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 poem starts with the question in the trunk of the tree, where we imagine that we are deciding to do or not to do something. Each level represents steps in making the decision, with the top indicating a resolution in the future. Phrases wander and change direction, leading to different results. How many paths to a resolution do you see?
Katherine Baker, Naomi A. Jessup, Victoria R. Jacobs, Susan B. Empson, and Joan Case
Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.
Christopher Harrow and Ms. Nurfatimah Merchant
Transferring fundamental concepts across contexts is difficult, even when deep similarities exist. This article leverages Desmos-enhanced visualizations to unify conceptual understanding of the behavior of sinusoidal function graphs through envelope curve analogies across Cartesian and polar coordinate systems.
Gabriel Matney, Julia Porcella, and Shannon Gladieux
This article shares the importance of giving K-12 students opportunities to develop spatial sense. We explain how we designed Quick Blocks as an activity to engage our students in both spatial reasoning and number sense. Several examples of students thinking are shared as well as a classroom dialogue.
This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.