This thesis examines children's arithmetic strategies and their relation to the concepts of commutativity and associativity. Two complementary methods were used in this research: empirical studies and computational models. Empirical studies were carried out to identify the strategies children used for solving problems like 3 + 4, and 3 + 4 + 7, and the conceptual knowledge associated with them. Their understanding of subtraction problems where the minuend is less than the subtrahend (e.g. 6-8) was also considered. A study with 105 subjects revealed a variety of strategies and information about children's knowledge of commutativity and associativity. Four levels of performance of commutativity were also identified. A longitudinal study was carried out with 12 children in order to obtain details of children's changes in strategy, and to double check the results obtained in the main study. The strategies observed to be used by children over a 20 month period parallel those found in previous studies, which show a general transition to more efficient methods. However, the longitudinal study revealed that development of such arithmetic strategies is a slow process. Furthermore, the studies indicated that knowledge of commutativity is a prerequisite for associativity. Models of the observed strategies have been implemented in the form of production rules in a computer program called PALM. The process of implementation highlighted features of children's problem solving that had not been 'detected during the studies. In addition to models that describe the space of strategies, a model of learning has been implemented for the transition from procedural knowledge of commutativity to that of associativity. The model is capable of generalizing its inbuilt knowledge, for instance, its ability to solve 2-term arithmetic expressions, to allow it to solve more complex problems, such as 3-term arithmetic expressions. A further model has been constructed for learning arithmetic strategies that are more efficient than those already represented in the program. It learns specific rules by adding conditions for efficient problem solving to its previous general rules.

As the range of models which tutoring systems can capture is extended, efficient diagnosis becomes more difficult. This thesis describes a solution to this problem based on the generation of 'Critical Problems'; their role in student modelling is analogous to that of the 'Crucial Experiment' in science. We argue that great diagnostic power can be obtained by generating discriminatory problem examples. In general, efficient diagnosis is just not possible without such an hypothesis-testing capability. We describe a program, PO, which given a pair of production rule models and a description of the class of problems which the student must solve, generates an abstract specification of the problems which discriminate between those two hypotheses. Through a process termed 'Abstract Interpretation', PO tips the balance in favour of diagnostic measurement. The key to this problem lies in the realisation that we are only interested in the abstract mapping between a model's inputs and outputs; from the point of view of generating a Critical Problem, the intermediate processing of the model is irrelevant.

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One of the greatest problems facing researchers in the sub field of Artificial Intelligence known as Intelligent Tutoring Systems (ITS) is the selection of a knowledge base designs that will facilitate the modification of the knowledge base. The Class-Entity-Relationship-Attribute (CERA), proposed by R. P. Brazile, holds certain promise as a more generic knowledge base design framework upon which can be built robust and efficient ITS. This study has a twofold purpose. The first is to demonstrate that a CERA knowledge base can be constructed for an ITS on a subset of the domain of Cretaceous paleontology and function as the "expert module" of the ITS. The second is to test the validity of the ideas that students guided through a lesson learn more factual knowledge, while those who explore the knowledge base that underlies the lesson through query at their own pace will be able to formulate their own integrative knowledge from the knowledge gained in their explorations and spend more time on the system. This study concludes that a CERA-based system can be constructed as an effective teaching tool. However, while an ITS - treatment provides for statistically significant gains in achievement test scores, the type of treatment seems not to matter as much as time spent on task. This would seem to indicate that a query-based system which allows the user to progress at their own pace would be a better type of system for the presentation of material due to the greater amount of on-line computer time exhibited by the users.

This paper sought to accomplish three goals. First, it provided a systematic, comparative review of several intelligent tutoring systems (ITS). Second, it summarized problems and solutions presented and solved by developers of ITS by consolidating the knowledge of the field into a single review. Third, it provided a unified language from which ITS can be reviewed and understood in the same context. The findings of this review centered on the 5-Component Framework. The first component, the domain model, showed that most ITS are focused on science, technology, and mathematics. Within these fields, ITS generally have mastery learning as the desired level of understanding. The second component, the tutor model, showed that constructivism is the theoretical strategy that informs most ITS. The tutoring tactics employed in the ITS stem from this paradigm. The third component, the student model, describes the several ways ITS infer what a student knows. It described the variety of data that is collected by an ITS and how it is used to build the student model. The fourth component, the interface, revealed that most ITS are now web-based, but vary in their capacity to interact with students. It also showed that user experience is underreported and ought to be included more in the research. Finally, the fifth component, learning gains, demonstrated that ITS are capable of producing learning gains equivalent to a human tutor. However, reporting learning gains does not seem to be a focus of the literature.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 124-127).

Thesis (PhD)--University of South Australia, 1998

Thesis (M. Sc.)--University of Canterbury, 2007. / Typescript (photocopy). "June 2007." Includes bibliographical references (p. 117-135). Also available via the World Wide Web.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Model Tracing; Intelligent Tutoring Systems; JESS production system; Debugging Tool; Cognitive Tutor Authoring Tools. Includes bibliographical references (p. 58-60).