TY - JOUR
T1 - Mathematicians' perspectives on their pedagogical practice with respect to proof
AU - Weber, Keith
N1 - Funding Information:
This work was supported by a grant from the National Science Foundation (DRL-0643734). The views expressed in this paper are not necessarily those of the National Science Foundation. I would like to thank Eric Knuth for useful comments about the design of this study as well as Tim Fukawa-Connelly and Evan Fuller for useful feedback on earlier versions of this manuscript.
PY - 2012/6
Y1 - 2012/6
N2 - In this article, nine mathematicians were interviewed about their why and how they presented proofs in their advanced mathematics courses. Key findings include that: (1) the participants in this study presented proofs not to convince students that theorems were true but for reasons such as conveying understanding and illustrating methods, (2) participants believed students did not appreciate the complex processes involved in reading a proof but often did not teach these processes to students, (3) the participants used superficial methods to assess students' understanding of a proof and (4) some participants questioned whether proof was the best way to convey mathematics to all of their students.
AB - In this article, nine mathematicians were interviewed about their why and how they presented proofs in their advanced mathematics courses. Key findings include that: (1) the participants in this study presented proofs not to convince students that theorems were true but for reasons such as conveying understanding and illustrating methods, (2) participants believed students did not appreciate the complex processes involved in reading a proof but often did not teach these processes to students, (3) the participants used superficial methods to assess students' understanding of a proof and (4) some participants questioned whether proof was the best way to convey mathematics to all of their students.
KW - mathematicians' pedagogy
KW - proof
KW - proof presentation
KW - undergraduate mathematics education
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U2 - 10.1080/0020739X.2011.622803
DO - 10.1080/0020739X.2011.622803
M3 - Article
AN - SCOPUS:84861470241
SN - 0020-739X
VL - 43
SP - 463
EP - 482
JO - International Journal of Mathematical Education in Science and Technology
JF - International Journal of Mathematical Education in Science and Technology
IS - 4
ER -