Levels of Tool Use

Non-Use

Non-use of software tools was difficult to examine directly in the context of this study since its occurrence can only be inferred rather than observed. Nonetheless, it is a most significant aspect in terms of understanding the phenomenon of mathematical software use, and must be considered at this point. The most specific instances of non-use of available tools were observed in association with the many review exercises undertaken by the students. Since they had been encouraged both to ensure to the best of their abilities that their responses were correct and to use available tools to assist in this regard, the frequent failure of individuals to do so when answering incorrectly may reasonably be considered as examples of this type of tool use.

Passive Software Use

Passive use was most clearly defined by being externally motivated. The extent to which other factors were demonstrated was dependent upon the intervention of the teacher/tutor, rather than the individual user. While confidence may have increased as a result of such use, it was also observed to result on occasion in decreased confidence and lack of understanding, particularly when the tool use extended beyond the zone of proximal development of the student. Such use by the tutor also served to discourage independence and initiative on the part of the students , and so led to limited personal commitment.

Random Software Use

Random use of mathematical software may be considered a sub-category of reflexive use. It was found only among the preservice teachers who, especially in their early encounters with the software tools, explored the limits of the "zone of free movement" offered them within the confines of the computer modules, and used the tools freely without regard for curricular context, or even any observable goal. Such use, while occasionally versatile, was observed to be low in goal-directedness and persistence.

Reflexive Software Use

Reflexive tool use appears more limited than strategic use in most regards. In terms of purpose, reflexive use is most commonly associated with verification of results and representation, and least commonly with exploration and manipulation. While goal-directedness may be high in some instances, reflexive use commonly features a lack of persistence on the part of the user, and a limited representational repertoire. In fact, such use was observed most commonly associated with a single representational category - the graph plotter. Confidence varies with such use, from very high to very low, and motivation for such use may be expected to be external, with less personal commitment on the part of the user than was observed for strategic use.

Strategic Software Use

Strategic software use may serve a variety of purposes, involving at different times all of the categories mentioned above. While open-ended exploration is most readily associated with this level of software use, it also frequently involves verification of results, which is active and often versatile (as the user deliberately and thoughtfully uses available tools as means to validate findings and to support conjecture). Strategic tool use tends to commonly involve both representational and manipulative actions as mathematical responses.

Strategic use is most clearly defined by its highly goal-directed nature. The selection and use of available tools is deliberate and thoughtful, with clear intention to achieve a particular desired end. It is frequently versatile in the use of both varied representations and a range of appropriate mathematical and computer-based strategies. Verification of results is commonly achieved through multiple sources. Confidence associated with strategic use is high, both with regard to the mathematical strategies deliberately chosen and with regard to the results achieved, and motivation may be expected to be dominated by intrinsic factors, especially interest and curiosity. While such use may have been initiated from external sources (such as the prompting of a teacher or tutor, or the requirements of an assessment task), without this critical feature of intrinsic motivation, the tool use appears unlikely to exhibit the important element of persistence, which appeared as a significant factor within this study.

"strategic software use"?

---