Journal ArticleDOI
High school geometry students' justification for their views of empirical evidence and mathematical proof
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In this article, the authors investigate students' understandings of the similarities and differences between the measurement of examples and deductive proof, focusing on students' reasons for viewing empirical evidence as proof and mathematical proof simply as evidence.Abstract:
Concerns about the use of computer-aided empirical verification in geometry classes lead to an investigation of students' understandings of the similarities and differences between the measurement of examples and deductive proof. The study reports in-depth interviews with seventeen high school students from geometry classes which employed empirical evidence. The analysis focuses on students' reasons for viewing empirical evidence as proof and mathematical proof simply as evidence.read more
Citations
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A study of proof conceptions in algebra
Lulu Healy,Celia Hoyles +1 more
TL;DR: This paper found that students simultaneously held two different conceptions of proof: those about arguments they considered would receive the best mark and those about argument they would adopt for themselves, and that algebraic arguments were popular.
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Proof and Proving in School Mathematics
TL;DR: In this article, the authors propose a conceptualization of the meaning of proof in school mathematics and use classroom episodes from third grade to elaborate elements of this conceptualization and to illustrate its applicability even in the early elementary grades.
Journal ArticleDOI
Secondary School Mathematics Teachers' Conceptions of Proof
TL;DR: This article examined 16 in-service secondary school mathematics teachers' conceptions of proof and found that teachers recognize the variety of roles that proof plays in mathematics; noticeably absent, however, was a view of proof as a tool for learning mathematics.
International group for the psychology of mathematics education
TL;DR: In this paper, the authors compare the way lessons on systems of linear equations unfold in a classroom in the Negev region of Israel with the way they unfold in Shanghai and Hong Kong classroom.
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How can the relationship between argumentation and proof be analysed
TL;DR: In this paper, Toulmin's model is used to detect and analyse the structure of an argumentation supporting a conjecture (abduction, induction, etc.) and its structure of its proof.
References
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Book
Proofs and Refutations
Margarita R. Levin,Imre Lakatos +1 more
TL;DR: In this article, the authors present a problem and a conjecture, and a proof of the problem and the conjecture, as well as a proof against the conjecture by lemma-incorp oration.
Journal ArticleDOI
The Mathematical Experience.
TL;DR: This edition of the book should find a new generation of general readers and students who would like to know what mathematics is all about and will prove invaluable as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications.
Book
The Mathematical Experience
Philip J. Davis,Reuben Hersh +1 more
TL;DR: The first edition of this book was published in 1983 and has been widely used as a course text for a general mathematics appreciation course, one in which the student can combine an appreciation for the esthetics with some satisfying and revealing applications.