Learning mathematics with recursive computer programs
Pages 116 - 130
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]
Aho, Hopcroft, Ullman, The Design and Analysis of Computer Algorithms Addison-Wesley, 1974, p. 55.
[2]
Berry, P. et al. "APL and Insight" "The Use of Programs to Represent Concepts in Teaching," IBM Technical Report #320-3020, March, 1973.
[3]
DeLong, H., "A Profile of Mathematical Logic (Notes Toward)", Trinity College, Hartford, Connecticut, 1968, p. 244.
[4]
Elliott, P., "Elementary Mathematics Teacher Training Via A Programming Language", (doctoral dissertation), University of Massachusetts, 1973.
[5]
Iverson, K. E., A Programming Language, Wiley, 1962.
[6]
Iverson, K. E., "APL in Exposition," IBM Technical Report #320-3010, January, 1972.
[7]
Pakin, S., APL/360 Reference Manual, 2nd Edition, S.R.A., 1972.
[8]
Papert, S. (and others), LOGO Memo Series, M.I.T., 1971-75.
[9]
Peelle, H. A. "COMPUTER GLASS BOXES: Teaching Children Concepts With A Programming Language," Educational Technology, Volume XIV, Number 4, April 1974.
[10]
Peelle, H. A., "Euclid, Fibonacci, and Pascal—Recursed!", to appear in International Journal of Mathematical Education in Science and Technology, 1975.
[11]
Skolem, T., "The Foundations of Elementary Arithmetic Established by Means of the Recursive Mode of Thought.", 1923.
Index Terms
- Learning mathematics with recursive computer programs
Recommendations
Learning mathematics with recursive computer programs
Proceedings of the SIGCSE-SIGCUE joint symposium on Computer science educationRecursion 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];...
Learning mathematics with recursive computer programs
SIGCSE '76: Proceedings of the ACM SIGCSE-SIGCUE technical symposium on Computer science and educationRecursion 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];...
Comments
Information & Contributors
Information
Published In
Copyright © 1976 ACM.
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]
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 01 February 1976
Published in SIGCSE Volume 8, Issue 1
Check for updates
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 470Total Downloads
- Downloads (Last 12 months)77
- Downloads (Last 6 weeks)20
Reflects downloads up to 29 Jan 2025
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in