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Loop invariants and mathematical games

Author:

David GinatAuthors Info & Claims

SIGCSE '95: Proceedings of the twenty-sixth SIGCSE technical symposium on Computer science education

Pages 263 - 267

https://doi.org/10.1145/199688.199812

Published: 15 March 1995 Publication History

Abstract

The concept of combining loop invariants with algorithm analysis and design is a significant programming tool. However, teaching this concept is not easy. One way of motivating and supporting the introduction of such a concept, is by illustrating it with attractive examples. In this paper we describe how to illustrate it with mathematical games. In our description, we emphasize the links between heuristic search strategies, pattern exploration, induction, and invariant construction.

References

[1]

Aho, A., and Ulman J.D., Foundations of Computer Science, Freeman and Co., 1992.

Digital Library

[2]

Amow, D., Teaching programming to liberal arts students: Using loop invariants, Proc of the 24th Tech Synp on CS Education, March 1994.

Digital Library

[3]

Astrachan, O., Loop invariants in pictures, Proc of the 22nd Tech Symp on CS Education, March 1991.

[4]

Bright, G.W., Harvey, J.G., and Wheeler, M.M., Game constraints, player verbalizations, and mathematical learning, The Journal of Experimental Education, 49, 1, 1980.

[5]

Chi, M.T.H., and Bassok, M., Learning from examples via self-explanations, Knowing, Learning, and Instruction, Resnick, L.B, editor, Lawrence Erlbaum Associates, 1989.

[6]

Dijkstra, E.W., A Discipline of Programming, Prentice-Hall, 1976.

Digital Library

[7]

Floyd, R., Assigning meaning to programs, Mathematical Aspects of Computer Science, XIX American Mathematical society, 1967.

[8]

Gries, D., The Science of Programming, Springer-Verlag, 1981.

[9]

Hoare, C.A.R., An Axiomatic basis for computer programming, CA CM, 12, 5, May 1969.

Digital Library

[10]

Manber, U., Using induction to design algorithms, CACM, 31,11, November 1988.

Digital Library

[11]

Nesher, P., Microworlds in mathematical education: a pedagogical realism. Knowing, Learning, and Instruction, Resnick, L.B, editor, Lawrence Erlbaum Associates, 1989.

[12]

Polya, G., How to solve it, Princeton Univ Press, 1957.

[13]

Schoenfeld, A., Mathematical problem solving, Academic-Press, 1985.

[14]

Sclaoenfeld, A., Learning to think mathematically" problem solving, metacognition, and sense making in mathematics, Handbook of Ra~areh on Mathematics Teaching and Learning, Macmillan, 1992.

[15]

Tam, W., Teaching Loop Invariants to Beginners by examples, Proc of the' 23rd Tech Symp on CS Education, March 1992.

Digital Library

[16]

Troeger, D., Experiences teaching loop invariants to beginners, Logic, Loops and Literacy Workshop, May 1993.

Cited By

Logas HVallejos ROsborn JCompton KWhitehead J(2015)Visualizing Loops and Data Structures in XylemProceedings of the 2015 IEEE/ACM 4th International Workshop on Games and Software Engineering10.1109/GAS.2015.16(50-56)Online publication date: 18-May-2015
https://dl.acm.org/doi/10.1109/GAS.2015.16
Shifroni EGinat D(1997)Simulation game for teaching communications protocolsACM SIGCSE Bulletin10.1145/268085.26815229:1(184-188)Online publication date: 1-Mar-1997
https://dl.acm.org/doi/10.1145/268085.268152
Shifroni EGinat DWhite CErickson CKlein B(1997)Simulation game for teaching communications protocolsProceedings of the twenty-eighth SIGCSE technical symposium on Computer science education10.1145/268084.268152(184-188)Online publication date: 1-Mar-1997
https://dl.acm.org/doi/10.1145/268084.268152
Show More Cited By

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cover image ACM Conferences

SIGCSE '95: Proceedings of the twenty-sixth SIGCSE technical symposium on Computer science education

March 1995

436 pages

ISBN:089791693X

DOI:10.1145/199688

Chairman:
Cary Laxer
Rose-Hulman Institute of Technology, Terre Haute, IN
,
Editors:
Curt M. White
Indiana Univ., Fort Wayne and Purdue Univ., West Lafayette, IN
,
James E. Miller
Univ. of Southern Mississippi, Hattiesburg
,
Judy Gersting
Univ. of Hawaii at Hilo, Hilo

ACM SIGCSE Bulletin Volume 27, Issue 1
March 1995
402 pages
ISSN:0097-8418
DOI:10.1145/199691
Editors:
Curt M. White
Indiana Univ., Fort Wayne and Purdue Univ., West Lafayette, IN
,
James E. Miller
Univ. of Southern Mississippi, Hattiesburg
,
Cary Laxer
Rose-Hulman Institute of Technology, Terre Haute, IN
,
Judy Gersting
Univ. of Hawaii at Hilo, Hilo
Issue’s Table of Contents

Copyright © 1995 ACM.

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Association for Computing Machinery

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Published: 15 March 1995

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SIGCSE95: 26th SIGCSE Technical Symposium on Computer Science Education

March 2 - 4, 1995

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Cited By

Logas HVallejos ROsborn JCompton KWhitehead J(2015)Visualizing Loops and Data Structures in XylemProceedings of the 2015 IEEE/ACM 4th International Workshop on Games and Software Engineering10.1109/GAS.2015.16(50-56)Online publication date: 18-May-2015
https://dl.acm.org/doi/10.1109/GAS.2015.16
Shifroni EGinat D(1997)Simulation game for teaching communications protocolsACM SIGCSE Bulletin10.1145/268085.26815229:1(184-188)Online publication date: 1-Mar-1997
https://dl.acm.org/doi/10.1145/268085.268152
Shifroni EGinat DWhite CErickson CKlein B(1997)Simulation game for teaching communications protocolsProceedings of the twenty-eighth SIGCSE technical symposium on Computer science education10.1145/268084.268152(184-188)Online publication date: 1-Mar-1997
https://dl.acm.org/doi/10.1145/268084.268152
Eriksson JParsa MBack R(2018)A Precise Pictorial Language for Array InvariantsIntegrated Formal Methods10.1007/978-3-319-98938-9_9(151-160)Online publication date: 9-Aug-2018
https://doi.org/10.1007/978-3-319-98938-9_9
Priester CAlphonce CTims JCaspersen MEdwards S(2016)Loop InvariantsProceedings of the 47th ACM Technical Symposium on Computing Science Education10.1145/2839509.2851069(727-727)Online publication date: 17-Feb-2016
https://dl.acm.org/doi/10.1145/2839509.2851069
Logas HVallejos ROsborn JCompton KWhitehead JScacchi WWhitehead J(2015)Visualizing loops and data structures in XylemProceedings of the Fourth International Workshop on Games and Software Engineering10.5555/2820144.2820157(50-56)Online publication date: 16-May-2015
https://dl.acm.org/doi/10.5555/2820144.2820157
Alexandron GArmoni MGordon MHarel D(2014)Scenario-Based Programming, Usability-Oriented PerceptionACM Transactions on Computing Education10.1145/264881414:3(1-23)Online publication date: 27-Oct-2014
https://dl.acm.org/doi/10.1145/2648814
Hamey L(2003)Teaching secure communication protocols using a game representationProceedings of the fifth Australasian conference on Computing education - Volume 2010.5555/858403.858426(187-196)Online publication date: 1-Jan-2003
https://dl.acm.org/doi/10.5555/858403.858426

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