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Computer science students' difficulties with proofs by induction: an exploratory study

Published: 10 March 2006 Publication History

Abstract

Induction is an important concept for computer science and yet students have difficulties understanding it. The current literature on students' difficulties with induction is concerned with difficulties students have while proving a statement by induction. My research focuses on identifying difficulties that students may have prior to proving a statement. In particular, the present paper is concerned with students' understanding of the recursive/inductive definition of the elements the statement is about. My study is contextualized within the undergraduate computer science curriculum, and its results show that students' performance with proofs by induction improves after class instruction, but not as it would be desirable. Moreover, they suggest that students who understand recursive/inductive definitions can successfully perform a proof by induction, while students who do not are either not able to perform proofs by induction, or if they are, they do so mechanically. In addition, students' performance is affected by their past knowledge and experience, as well as the context in which a problem is presented.

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Cited By

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  • (2025)Mathematical induction in education research: a systematic reviewEducational Studies in Mathematics10.1007/s10649-024-10373-xOnline publication date: 6-Jan-2025
  • (2023)How Do We Read Formal Claims? Eye-Tracking and the Cognition of Proofs about AlgorithmsProceedings of the 45th International Conference on Software Engineering10.1109/ICSE48619.2023.00029(208-220)Online publication date: 14-May-2023
  • (2011)Probing student problem solving skills in mathematical induction using a scenario based think aloud protocolProceedings of the 16th Western Canadian Conference on Computing Education10.1145/1989622.1989631(33-37)Online publication date: 6-May-2011
  • Show More Cited By

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cover image ACM Other conferences
ACMSE '06: Proceedings of the 44th annual ACM Southeast Conference
March 2006
823 pages
ISBN:1595933158
DOI:10.1145/1185448
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 10 March 2006

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Author Tags

  1. inductive/recursive definitions
  2. proofs by induction
  3. structural induction
  4. undergraduate computer science curricula

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ACM SE06
ACM SE06: ACM Southeast Regional Conference
March 10 - 12, 2006
Florida, Melbourne

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ACMSE '06 Paper Acceptance Rate 100 of 244 submissions, 41%;
Overall Acceptance Rate 502 of 1,023 submissions, 49%

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Cited By

View all
  • (2025)Mathematical induction in education research: a systematic reviewEducational Studies in Mathematics10.1007/s10649-024-10373-xOnline publication date: 6-Jan-2025
  • (2023)How Do We Read Formal Claims? Eye-Tracking and the Cognition of Proofs about AlgorithmsProceedings of the 45th International Conference on Software Engineering10.1109/ICSE48619.2023.00029(208-220)Online publication date: 14-May-2023
  • (2011)Probing student problem solving skills in mathematical induction using a scenario based think aloud protocolProceedings of the 16th Western Canadian Conference on Computing Education10.1145/1989622.1989631(33-37)Online publication date: 6-May-2011
  • (2008)A conceptual approach to teaching induction for computer scienceACM SIGCSE Bulletin10.1145/1352322.135214240:1(9-13)Online publication date: 12-Mar-2008
  • (2008)A conceptual approach to teaching induction for computer scienceProceedings of the 39th SIGCSE technical symposium on Computer science education10.1145/1352135.1352142(9-13)Online publication date: 12-Mar-2008

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