Strategic Software Use

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:

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).

Within this context, five specific dimensions of mathematical software use were identified:

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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