A New Framework Based on the Methodology of Scientific Research Programs for Describing the Quality of Mathematical Activities

Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education Volume 4 Page 291-298 published_at 2016-10-15
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Title ( eng )
A New Framework Based on the Methodology of Scientific Research Programs for Describing the Quality of Mathematical Activities
Creator
Source Title
Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education
Volume 4
Start Page 291
End Page 298
Abstract
This paper proposes a new framework for describing the quality of mathematical activities under radical constructivism. It is based on Lakatos' philosophy of science, instead of his philosophy of mathematics. We focus on a structural similarity between mathematical problem-solving activities and scientific research programs. While Lakatos 'philosophy of mathematics is only a model of a progressive activity, the new framework can distinguish between progressive and degenerative activities. To show its usefulness, we provide a sample analysis. Based on the analysis, we hypothesize that the zig-zag process of solving a mathematical problem is driven by a hard core: A set of one's unrevised assumptions that one would like to continue to maintain. The necessity of further research with the proposed framework is suggested.
Descriptions
Place; Szeged, HUNGARY Date; 3-7 August, 2016
NDC
Mathematics [ 410 ]
Language
eng
Resource Type conference paper
Publisher
PME
Date of Issued 2016-10-15
Rights
Copyright (c) 2016 left to authors (Standard Copyright License)
Publish Type Version of Record
Access Rights open access
Source Identifier
[ISBN] 9781365463457