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dc.contributor.authorCalder, Nigel Stuarten_NZ
dc.date.accessioned2008-12-16T10:49:57Z
dc.date.available2008-12-18T15:54:05Z
dc.date.issued2008en_NZ
dc.identifier.citationCalder, N. S. (2008). Processing mathematical thinking through digital pedagogical media: the spreadsheet (Thesis, Doctor of Philosophy (PhD)). The University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/2662en
dc.identifier.urihttps://hdl.handle.net/10289/2662
dc.description.abstractAbstract This study is concerned with the ways mathematical understanding emerges when mathematical phenomena are encountered through digital pedagogical media, the spreadsheet, in particular. Central to this, was an examination of the affordances digital technologies offer, and how the affordances associated with investigating mathematical tasks in the spreadsheet environment, shaped the learning trajectories of the participants. Two categories of participating students were involved, ten-year-old primary school pupils, and pre-service teachers. An eclectic approach to data collection, including qualitative and quantitative methods, was initially undertaken, but as my research perspective evolved, a moderate hermeneutic frame emerged as the most productive way in which to examine the research questions. A hermeneutic process transformed the research methodology, as well as the manner in which the data were interpreted. The initial analysis and evolving methodology not only informed this transition to a moderate hermeneutic lens, they were constitutive of the ongoing research perspectives and their associated interpretations. The data, and some that was subsequently collected, were then reconsidered from this modified position. The findings indicated that engaging mathematical tasks through the pedagogical medium of the spreadsheet, influenced the nature of the investigative process in particular ways. As a consequence, the interpretations of the interactions, and the understandings this evoked, also differed. The students created and made connections between alternative models of the situations, while the visual, tabular structuring of the environment, in conjunction with its propensity to instantly manage large amounts of output accurately, facilitated their observation of patterns. They frequently investigated the visual nature of these patterns, and used visual referents in their interpretations and explanations. It also allowed them to pose and test their informal conjectures and generalisations in non-threatening circumstances, to reset investigative sub-goals easily, hence fostering risk taking in their approach. At times, the learning trajectory evolved in unexpected ways, and the data illustrated various alternative ways in which unexpected, visual output stimulated discussion and extended the boundaries of, or reorganised, their interaction and mathematical thinking. An examination of the visual perturbations, and other elements of learning as hermeneutic processes also revealed alternative understandings and explanations. Viewing the data and the research process through hermeneutic filters enhanced the connectivity between the emergence of individual mathematical understanding, and the cultural formation of mathematics. It permitted consideration of the ways this process influences the evolution of mathematics education research. While interpretive approaches are inevitably imbued with the researcher perspective in the analysis of what gets noticed, the research gave fresh insights into the ways learning emerges through digital pedagogical media, and the potential of this engagement to change the nature of mathematics education.en_NZ
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherThe University of Waikatoen_NZ
dc.rightsAll items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
dc.subjectmathematics educationen_NZ
dc.subjectICTen_NZ
dc.subjectproblem solvingen_NZ
dc.subjectprimaryen_NZ
dc.subjectspreadsheetsen_NZ
dc.subjectmathematical thinkingen_NZ
dc.titleProcessing mathematical thinking through digital pedagogical media: the spreadsheeten_NZ
dc.typeThesisen_NZ
thesis.degree.disciplineEducationen_NZ
thesis.degree.grantorUniversity of Waikatoen_NZ
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (PhD)en_NZ
uow.date.accession2008-12-16T10:49:57Zen_NZ
uow.date.available2008-12-18T15:54:05Zen_NZ
uow.identifier.adthttp://adt.waikato.ac.nz/public/adt-uow20081216.104957en_NZ
uow.date.migrated2009-06-14T21:35:46Zen_NZ
pubs.elements-id55711
pubs.place-of-publicationHamilton, New Zealanden_NZ


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