Abstract for a thesis submitted for the DPhil degree, Hilary term 2011. Given the central functions of reasoning in mathematics learning, knowledge of students' reasoning is crucial for mathematics educators. Yet there is little research evidence about the reasoning of students with low prior attainment. Reasoning can be understood as argumentation, or as thinking used to draw conclusions from available evidence. I address theoretical and tactical difficulties in researching both senses of students' reasoning in classroom context: the fragmented nature of interactive mathematical talk, and the multiple possible connections between what is said and underlying inferential thought. Toulmin's model of argument is adapted using pragmatics, to enable constrained inference to plausible interpretations of students' reasoning as argumentation. Analysis of novelty in each teacher-mediated task, in the constantly developing context of the knowledge and problem-solving skills made available to students, is used to identify opportunities for reasoning as thinking. This eclectic framework was used to produce a description and evaluation of reasoning from students with low prior attainment in mathematics. In a six-week focused case study of two classes of 15-16 year old students, mathematical conversation was transcribed and analysed for argumentation, using multiple data sources to support analytical inferences. Reasoning as thinking was identified from successful argumentation on novel tasks. The core Toulmin argument abstracted from students' explicit argumentation was often only partly stated, but once minimal inferred content was taken into account, core arguments were usually complete. The students worked on geometry, but few provided perceptual warrants. Most students worked with appropriate deductive warrants when deriving information about figures from theorems. Students often struggled with the calculation elements of geometrical work, so some argumentation appeared procedural. Opportunities for students' reasoning as thinking were limited, with little opportunity to generalise. When tasks did involve novelty, many students showed facility in use of deductive derivation, and there was some use of visual transformation of mathematical structure. Supplementing Toulmin argument analysis with pragmatics provides a tool for further research on incomplete and procedural argumentation, and a framework for use in professional development with teachers. Findings on students' reasoning as thinking are used to raise questions about teacher and curricular assumptions about other groups of low attaining students.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:559821 |
| Date | January 2011 |
| Creators | Clarke, Nichola |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
Page generated in 0.0021 seconds