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.
Deanna Pecaski McLennan
Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton
We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.
Atara Shriki and Dorit Patkin
Success in STEM fields depends largely on robust spatial skills, in particular on the ability to perform a mental rotation. Given that this ability can be nurtured, this article includes examples of diverse relevant tasks appropriate for grades 6–8 students.
Sarah Brand, Hyunyi Jung, Ashley Dorlack, and Samuel Gailliot
Five teacher discussion strategies and outcomes of students’ responses to each are illustrated with examples.
Thomas Edwards, S. Asli Özgün-Koca, and Kenneth Chelst
A quadratic equation was the basis for activities involving both concrete and technological representations.
Amber G. Candela, Melissa D. Boston, and Juli K. Dixon
We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.
Erell Germia and Nicole Panorkou
We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.
Debasmita Basu, Nicole Panorkou, Michelle Zhu, Pankaj Lal, and Bharath K. Samanthula
We provide an example from our integrated math and science curriculum where students explore the mathematical relationships underlying various science phenomena. We present the tasks we designed for exploring the covariation relationships that underlie the concept of gravity and discuss the generalizations students made as they interacted with those tasks.