Learning mathematics through inquiry : the relationship between induction and deduction in Inquiry Maths

• Main Author: Blair, Andrew Ian
• Other Authors: Hodgen, Jeremy ; Kutnick, Peter
• Published: King's College London (University of London) 2018
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.754894

The thesis examines whether an inquiry model of learning mathematics is compatible with the nature of the discipline. Characterising mathematics as a combination of induction and deduction, the research questions focus on whether inquiry, which is associated with inductive processes related to discovery, meaning-making and dialogue, can include the deductive side of the subject. In particular, the thesis addresses the relationship between induction and deduction in a model called Inquiry Maths. The writings of Marx and Vygotsky offer us an understanding of that relationship: induction is ‘sublated’ – that is, simultaneously negated and preserved – in deduction. While drawing on the same sources, Davydov’s mathematics curriculum promotes a one-sided deduction. In Zuckerman’s classroom research, we identify the potential of inquiry to incorporate ‘everyday’ induction in the general movement towards ‘scientific’ deduction. In line with the theoretical positioning of the thesis, the research is carried out as a formative experiment inspired by Vygotsky’s methodology of double stimulation. The stimulus-object acts to generate inquiry, while the stimulus-means mediate between the student and forms of mathematical reasoning. The research employs a novel unit of analysis, the regulatory statement, through which the thesis maps the connections between induction and deduction that occurred in the inquiry lessons of one class during the first two years of secondary school. The thesis confirms the idea that the inquiry teacher promotes deduction by building upon, rather than against, inductive thinking. From the inquiries, the connection is described as linear (with transitional forms acting as a bridge), fragmentary or a zig-zag. The major innovation lies in the development of regulatory cards as stimulus-means. The researcher uses the cards to both form and analyse instances of induction and deduction. While the cards enabled students to express their agency during classroom inquiry, their emergence, paradoxically, signalled a reduction in the teacher’s agency.