo

In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a “Math Buddy") on mathematics for 30 minutes per day. We focus on the development of PSTs’ skills for exploring children’s thinking and the structures and tools that we used to support this development. Data sources include screencast recordings of interactions with Math Buddies and written reflections completed by PSTs. Although the responsiveness of interactions varied across individuals and interactions, in general, PSTs showed improvements in exploring children’s thinking. We share implications of these findings for similar field experience models and for practice-based approaches to teacher education generally.