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De Hoyos, Maria
Languages: English
Types: Doctoral thesis
Subjects: LB, QA
The aim of this study was to generate a model (or theory) that explains students’ concerns as they tackle non-routine mathematical problems. This was achieved by using the grounded theory approach as suggested by Glaser and Strauss (1967) and further developed by Glaser (1978; 1992; 1998; 2001; 2003). The study took place in the context of a problem-solving course offered at the undergraduate level. As methods of data collection, the study made use of the problem-solving rubrics (or scripts) that students generated during the course. Other sources of data included interviews with the students and observations in class.\ud \ud The model generated as a result of this study suggests that problem solving can be seen as a four-stage process. The process was labelled ‘solutioning’ and is characterised by students trying to resolve the following concerns: Generating knowledge; Generating solutions; Validating the results, and Improving the results.\ud \ud The model also makes reference to pseudo-solutioning as an alternative approach to solutioning. During pseudo-solutioning, instead of trying to resolve the concerns listed above, students focus on trying to satisfy the academic requirement to submit an acceptable piece of work. Thus, pseudo-solutioning can be seen as an important variation to solutioning.\ud \ud After presenting the model of ‘solutioning’, the study provides an illustration of how it can be used to describe students’ processes. This is done in set of case studies in which three problem-solving processes are considered. The case studies provide a view of how the model developed fits the data and serves to highlight relevant patterns of behaviour observable as students solve problems. The case studies illustrate how the concepts suggested by the model can be used for explaining success and failure in the processes considered.\ud \ud This study contributes to the study of problem solving in mathematics education by providing a conceptualisation of what students do as they try to solve problems. The concepts that the model suggests are relevant for explaining how students resolve their main concerns as they tackle problems during the course. However, some of these concepts (e.g., ‘reducing complexity’, ‘blinding activities’, ‘transferring’) may also be of relevance to problem solving in other areas.
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