Rethinking teaching strategies : a framework and demonstration through augmenting Maple

Paraskakis, Iraklis (2001). Rethinking teaching strategies : a framework and demonstration through augmenting Maple. PhD thesis The Open University.



In this work, an interdisciplinary approach has been adopted for the study of
• teaching strategies of an Intelligent Tutoring System, in the paradigm of multiple teaching strategies, and
• the use of Computer Algebra Systems (CAS) in teaching problem solving in university mathematics.

As a result, the SIMTA (Styles Implemented by Methods Tactics Actions) theoretical framework has been developed to support and sustain teaching strategies in the paradigm of multiple teaching strategies. TeLoDe (TEaching Linear Ordinary Differential Equations), is a prototype Intelligent Tutoring System, teaching the ,solution of linear second order differential equations with constant coefficients in a novel way. This novel way, which has been empirically tested, has been achieved by augmenting Maple and represents an alternative use of CASs where the human lecturer and Maple are interlocked in a symbiotic and interdependent manner.

In SIMTA, the contemporary concept of teaching strategy is rethought and proposed to be viewed at two fundamental levels:
• the organisational level
• and the operational level.
The organisational level deals with the structure of the teaching strategy whereas the operational level deals with the manifestation of that structure.

In SIMTA the organisational level is represented by a triple generic structure, method, tactic(s), action(s). A method is a mechanism for structuring the subject matter (e.g. analogy, examples, generalisation, specialisation). Likewise, a tactic is a mechanism for facilitating the interaction (e.g. explicit interaction, implicit interaction). An action is a low level activity such as display this message, ask this question.

In SIMTA, the exact manifestation of the above generic structures (analogies, examples, implicit interaction, explicit interaction) depends on the concept of style: different styles result in different manifestations of the same generic structures. Thus, in SIMTA the concept of multiple teaching strategies is seen as merely a collection of teaching strategies manifested under the same style. These strategies operate with the aim of offering alternative representations of the same task at hand and ensuring that the lea~er is active by activating, directing and maintaining exploration.
To help demonstrate the feasibility of SIMTA, two styles, the expository style and the , guided discovery style have been formed. The expository style draws on Ausubel's theory of meaningful learning, whereas, the guided discovery style draws on Bruner's work. These styles have been implemented in TeLoDe.

TeLoDe, incorporates a teaching strategy module, based on a style, and declarative knowledge. Its purpose is threefold:
(i) to serve as a research tool for the SIMTA framework,
(ii) to serve as a prototype, demonstrating clearly how a 'second generation' CAS which undertakes the procedural aspect of mathematics allowing the human tutor to concentrate on its conceptual aspect, could be developed,
(iii) to demonstrate how Maple and human lecturers are given clear roles which are, nevertheless, interdependent in carrying out the teaching of university mathematics.

Two small-scale empirical studies were carried out in order to test SIMTA and TeLoDe respectively. The first study involved lecturers whereas the second study was carried out in a classroom environment. The results found from these studies demonstrate that TeLoDe has a potential as a teaching tool for problem solving in university mathematics in a novel way.

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