Making the transition to formal proof
 Robert C. Moore
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Abstract
This study examined the cognitive difficulties that university students experience in learning to do formal mathematical proofs. Two preliminary studies and the main study were conducted in undergraduate mathematics courses at the University of Georgia in 1989. The students in these courses were majoring in mathematics or mathematics education. The data were collected primarily through daily nonparticipant observation of class, tutorial sessions with the students, and interviews with the professor and the students. An inductive analysis of the data revealed three major sources of the students' difficulties: (a) concept understanding, (b) mathematical language and notation, and (c) getting started on a proof. Also, the students' perceptions of mathematics and proof influenced their proof writing. Their difficulties with concept understanding are discussed in terms of a conceptunderstanding scheme involving concept definitions, concept images, and concept usage. The other major sources of difficulty are discussed in relation to this scheme.
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 Title
 Making the transition to formal proof
 Journal

Educational Studies in Mathematics
Volume 27, Issue 3 , pp 249266
 Cover Date
 19941001
 DOI
 10.1007/BF01273731
 Print ISSN
 00131954
 Online ISSN
 15730816
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Industry Sectors
 Authors

 Robert C. Moore ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Southern College of SeventhDay Adventists, 37315, Collegedale, TN, USA