New Tools for Mathematics Learning:

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USING THE TOOLS EFFECTIVELY

In observing the ways in which individuals chose to make use of available mathematical software tools, I learned much about both the tools and the users. The study revealed a strong preference for the graphical representation across all groups of participants. A much greater reluctance was observed regarding the use of computer algebra tools. Although participants invariably spoke positively of their use of such tools and found them helpful in a wide variety of mathematical situations, the majority rarely, if ever, chose them spontaneously. When they did use them, this was most often to verify results which they had obtained by traditional means. It appears that computer algebra tools were viewed as somehow "illegitimate." To use them to support an algebraic computation was seen as akin to "looking up the answer in the back of the textbook." This analogy is further supported by their use for verification purposes after completion of the process. While it is quite acceptable to "check your answer in the back of the book," it is a form of "cheating" if such use occurs earlier. The message was clear, from students, preservice teachers and even classroom teachers - algebra is a solitary activity which must be mastered through repetition and individual practice.

Interestingly, this conflict with perceptions of "acceptable mathematical practice" was observed only in relation to computer algebra tools; representational tools (especially graph plotters) appear to fit comfortably alongside existing instructional patterns, while tools which support the manipulations of algebra directly confront them. In considering the beliefs and perceptions of the participants in this study regarding the nature of algebra, the ways in which it may best be learned and the role of computers in this process, consistent evidence was found to support the notion of a culture of mathematics learning: a shared set of beliefs and experiences which extended across all groups of participants.

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This culture served largely as an impeding factor for the use of algebra software, characterised as it was by such features as:

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Factors such as these militate against both the use and the perceived need for open-ended software tools which support and extend mathematical learning.

The use of the tools itself took on several quite distinct forms:

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Clearly there are some dangers associated with poor use of technology. There is also a goal for all who would use technology to encourage, as some have called it, an "intelligent partnership" between user and tool, characterised here by "strategic software use."

How then may we best achieve such a goal? The evidence of my study suggests that teachers may encourage strategic software use through the creation of a learning environment within which:

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The strategic use of mathematical software tools is indicative, not only of a high level of computer-based competence, but of insightful and strongly connected mathematical thinking. Conditions under which such use may be encouraged should be a feature common to all mathematics learning situations. Use of the technology is not an end in itself; rather, the technology may serve as a catalyst, encouraging changes in the current culture of mathematics learning towards the creation of a learning environment which is active on the part of the learner, which rewards exploration and understanding rather than recall, and within which mathematics assumes a vitality and significance which has been missing for so many learners in the past.

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REFERENCES

Arnold, S. M. (1996) Learning to use new tools: A study of mathematical software use for the learning of algebra. Unpublished doctoral dissertation, UNSW.

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.

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Comments & suggestions? Contact:-smarnold@mac.com