This study focused on understanding the evaluation of the area of a rectangular region as a multiplicative relationship between the lengths of the sides. The analysis of data from a whole-class teaching experiment involving prospective elementary teachers resulted in the development of a description of the quantitative reasoning involved. Important aspects of this reasoning include the anticipation of a rectangular array of units as the structure of the area quantity and the subsequent constituting of the units based on the linear measures. The analysis of the prospective teachers' understandings proved useful in generating additional problems. The teachers' engagement with these problems resulted in their developing more complete understandings of the constitution of area units.
Martjn A. Simon, Associate Professor. Department of Curriculum and Instruction. Chambers Building. University Park. PA 16802
Glendon W. Blume. Associate Professor, Department of Curriculum and Instruction. Chambers Building, University Park, PA 16802