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Learning mathematics with recursive computer programs

Published:01 February 1976Publication History
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Abstract

Recursion is a powerful idea*—with correspondingly powerful implications for learning and teaching mathematics. Computer scientists have previously pointed out that the use of recursion often permits more lucid and concise descriptions of algorithms [1]; mathematicians know that recursion is a fundamental concept upon which entire systems of mathematics can be built [11]; and, the theory of recursive functions is now developing into an area of mathematics whose importance has been compared with that of geometry and algebra [3].

The purposes of this paper are to illuminate the fundamentals of recursion; to illustrate several recursive computer programs which provide perspicuous representations of certain mathematical procedures; and to invite students and teachers of mathematics to reach greater understandings by trying them.

References

  1. 1 Aho, Hopcroft, Ullman, The Design and Analysis of Computer Algorithms Addison-Wesley, 1974, p. 55. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 2 Berry, P. et al. "APL and Insight" "The Use of Programs to Represent Concepts in Teaching," IBM Technical Report #320-3020, March, 1973.Google ScholarGoogle Scholar
  3. 3 DeLong, H., "A Profile of Mathematical Logic (Notes Toward)", Trinity College, Hartford, Connecticut, 1968, p. 244.Google ScholarGoogle Scholar
  4. 4 Elliott, P., "Elementary Mathematics Teacher Training Via A Programming Language", (doctoral dissertation), University of Massachusetts, 1973.Google ScholarGoogle Scholar
  5. 5 Iverson, K. E., A Programming Language, Wiley, 1962. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. 6 Iverson, K. E., "APL in Exposition," IBM Technical Report #320-3010, January, 1972.Google ScholarGoogle Scholar
  7. 7 Pakin, S., APL/360 Reference Manual, 2nd Edition, S.R.A., 1972.Google ScholarGoogle Scholar
  8. 8 Papert, S. (and others), LOGO Memo Series, M.I.T., 1971-75.Google ScholarGoogle Scholar
  9. 9 Peelle, H. A. "COMPUTER GLASS BOXES: Teaching Children Concepts With A Programming Language," Educational Technology, Volume XIV, Number 4, April 1974.Google ScholarGoogle Scholar
  10. 10 Peelle, H. A., "Euclid, Fibonacci, and Pascal—Recursed!", to appear in International Journal of Mathematical Education in Science and Technology, 1975.Google ScholarGoogle Scholar
  11. 11 Skolem, T., "The Foundations of Elementary Arithmetic Established by Means of the Recursive Mode of Thought..", 1923.Google ScholarGoogle Scholar

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        • Published in

          cover image ACM SIGCSE Bulletin
          ACM SIGCSE Bulletin  Volume 8, Issue 1
          Proceedings of the SIGCSE-SIGCUE joint symposium on Computer science education
          February 1976
          399 pages
          ISSN:0097-8418
          DOI:10.1145/952989
          Issue’s Table of Contents
          • cover image ACM Conferences
            SIGCSE '76: Proceedings of the ACM SIGCSE-SIGCUE technical symposium on Computer science and education
            February 1976
            403 pages
            ISBN:9781450374125
            DOI:10.1145/800107

          Copyright © 1976 ACM

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 1 February 1976

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