Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

may be more a consequence of homogeneous learning/teaching experiences than some underlying invariant features. As such, the detail associated with each level may change. The key point for future research is that, as an evaluative tool, SOLO is sufficiently robust and fine-grained to assist such explorations.

Another major strength of the SOLO model lies in its advocacy of continued development of earlier acquired modes. Instead of being replaced by later developing modes, these earlier modes continue to evolve, complement, and support development in other modes. Research is only beginning to address this aspect of the model. Of particular interest is (a) the nature of growth in the ikonic mode and (b) how the SOLO model can be used to document integrative development involving more than one mode. Information, for this last point, would offer a valuable alternative to a strict hierarchical view of learning.

SOLO also provides the means for the van Hiele model to move to a new phase of development, namely, the exploration and explanation of individuality in geometry education. The challenge for researchers and teachers is to investigate and identify individual paths of development: to seek out variability. It is only in this way, with a move away from a single- dimension learning path, that a true understanding of the nature of individual cognitive growth in geometry can be achieved. With this more proactive and relevant stance taken, students will potentially achieve a greater understanding of geometric concepts, and many more students may be challenged in their own way, as Einstein was when, at the age of 12, he was presented with a textbook on Euclidean geometry. As he recollected years later:

Here were assertions, as for example the interaction of three altitudes of a triangle in one point, which--though by no means evident-- could nevertheless be proved with such certainty that any doubt appeared to be out of the question. This lucidity and certainty made an indescribable impression on me. ( Little, 1980, pp. 626-628)


ACKNOWLEDGMENT

The authors wish to acknowledge the support that they received from the Australian Research Council toward carrying out research reported in this chapter ( ARC Ref. No. A79231258).


REFERENCES

Biggs, J., & Collis, K. ( 1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Acadentic Press.

Biggs, J. & Collis, K. ( 1991). Multimodal learning and the quality of intelligent behavior. In H. Rowe (Ed.), Intelligence, reconceptualization and measurement (pp. 57-76). Hillsdale, NJ: Lawrence Erlbaum Associates.

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