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Reduction -- an abstract thinking pattern: the case of the computational models course

Authors:

Michal Armoni,

Judith Gal-EzerAuthors Info & Claims

ACM SIGCSE Bulletin, Volume 38, Issue 1

Pages 389 - 393

https://doi.org/10.1145/1124706.1121461

Published: 03 March 2006 Publication History

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Abstract

Abstraction has been the focus of many researches in mathematics education and to some extent in computer science education. Abstract thinking characterizes the theoretical foundations of computer science, where reduction is one important abstract thinking pattern. In a previous work, we discussed the issue of reductive thinking among high school students in relation to computational models -- a theoretical unit. This unit requires abstract thinking in many aspects. Our findings in relation to reductive thinking showed that many students preferred direct, non-reductive solutions, even if reductive solutions could have significantly decreased the design complexity of the solution. This study motivated the current study where we examine the issue of reductive thinking among university students. The findings of this preliminary study are demonstrated by students' solutions to questions in assignments given in the computational models course. We found that even among university students in a very prestigious academic institution with very high entrance requirements abstraction is a real obstacle as reduction is not easily understood and used. This encourages us to further investigate this phenomenon.

References

[1]

Armoni, M. and Gal-Ezer, J., Introducing non-determinism. Submitted.

Google Scholar

[2]

Armoni, M. and Gal-Ezer, J., Non-Determinism in CS high school curricula, Proceedings of the 33rd ASEE/IEEE Frontiers in Education Conference (FIE03), F2C-18-23, 2003.

Crossref

Google Scholar

[3]

Armoni, M. and Gal-Ezer, J., On the achievements of high school students studying computational models, Proceedings of the 9th Annual SIGCSE conference on Innovation and Technology in Computer Science Education (ITiCSE04), 12--16, 2004.

Digital Library

Google Scholar

[4]

Armoni, M., Gal-Ezer, J. and Tirosh, D., Solving problems reductively, Journal of Educational Computing Research, 32(2), 113--129, 2005.

Crossref

Google Scholar

[5]

Armoni, M. and Gal-Ezer, J., Teaching reductive thinking. Mathematics and Computer Education, 39(2), 131--142, 2005.

Google Scholar

[6]

Hazzan, O., Reducing abstraction level when learning computability theory concepts, Proceedings of the 7th Annual SIGCSE conference on Innovation and Technology in Computer Science Education (ITiCSE02), 156--160, 2002.

Digital Library

Google Scholar

[7]

Hazzan, O. & Tomayko J.E., Reflection and abstraction in learning software engineering's human aspects, COMPUTER, 38(6), 39--45, 2005.

Digital Library

Google Scholar

[8]

Hershkovitz, R., Schwartz, B. B., & Dreyfus, T., Abstraction in context: epistemic actions, Journal of Research in Mathematics Education, Vol. 32, 195--222, 2001.

Crossref

Google Scholar

[9]

Hopcroft, J. E. and Ullman, J. D., Introduction to automata theory, languages and computations, Addison-Wesley, Reading, MA, 1979.

Digital Library

Google Scholar

[10]

Tsamir, P. & Dreyfus, T., Comparing infinite sets - a process of abstraction, The case of Ben, Journal of Mathematics Behavior, Vol.21, 1--23, 2002.

Crossref

Google Scholar

Cited By

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Statter DArmoni M(2020)Teaching Abstraction in Computer Science to 7th Grade StudentsACM Transactions on Computing Education10.1145/337214320:1(1-37)Online publication date: 27-Jan-2020
https://dl.acm.org/doi/10.1145/3372143
Statter DArmoni M(2017)Learning Abstraction in Computer ScienceProceedings of the 12th Workshop on Primary and Secondary Computing Education10.1145/3137065.3137081(5-14)Online publication date: 8-Nov-2017
https://dl.acm.org/doi/10.1145/3137065.3137081
Armoni MGal-Ezer JHazzan O(2006)Reductive thinking in computer scienceComputer Science Education10.1080/0899340060093784516:4(281-301)Online publication date: Dec-2006
https://doi.org/10.1080/08993400600937845
Show More Cited By

Index Terms

Reduction -- an abstract thinking pattern: the case of the computational models course
1. Social and professional topics
  1. Professional topics
    1. Computing education
      1. Computing education programs
        Computer science education

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Published In

ACM SIGCSE Bulletin Volume 38, Issue 1

March 2006

553 pages

ISSN:0097-8418

DOI:10.1145/1124706

Issue’s Table of Contents

SIGCSE '06: Proceedings of the 37th SIGCSE technical symposium on Computer science education
March 2006
612 pages
ISBN:1595932593
DOI:10.1145/1121341
Program Chairs:
Doug Baldwin
SUNY Geneseo
,
Paul Tymann
Rochester Institute of Technology
,
Susan Haller
SUNY Potsdam
,
Ingrid Russell
University of Hartford

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: 03 March 2006

Published in SIGCSE Volume 38, Issue 1

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Statter DArmoni M(2020)Teaching Abstraction in Computer Science to 7th Grade StudentsACM Transactions on Computing Education10.1145/337214320:1(1-37)Online publication date: 27-Jan-2020
https://dl.acm.org/doi/10.1145/3372143
Statter DArmoni M(2017)Learning Abstraction in Computer ScienceProceedings of the 12th Workshop on Primary and Secondary Computing Education10.1145/3137065.3137081(5-14)Online publication date: 8-Nov-2017
https://dl.acm.org/doi/10.1145/3137065.3137081
Armoni MGal-Ezer JHazzan O(2006)Reductive thinking in computer scienceComputer Science Education10.1080/0899340060093784516:4(281-301)Online publication date: Dec-2006
https://doi.org/10.1080/08993400600937845
Armoni MGal-Ezer J(2023)Computer Science Education Research in IsraelPast, Present and Future of Computing Education Research10.1007/978-3-031-25336-2_18(395-420)Online publication date: 18-Apr-2023
https://doi.org/10.1007/978-3-031-25336-2_18
Gaber IArmoni MStatter D(2021)Teaching Reduction as an Algorithmic Problem-Solving Strategy2021 3rd International Conference on Computer Science and Technologies in Education (CSTE)10.1109/CSTE53634.2021.00012(19-26)Online publication date: May-2021
https://doi.org/10.1109/CSTE53634.2021.00012
Mueller FGibbs MVetere FEdge D(2017)Designing for Bodily Interplay in Social Exertion GamesACM Transactions on Computer-Human Interaction10.1145/306493824:3(1-41)Online publication date: 10-May-2017
https://dl.acm.org/doi/10.1145/3064938
Back JSegura EWaern A(2017)Designing for Transformative PlayACM Transactions on Computer-Human Interaction10.1145/305792124:3(1-28)Online publication date: 28-Apr-2017
https://dl.acm.org/doi/10.1145/3057921
Rambally G(2015)The Synergism of Mathematical Thinking and Computational ThinkingCases on Technology Integration in Mathematics Education10.4018/978-1-4666-6497-5.ch021(416-437)Online publication date: 2015
https://doi.org/10.4018/978-1-4666-6497-5.ch021
Ginat DAlankry RLapidot TGal-Ezer JCaspersen MHazzan O(2012)Pseudo abstract compositionProceedings of the 17th ACM annual conference on Innovation and technology in computer science education10.1145/2325296.2325307(28-33)Online publication date: 3-Jul-2012
https://dl.acm.org/doi/10.1145/2325296.2325307
McMaster KRague BAnderson N(2010)Integrating Mathematical Thinking, Abstract Thinking, and Computational Thinking2010 IEEE Frontiers in Education Conference (FIE)10.1109/FIE.2010.5673139(S3G-1-S3G-6)Online publication date: Oct-2010
https://doi.org/10.1109/FIE.2010.5673139
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