How do students think about proof? A DVD resource for mathematicians

This article is about an MSOR Network-funded project with the same title. I describe the construction and initial testing of a DVD resource designed to help mathematicians learn more about their students’ reasoning at the transition-to-proof level. The DVD uses specially annotated video data, together with screens of prompts for reflection, to encourage discussion among mathematicians about students’ difficulties and successes. I describe part of the content, indicating how a short episode can raise many of the major issues that have been investigated and discussed in the mathematics education literature. I also report on design issues in the structure of the DVD and on mathematicians’ responses to an early version of the content. Finally, I describe the progress of the project and outline how I think it might be used in training for new lecturers and for graduate students involved in teaching.

[1]  Keith Weber.  How Mathematicians Determine if an Argument Is a Valid Proof , 2008 .

[2]  John Mason,et al.  EXEMPLIFICATION IN MATHEMATICS EDUCATION , 2006 .

[3]  L. Alcock,et al.  Semantic and Syntactic Proof Productions , 2004 .

[4]  Judith Segal.  Learning About Mathematical Proof: Conviction and Validity , 1999 .

[5]  Shlomo Vinner,et al.  The Role of Definitions in the Teaching and Learning of Mathematics , 2002 .

[6]  Annie Selden,et al.  Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? , 2003 .

[7]  Barbara Jaworski,et al.  Research Practice into/influencing Mathematics Teaching and Learning Development: Towards a Theoretical framework based on co-learning partnerships , 2003 .

[8]  David Tall,et al.  Concept image and concept definition in mathematics with particular reference to limits and continuity , 1981 .

[9]  David Mond.  Warwick Teaching Certificate (Mathematics) - An experiment in departmentally-based training , 2005 .

[10]  Randall P. Dahlberg,et al.  Facilitating Learning Events Through Example Generation , 1997 .

[11]  Annie Selden,et al.  Unpacking the logic of mathematical statements , 1995 .

[12]  Lara Alcock,et al.  Definitions : dealing with categories mathematically. , 2002 .

[13]  Angel M. Recio,et al.  Institutional and personal meanings of mathematical proof , 2001 .

[14]  Robert C. Moore.  Making the transition to formal proof , 1994 .

[15]  Mary K. Porter,et al.  Proof schemes and learning strategies of above-average mathematics students , 2003 .

[16]  Keith Weber,et al.  REFERENTIAL AND SYNTACTIC APPROACHES TO PROOF: CASE STUDIES FROM A TRANSITION COURSE , 2005 .

[17]  M. Raman.  Key Ideas: What are they and how can they help us understand how people view proof? , 2003 .

[18]  Elena Nardi,et al.  ON THE FRAGILE, YET CRUCIAL, RELATIONSHIP BETWEEN MATHEMATICIANS AND RESEARCHERS IN MATHEMATICS EDUCATION , 2004 .

[19]  G. Harel,et al.  The General, the Abstract, and the Generic in Advanced Mathematics , 1991 .