Exploring children's geometric thinking.

Abstract

This study examined seven 4th and 5th graders' geometric thinking, specifically their understanding in the areas of area and volume. Base Ten Blocks, Tangrams, questions on 2-D and 3-D are three categories of geometric tasks given during exploration. Data were gathered over fifteen weeks through video-taped one-on-one interview sessions as well as frequent classroom observations. Findings indicate that these students have exhibited a wide range of maturity in understanding the concepts of area and volume. Students' conceptions of area range from believing that only congruent figures have the same space, that the space occupied by figures are the same regardless of their shapes or arrangements, to the idea that the space exists in its own right whether or not it is occupied. As for volume, some students view a 3-D block as a "box" consisting of six separate sides; some recognize the interior of a block but not its connecting or shared edges; some see the block in terms of layers; one has conceptualized a 3-D cube as one coherent, integrated, and coordinated block. Moreover, the data also supports that those who are not capable of thinking multiplicatively struggle in solving problems dealing with 3-D blocks. The educational implications of this study are briefly discussed.