We examine the effects of 3 interventions designed to support Grades 2–5 children's growth in measuring rectangular regions in different ways. We employed the microgenetic method to observe and describe conceptual transitions and investigate how they may have been prompted by the interventions. We compared the interventions with respect to children's learning and then examined patterns in observable behaviors before and after transitions to more sophisticated levels of thinking according to a learning trajectory for area measurement. Our findings indicate that creating a complete record of the structure of the 2-dimensional array—by drawing organized rows and columns of equal-sized unit squares—best supported children in conceptualizing how units were built, organized, and coordinated, leading to improved performance.
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Effects of Three Interventions on Children's Spatial Structuring and Coordination of Area Units
Amanda L. Cullen, Cheryl L. Eames, Craig J. Cullen, Jeffrey E. Barrett, Julie Sarama, Douglas H. Clements, and Douglas W. Van Dine
Students' Conceptions of Sine and Cosine Functions When Representing Periodic Motion in a Visual Programming Environment
Anna F. DeJarnette
In support of efforts to foreground functions as central objects of study in algebra, this study provides evidence of how secondary students use trigonometric functions in contextual tasks. The author examined secondary students' work on a problem involving modeling the periodic motion of a Ferris wheel through the use of a visual programming environment. This study illustrates the range of prior knowledge and resources that students may draw on in their use of trigonometric functions as well as how the goals of students' work inform their reasoning about trigonometric functions.
How to Leverage the Potential of Mathematical Errors
Wendy S. Bray
Incorporating a focus on students' mistakes into your instruction can advance their understanding.
