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.
Michael Daiga and Shannon Driskell
The two provided activities are geared for students in middle school to facilitate and deepen their understanding of the arithmetic mean. Through these activities, students analyze visual representations and use a special type of statistical thinking called transnumerative thinking.
Kyle T. Schultz and Stephen F. Bismarck
A geometric approach using exact square manipulatives can promote an understanding of the algorithm to dismantle radical expressions.
Trena L. Wilkerson, Tommy Bryan, and Jane Curry
Using candy bars as models gives students a taste for learning to represent fractions whose denominators are factors of twelve.
Jeffrey J. Wanko, Michael Todd Edwards, and Steve Phelps
The Measure-Trace-Algebratize (MTA) approach allows students to uncover algebraic relationships within familiar geometric objects.