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ERIC Number: EJ1099344
Record Type: Journal
Publication Date: 2016-Jun
Pages: 16
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0013-1954
A Framework for Proofs and Refutations in School Mathematics: Increasing Content by Deductive Guessing
Komatsu, Kotaro
Educational Studies in Mathematics, v92 n2 p147-162 Jun 2016
The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of heuristic rules formulated by Lakatos. A salient feature of this framework resides in the notion of increasing content by deductive guessing, which Lakatos considered to be one of the cores of proofs and refutations, where deductive reasoning is used to create a general conjecture that is true even for counterexamples of an earlier conjecture. Two case studies involving a pair of fifth graders and a pair of ninth graders are presented to illustrate that the notion of increasing content by deductive guessing is useful in examining student processes of generalisation of conjectures. The framework shown in this paper contributes to the current knowledge of mathematics education researchers about proof and proving by providing a tool to investigate how a proof can be used not only to establish the truth of a given statement but also to generate new mathematical knowledge.
Springer. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail: service-ny@springer.com; Web site: http://www.springerlink.com
Publication Type: Journal Articles; Reports - Research
Education Level: Grade 5; Intermediate Grades; Middle Schools; Elementary Education; Grade 9; Junior High Schools; Secondary Education; High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A