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Magister Educationis - MEd / Problem-solving in Mathematics is an important skill. The poor performance of South African learners in international tests such as the Trends in International Mathematics and Science Study (TIMSS) and in schools in general indicates that emphasis should be placed on problem-solving in the teaching and learning of Mathematics. The new national senior certificate curriculum in South Africa encourages group work amongst learners. The thesis proposes that learning is enhanced in a small-group setting, since learners actively engage with the problems. Furthermore, Euclidean Geometry is perceived by learners to be a „difficult‟ section of Mathematics. However, Geometry is important since the skills acquired while doing Geometry can be applied to various fields of study. This research focused on Geometry problem-solving in collaborative small-group settings. An inductive approach was taken that focused on what learners were doing while they were doing problem-solving in geometry in collaborative groups. Problem-solving is viewed as a situated and contextually-determined activity. The research focused on how learners appropriated tools (physical as well as intellectual) and how they interacted with one other and the subject matter. The socio-cultural perspective was the theoretical framework underpinning the study. In this perspective, learning is seen as a social process in which learners actively participate and contribute with ideas and arguments. In addition, learning is seen as a situated activity. The research was carried out in the form of a case study that focused on three groups of three learners each, from a secondary school in Khayelitsha, a township approximately 30 km outside Cape Town, South Africa. The small groups were monitored and observed in a school setting and special attention was given to their interaction within their group, given their social and cultural context. The ethnographic approach to data gathering, which allows for the routine, everyday, taken-for-granted aspects of school and classroom life, was used. Data were collected by means of audio and video recordings, interviews with learners and teacher observations. The data analysis included analysis of field notes, audio and video transcripts and learners‟ written work. The data were analysed in terms of Pickering‟s theory that all scientific practice is a “dialectic of resistance and accommodation” and that this constitutes a “mangle of practice” (Pickering, 1995).

"The purpose of this study was to investigate the conjecture that instruction in the strategies of Pattern Discovery, Trial and Error, Working Backward, Contradiction, Substitution, and Use of Diagrams would result in the development of problem-solving ability and that students under this instruction are likely to exhibit better achievement than students who do not receive explicit instruction in problem-solving strategies"--Introduction. / Typescript. / "August, 1985." / "Submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: Eugene D. Nichols, Professor Directing Dissertation. / Includes bibliographical references (leaves 78-85).

This research extends a tradition of distributed theories of mind into the implementation of a distributed problem solver. In this problem solver a number of ideas from Minsky's Society of Mind are implemented and are found to provide powerful abstractions for the programming of distributed systems. These abstractions are the cauldron, a mechanism for instantiating reasoning contexts, the frame, a way of modularly describing those contexts and the goal-node, a mechanism for bringing a particular context to bear on a specific task. The implementation of both these abstractions and the distributed problem solver in which they run is described, accompanied by examples of their application to various domains.

Scientific communnities have proven to be extremely successful at solving problems. They are inherently parallel systems and their macroscopic nature makes them amenable to careful study. In this paper the character of scientific research is examined drawing on sources in the philosophy and history of science. We maintain that the success of scientific research depends critically on its concurrency and pluralism. A variant of the language Ether is developed that embodies notions of concurrency necessary to emulate some of the problem solving behavior of scientific communities. Capabilities of scientific communities are discussed in parallel with simplified models of these capabilities in this language.

Thesis (Ph. D.)--Ohio State University, 1984. / Includes bibliographical references (leaves 183-188). Available online via OhioLINK's ETD Center

Thesis (M.Ed.)--Memorial University of Newfoundland, 2005. / Bibliography: leaves 41-44.

This qualitative research study explores the complex phenomenon of intuition within the Creative Problem Solving process. The first part of the study utilized 100 alumni, students, professors, and visiting professors of the International Center for Studies in Creativity (ICSC). These participants were asked a series of questions in order to help the researcher answer the questions: How do creativity practitioners construe intuition? What role does intuition play in the Creative Problem Solving (CPS) (Miller, Vehar & Firestein, 2001; Noller, Parnes & Biondi, 1976; Osborn, 1953; Puccio, Murdock & Mance, 2006) process? The second part of the study involved eleven graduate students enrolled as Creative Studies majors at ICSC who were participants in a course on holistic approaches to Creative Problem Solving. The study explored the questions: Are intuitive tools and techniques effective in CPS? If so, when are they effective? When CPS is taught from a holistic perspective, is transformation likely to occur? Four theoretical models, including: a definitional model of intuition; a skill set for intuition, a process to improve the effectiveness of intuitive tools; and a transformational model of learning, were developed. These models were designed as a way for creativity practitioners to understand this phenomenon and to incorporate it into their practices.