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Title: Using and applying mathematics : developing mathematical thinking through practical problem solving and modelling
Author: Tanner, H. F. R.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 1998
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Using and Applying Mathematics in the National Curriculum focuses on the development of reasoning skills through problem solving, and links the processes involved in learning new mathematics with the application of existing knowledge to new situations. This thesis begins by examining how mathematical knowledge is constructed and how children make sense of it. The nature of practical problem solving and modelling is considered and the literature on teaching and learning problem solving and modelling is reviewed with particular emphasis on metacognition and social practices. The research reports a quasi-experiment in which 314 pupils aged between 11 and 13 followed a mathematical thinking skills course and were compared with matched control pupils using pre-tests, post-tests, delayed texts and structured interviews. Assessment instruments were devised to assess pupils' mathematical cognitive development, their metacognitive skills and their metacognitive self knowledge. Statistical data were supported by participant observations. On average, experimental pupils performed slightly better than control pupils in metacognitive skill and mathematical development in the post and delayed-tests. The content of the mathematical development test had not been taught directly by the course and far transfer is claimed. The teachers were divided into four groups according to teaching approach, based on analysis of the qualitative data. The most successful teachers used a flexible form of scaffolding and encouraged reflection. Their classes demonstrated a substantial advantage over their controls in metacognitive skill, metacognitive self knowledge and mathematical development. Recommendations are made about teaching approaches.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available