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© 1996: The University of Newcastle: Faculty of Education
The Nature of the Tool Use
A range of factors was discerned as defining the nature of the tool use. These were found to include:Within this context, five specific dimensions of mathematical software use were identified:
- purpose (whether for verification of results, for representation, manipulative support, exploration or simply for convenience);
- goal-directedness (the extent to which goals were well-defined and achievable, and the persistence shown in working towards these);
- versatility (particularly with regard to the use of a range of tools and access to several appropriate representations);
- confidence (in both use of the software tools and in the mathematical results obtained);
- motivation (both intrinsic, resulting from interest and curiosity, or extrinsic, resulting from the demands of teacher or assessment).
- Level 0: Non-Use: Although the software is available and appropriate, and the user has sufficient skill, no use is made.
- Level 1: Passive: The user is content for the tools to be operated by another, but takes no personal initiative.
- Level 2: Random: Use is not goal-directed and bears no relation to the instructional context.
- Level 3: Reflexive: The user makes superficial and automatic use of appropriate tools.
- Level 4: Strategic: Use of the tools is deliberate. goal-directed and flexible, frequently involving multiple strategies for both exploration and verification.
Encouraging Strategic Use
Teachers may encourage strategic software use through the creation of a learning environment within which:
- students are comfortable with the available software tools. The interface should support ease of entry of mathematical forms and make the range of mathematical functions clearly available.
- mathematical tasks lie within the zone of proximal development of the students. Students must perceive the task as potentially achievable, although beyond their present capabilities unaided.
- students must be able to elicit from the task a mathematical object which is capable of signalling appropriate action strategies involving the integration of mathematical and computer-based actions.
- open-ended investigation is perceived as a valid means of achieving a solution, which may be only one of several appropriate responses to the task.
- The use of multiple strategies for verification must be perceived as a necessary component of mathematical enquiry.
- students must be motivated: persistence and some measure of personal commitment to the solution process must be evident.
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.
Characteristics of GOOD software
A culture of mathematics learning
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© 1996: The University of Newcastle: Faculty of Education