Sixth-grade students’ conceptions of stability in engineering contexts

Geometry, as a curricular subject for primary-and middle-school students, provides a descriptive medium by which real-world actions and objects can be described in terms of their physical properties. Geometric models can be applied to real-world problems to simplify complex problem situations, and many algebraic and numeric ideas can be fostered by looking at them through a geometric perspective (National Council of Teachers of Mathematics [NCTM], 1989). The complex spatial patterns of the real world can be simplified into component relationships such as points, lines, angles, transformations, similarity, and dimensionality, and these physically simpler (but cognitively more abstract) ideas can be operated on mentally--changed, recombined, transformed-whereas the physical objects themselves may not be. In other words, the field of geometry can be applied to realistic situations, and conversely, realistic situations give rise to geometric thinking: As Freudenthal went on to describe, the development of students’ knowledge of geometry reflects a tension between experience in an irregular world and this notational/representational system (or conceptual substratum) that explains physical reality in terms of abstract regularities. As students gain experience manipulating objects and thinking about similarities and differences of the objects, “frequently used sequences of movements establish relational links between parts of figures, between figures and their parts, and between different figures�? (Battista, 1994, p. 89). These relational links become the basis for a larger network of geometric ideas. This emphasis on realistic experience and observation is prevalent in European curricula, especially that of the Dutch (see de Moor, 1991), but is only now gaining support in the United States.