Document Type

Theses, Ph.D

Rights

Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence

Disciplines

1.1 MATHEMATICS, Statistics, 5.3 EDUCATIONAL SCIENCES, *training, *pedagogy, *didactics, 6. HUMANITIES

Publication Details

Thesis presented for the award of Doctor of Philosophy 2013.

Abstract

This thesis is concerned with the idea that people may know more about mathematics than they think they do and rely on it more than they realize, especially in work. That they more readily account for what they ‘do’, dismissing what they ‘know’ as ‘commonsense’ or ‘part of the job’, seems to extend a self-perception of not ‘being a maths person’ and permits it to be transmitted within families, across generations and throughout communities. At the same time, the pervasiveness of modern technology, and the proliferation of information represented in mathematical shapes, patterns, relationships, quantities and chance, would seem to be embraced by people with relative ease. This is the paradox lying at the heart of this research, as it indicates that the reported disconnection with mathematics is rooted in perception and not due to some innate inability.

This research is important because it intends to make the use of mathematics in work more visible in formal terms, and enable a reviewed self-perception as being mathematics-capable and all that that implies for long term employability and well being. This research is timely because it coincides with widespread concern in Ireland regarding mathematics ability, engagement with mathematics education, and failing levels of performance in international comparative studies. This research is ground-breaking because it attends to the topic in a novel combination of methodologies that were especially designed and adapted for purpose. In the absence of pre-existing models, case studies were selected for their apparent absence of mathematics activity. They were closely observed and the surrounding discourse recorded for later analysis, on the basis that the absence of mathematics terminology did not confirm the absence of mathematics. . The case studies enabled the ‘hidden’ mathematics to be uncovered and aligned with the National Framework of Qualifications in Ireland in terms of complicatedness, but revealed a depth of workplace context-complexity that had been hitherto un-documented.

The methodology featured a parallel National Survey of People in Work in Ireland, in order to hear what they had to say about their mathematics, albeit expressed in non-mathematical terms The findings of the National Survey, while confirming the initiating paradox, provided insights into how mathematics may be hidden from view until brought to the fore to solve a problem or manage a situation. These emergent issues propelled the research into a new paradigm viz., to account for context-complexity, to

propose an extension to the NFQ to document it, and to introduce the concept of Subject-centric Activity Theory to help explain the mathematics use/denial paradox. The benefits enabled by this combination of methods accrue to many stakeholders. Individuals, being more fully informed, may re-contextualise what they ‘know’ for long term employability and continuing development, and may reverse their ‘non-maths person’ self-perception. Employers may develop a heightened sense of the capabilities of their workers and match them to the demands of their job. Providers of learning opportunities may reflect their appreciation of the workplace context-complexity and adjust their curricula accordingly. The richness and depth of learning acquired by tacit, informal and non-formal means, may be able to be formally recognized, and serve as a platform for further learning, development and innovation.

Funder

Government of Ireland

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