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.
This article shows how to empower students in their own learning by their own creation of instructional videos and assessment.
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.
Tiara Hicks and Jonathan D. Bostic
We describe a formative assessment approach called whole-class think alouds, which foster evidence-based instructional practices and promote the goal of assessment to promote learning. They allow students to collaborate and orally communicate their problem solving.
The questions that teachers ask to elicit student reasoning—often referred to as press for reasoning—help students explicate the concepts and principles that undergird their strategies. This article describes the term, addresses its benefits and challenges, and offers three routines.
Juli K. Dixon, Treshonda Rutledge, Jennifer C. Caton, and Edward C. Nolan
Constraints for social distancing require teachers to find creative ways to engage students. Consider this fun strategy for exploring fraction equivalence, addition, and subtraction in a game environment where students use self-made or digital manipulatives.
This article examines action research findings within a fourth-grade mathematics classroom. The researcher explores the effects of positive communication to family members on the engagement of learners receiving Tier 2 behavioral support, as well as potential considerations for building young learners’ mathematical identities.
Rui Kang, Sheri Johnson, Emily Lambert,, and Candi Davidson
Inspired by earlier articles on the classic drawing toy that targeted higher grade levels, the authors adopt and create activities that make Spirograph mathematics accessible to middle-grade learners.
Susan Baker Empson, Victoria R. Jacobs, Naomi A. Jessup, Ms. Amy Hewitt, D'Anna Pynes, and Gladys Krause
The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing this understanding are provided.
Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty
Try these meaningful alternative approaches to helping students make sense of word problems.