Supporting dynamic conceptions of area and its measure

Abstract

Design research was conducted to investigate the development of dynamic conceptions of area. Students used simple physical instruments, squeegees, and paint, to generate rectangular areas continuously as a sweeping motion of one length through another. Then, they dissected the resulting swept space into discrete units of measure by coordinating measures of the lengths of the sides, including side lengths measured in different units, such as “squeegee” and inch. Analysis of classroom discourse, formative assessments, and flexible interviews conducted 2 months after instruction illustrated that students developed dynamic images and meanings of area and its measure. These expanded their understanding of multiplicative product to include referent-transforming quantity and provided means for re-envisioning the meaning of the commutative and distributive properties of multiplication. Students employed these properties to relate fractional and whole number area products. Dynamic generation and dissection in tandem helped students bridge discrete and continuous conceptions of area and its measure.