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Teaching proofs and algorithms in discrete mathematics with online visual logic puzzles

Published: 01 June 2005 Publication History

Abstract

Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete examples, in addition to the algebraic proofs that make up most of the examples in textbooks. Creating specialized, pedagogical applets allows more automation of repetitive tasks as well as a framework for discussing and implementing algorithms for solving the puzzles. One such applet is presented here and several possible exercises using it are described.

References

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Dossey, J.A., Otto, A.D., Spence, L.E. and Vanden Eynden, C. 2002. Discrete Mathematics, 4 th edition. Addison Wesley, Boston, MA, 88--9.
[2]
Ensley, D. and Crawley, W. 2005. Discrete Mathematics: Mathematical Reasoning with Puzzles, Patterns and Games. Wiley, New York, NY.
[3]
Fujiwara, H. 1996. Nonogram v0.5, http://www.pro.or.jp/~fuji/java/copyright-eng.html
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Greenwald, S.J. 2003. Proof-Writing. http://www.mathsci.appstate.edu/~sjg/class/4710/sampleproofs.html.
[5]
Lock, P.F., and Struthers, A.A. 1999. Using the game Minesweeper to introduce students to proofs.Abstracts of Papers Presented to the American Mathematical Society 20(1), 189.
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Rosen, K.H. 2003. Discrete Mathematics and Its Applications, 5th edition. McGraw-Hill, New York, 2003, 247--8.

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Published In

cover image Journal on Educational Resources in Computing
Journal on Educational Resources in Computing  Volume 5, Issue 2
June 2005
84 pages
ISSN:1531-4278
EISSN:1531-4278
DOI:10.1145/1141904
Issue’s Table of Contents
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: 01 June 2005
Published in JERIC Volume 5, Issue 2

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Author Tags

  1. Logic
  2. education
  3. proof

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Cited By

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  • (2021)Discrete Math with ProgrammingProceedings of the 52nd ACM Technical Symposium on Computer Science Education10.1145/3408877.3432537(1156-1162)Online publication date: 3-Mar-2021
  • (2021) On Solving Link-a-Pix Picture Puzzles IEEE Transactions on Games10.1109/TG.2020.302375613:3(321-324)Online publication date: Sep-2021
  • (2019)Undergraduate Students’ Solutions of Modeling Problems in Algorithmic Graph TheoryMathematics10.3390/math70705727:7(572)Online publication date: 26-Jun-2019
  • (2018)Analyzing rich qualitative data to study pencil-puzzle-based assignments in CS1 and CS2Proceedings of the 23rd Annual ACM Conference on Innovation and Technology in Computer Science Education10.1145/3197091.3197109(212-217)Online publication date: 2-Jul-2018
  • (2018)An Active and Collaborative Approach to Teaching Discrete StructuresProceedings of the 49th ACM Technical Symposium on Computer Science Education10.1145/3159450.3159582(822-827)Online publication date: 21-Feb-2018
  • (2015)Teaching undergraduate algorithms with case studies and quizzes in interactive tutorials2015 IEEE International Conference on Teaching, Assessment, and Learning for Engineering (TALE)10.1109/TALE.2015.7386057(272-276)Online publication date: Dec-2015
  • (2013)Integrating theoretical and empirical computer science in a data structures courseProceeding of the 44th ACM technical symposium on Computer science education10.1145/2445196.2445211(23-28)Online publication date: 6-Mar-2013
  • (2011)Teaching Using Computer GamesJournal of Educational Technology Systems10.2190/ET.39.3.g39:3(321-343)Online publication date: 24-May-2011
  • (2011)Teaching discrete structuresProceedings of the 42nd ACM technical symposium on Computer science education10.1145/1953163.1953247(275-280)Online publication date: 9-Mar-2011

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