The initial grounding of rational numbers : an investigation

Brown, Bruce John Lindsay

Title: The initial grounding of rational numbers : an investigation
Creator: Brown, Bruce John Lindsay
Subject: Number theory Numbers, Rational -- Study and teaching (Elementary) Numeracy -- Study and teaching (Elementary) Mathematics -- Study and teaching (Elementary)
Date Issued: 2007
Date: 2007
Type: Thesis
Type: Masters
Type: MEd
Identifier: vital:1904
Identifier: http://hdl.handle.net/10962/d1006351
Description: This small scale exploratory research project investigated the grounding of rational number concepts in informal, everyday life situations. A qualitative approach was taken to allow for the identification and then in depth investigation, of issues of importance for such a grounding of rational number understanding. The methodology followed could be seen as a combination of grounded theory and developmental research. And the data was generated through in-depth and clinical interviews structured around a number of grounded tasks related to rational numbers. The research comprised three cycles of interviews that were transcribed and then analysed in detail, interspersed with periods of reading and reflection. The pilot cycle involved a single grade three teacher, the second cycle involved 2 grade three teachers and the third cycle involved 2 grade three children. The research identified a number of different perspectives that were all important for the development of a fundamental intuitive understanding that could be considered personally meaningful to the individual concerned and relevant to the development of rational number concepts. Firstly in order to motivate and engage the child on a personal level the grounding situation needed to be seen as personally significant by the child. Secondly, coordinating operations provided a means of developing a fundamental intuitive understanding, through coordination with affording structures of the situation that are relevant to rational numbers. Finally, goal directed actions that are deliberately structured to achieve explicit goals in a situation are important for the development of more explicit concepts and skills fundamental for rational number understanding. Different explicit structures give rise to different interpretations of rational numbers in grounding situations. In addition to these perspectives, it became evident that building and learning representations was important for developing a more particularly mathematical understanding, based on the fundamental understanding derived from the child's grounded experience. The conclusion drawn in this research as a result of this complexity, is that to achieve a comprehensive and meaningful grounding, children's learning of rational numbers will not follow a simple linear trajectory. Rather this process forms a web of learning, threading coordinating operations for intuitive development, interpretations for explicit grounding and representations to develop more formal mathematical conceptions.
Format: 262 leaves
Format: pdf
Publisher: Rhodes University
Publisher: Faculty of Education, Education
Language: English
Rights: Brown, Bruce John Lindsay

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