Geometric knowledge of middle school students in a reform-based mathematics curriculum

School Science and Mathematics, Apr 1998 by Carroll, William M

A number of reform-based curricula attempt to implement the current research on how students learn geometry. Often these curricula apply a problem-solving-based approach, as suggested by the NCTM Standards (NCTM 1989,1991). One of these reform-based elementary programs in widespread usage is the University of Chicago School Mathematics Project's (UCSMP) elementary program, Everyday Mathematics. The UCSMP curriculum differs from more traditional mathematics programs in several ways. First, much more emphasis is given to topics traditionally underrepresented in elementary school, such as geometry, statistics, and algebra. Geometry receives an especially strong emphasis at all grade levels. For example, at fourth grade, 5 of the 13 instructional units focus on geometric skills and concepts, including investigations of two- and three-dimensional figures, properties of symmetry, measures of angles, and area concepts and skills. Because mathematical connections and representations are also stressed, children develop an understanding of geometric relationships while learning other mathematical topics. For example, in an introduction to equivalent fractions, fourth graders use pattern blocks to represent the relationships between the fractions.

Second, many activities in the UCSMP curriculum are hands on, with students using pattern blocks, straws and connectors, geometric templates, compasses and protractors, and other manipulatives and tools. In this way, students investigate properties and relationships, rather than simply memorizing names or rules. Activities emphasize applications of geometry, often relevant to everyday life, and lessons and activities emphasize reasoning, problem solving, and discussion, both in whole class and small group formats. While time is spent in kindergarten and first grade identifying and naming geometric properties, more attention is given in later grades to investigations of geometric figures and discussions of how they are related. In many ways, this structure and sequence matches the van Hiele model: Geometry is included as an important topic at each grade, students explore shapes at their own level of reasoning, and activities move from simple identification toward meaningful investigations of the relationships and properties.

This study was conducted in conjunction with the field test of the sixth-grade UCSMP curriculum. The purpose was to investigate the geometric understandings of students using one of the reform-based mathematics curricula. Given the generally poor performance of U.S. students in geometry, it was expected that students who have used the UCSMP curriculum since kindergarten would have a much stronger knowledge of geometry. However, while some research studies have shown that students can make good progress when provided with a rich variety of geometric activities, these studies are generally short-term projects in which small groups of students receive intensive work under the direct supervision of experts (e.g., Fuys, Geddes, & Tischler, 1988). Less is known about the progress of students who have studied geometry as an integral part of their mathematics curriculum throughout elementary school. In short, this study examined the question, what level of geometric reasoning might students in typical classes reach when curriculum is the treatment?