Artikel i History and Epistemology in Mathematics Education. Proceedings of the Seventh European Summer University

Kristian Danielsen og Henrik Kragh Sørensen udgiver "Formal proof and exploratory experimentation: A Lakatosian view on the interplay between examples and deductive proof practices in upper-secondary school" (med M. Misfeldt) og "Using authentic sources in teaching logistic growth: A narrative design perspective"

23.02.2016 | Kristian Hvidtfelt Nielsen

FORMAL PROOF AND EXPLORATORY EXPERIMENTATION: A LAKATOSIAN VIEW ON THE INTERPLAY BETWEEN EXAMPLES AND DEDUCTIVE PROOF PRACTICES IN UPPER.SECONDARY SCHOOL

Abstract

This paper investigates conceptions of mathematical investigation and proof in upper-secondary students. The focus of the paper is an intervention that scaffolds the interaction between open explorative activities and the development of proof sketches through explorations of lattice polygons, aiming at proving Pick’s theorem. In the process we investigate whether and how the conceptions of proofs and explanations in mathematics change. We work with the hypothesis that the problem of supporting the transition to deductive proofs in upper-secondary school students can at least partly be explained as a problem of bringing their empirical investigations into the deductive proof process in relevant and productive ways. Through our analyses of the portfolios and deliberations of the students, we are able to assess their performance of proofs and the conceptions of mathematical methodology before and after the intervention. 

USING AUTHENTIC SOURCES IN TEACHING LOGISTIC GROWTH: A NARRATIVE DESIGN PERSPECTIVE

Abstract

In this paper, we present and discuss newly designed materials intended to teach logistic growth in Danish upper-secondary mathematics classes using an authentic source. The material was developed in conjunction with teaching a university-level course for future mathematics teachers and published in the form of a small booklet that introduces, contextualises, explains and discusses an original source by the Belgian mathematician Pierre Fran ois Verhulst (published 1838). The material offers multiple strategies for classroom implementation, ranging from a basic introduction to the topic to a full-scale teaching unit, as well as detailed suggestions for its cross-disciplinary integration with other subjects such as history, languages, art and social science. Our approach has shown potential for engaging students in enquiry-driven learning of both mathematics and its history.

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