Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

CONCLUSIONS

The simplicity of the KidCAD software stands in stark contrast to the excitement of dynamic geometric construction, the measuring and conjecturing tools now widely used in secondary schools. We argue, however, that the secret of the success of any educational software as a vehicle for promoting mathematical power lies not merely within the software itself, but in the way that the software supports students' experiences with mathematical concepts and allows students to make mathematical models. The success of the experiences described in this chapter lies in the way the curriculum and software supported students in making mathematical models of their real-world classroom space and in checking those models against reality by physically measuring distances and objects on their printouts and by comparing what they had created to the creations of other students. This connection between online and off-line activities-- this negotiation between model (the scale drawing) and reality (the actual space and the real objects inside it)--stands in strong contrast to many computer learning experiences and is what made these activities a powerful learning experience.

One last thought, a caution. Looking at the differences between students' freehand drawings of their classrooms and the scale representations produced by KidCAD, we cannot fail to notice that the gain in mathematical visualization, seen in the latter, is accompanied by a loss of the individual perspective, imagination, and creativity seen in the former. As educators we must be careful not to stress "mathematical" as superior to "artistic." It would be a shame if through this type of experience students come to feel that their own personalized, idiosyncratic representations of the world around them are somehow less important, or less useful, than the uniformity and consistency of the computer-assisted scale drawing. We need both mathematics and art to enrich and give meaning to our lives and to our work.


REFERENCES

National Council of Teachers of Mathematics. ( 1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

Papert, S. ( 1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.

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