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Courses | Software | Readings | Links Good Software | Strategic Software Use | Mathematics Learning Culture | New Questions | Challenge and Support | Comments?

© 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:

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 UseTeachers may encourage strategic software use through the creation of a learning environment within which:

- students are
comfortablewith 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 developmentof 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 investigationis 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 strategiesfor 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

Courses | Software | Readings | Links Good Software | Strategic Software Use | Mathematics Learning Culture | New Questions | Challenge and Support | Comments?

© 1996: The University of Newcastle: Faculty of Education