Abstract
The contribution of programming in the learning of school mathematics has been demonstrated in numerous project and research settings. However, it would appear that this activity has failed to permeate the system on any large and systemic scale.
I suggest here that one reason for the current situation is that the exciting developments have not themselves been a required component embedded in a major curriculum theme. Further, the position that the programming environments themselves, e.g., Logo microworlds, would become the school mathematics curriculum has clearly failed to gain the support of the educational system. However, discrete mathematics and algorithmics, a strand within discrete mathematics, provides a natural ‘home’ for programming. This in turn supports the use of a programming language in mathematical contexts for which pupil designed algorithms can be used to explore concepts and relationships.
Similar content being viewed by others
References
Abelson, H. and diSessa, A. (1980) Turtle Geometry: The Computer as a Medium for Exploring Mathematics. The MIT Press, Cambridge (MA).
Ball, D. (1987) Logic programming and mathematics. Informatics and the Teaching of Mathematics, D.C. Johnson & F. Lovis (eds), North-Holland, Amsterdam, p. 25-32.
Booth, L. (1984) Algebra: Children's Strategies and Errors. NFER-Nelson, Windsor.
Clements, D. and Battista, M. (1990) The effects of Logo of children's conceptualization of angle and polygons. Journal for Research in Mathematics Education, 21, 356-371.
Cope, P. & Walsh, T. (1990) Programming in schools: 10 y on. Journal of Computer Assisted Learning, 6, 119-127.
Department for Education (DfE) (1995) Mathematics in the National Curriculum. HMSO, London.
diSessa, A. (1988) Social niches for future software. Towards a Scientific Practice of Science Education, A. diSessa, M. Gardener, J. Greeno, F. Reif, A. Schoenfeld & E. Stage (eds), Lawrence Erlbaum Associates, Hillsdale (New Jersey).
Edwards, L. (1992) A Logo microworld for transformation geometry. Learning Mathematics and Logo. C. Hoyles & R. Noss (eds), The MIT Press, Cambridge, MA, 127-155.
Feurzeig, W. Papert, S. Bloom, M. Grant, R. and Solomon, C. (1969) Programming languages as a conceptual, framework for teaching mathematics. Report No. 1889. Final report of the first 15 months of the Logo project. Bolt, Beranek and Newman, Cambridge, MA.
Fullan, M. (1991) The New Meaning of Educational Change. Cassell, London, UK.
Hatfield, L. and Johnson, D.C. (1968) CAMP First Course. Scott-Foresman, Glenview (Illinois).
Hatfield, L. and Kieren, T. (1972) Computer-assisted problem solving in school mathematics. Journal for Research in Mathematics Education, 3, 99-112.
Hoyles, C. and Noss, R. (eds) (1992) Learning Mathematics and Logo. The MIT Press, Cambridge, MA.
Johnson, D.C. (1986) Teaching and learning mathematics-will programming help? Exploring Mathematics with Microcomputers, N. Bufton (ed), MEP Reader 8. National Council for Educational Technology, London, p. 115-125.
Johnson, D.C. (1992) Algorithmics in school mathematics: why, what and how? Developments in School Mathematics Education Around the World (Volume three), I. Wirszup & R. Streit (eds). National Council of Teachers of Mathematics, Reston, (Virginia), p. 330-345.
Johnson, D.C. and Harding, R. (1979) University level computing and mathematical problem-solving ability. Journal for Research in Mathematics Education, 10, 37-55.
Katzman, P. and Johnson, D.C. (1970) CAMP Geometry. Scott-Foresman, Glenview (Illinois).
Kenney, M. and Hirsh, C. (eds) (1991) Discrete Mathematics Across the Curriculum, K-12. National Council of Teachers of Mathematics, Reston (Virginia).
Leron, U. & Hazzan, O. (1998) Computers and applied constructivism. Information and Communications Technologies in School Mathematics, D. Tinsley & D.C. Johnson (eds), Chapman & Hall, London, p. 195-204.
Maurer, S. (1992) What are algorithms? What is algorithmics? The Influence of Computers and Informatics on Mathematics and its Teaching, B. Cornu & T. Ralston (eds), Science and Technology Education Document Series #44. UNESCO, Paris.
Maurer, S. and Ralston, A. (1991) Algorithms: you cannot do discrete mathematics without them. Discrete Mathematics Across the Curriculum, K-12, M. Kenney & C. Hirsh (eds), National Council of Teachers of Mathematics, Reston (Virginia), p. 195-206.
MicroMath. A publication of the Association of Teachers of Mathematics (ATM). Address: MicroMath, ATM, 7 Shaftesbury Street, Derby DE23 8YB, England.
NCTM (1989) Curriculum and Evaluation Standards for School Mathematics. National Council of Teachers of Mathematics, Reston (Virginia).
NCTM Computer-oriented Mathematics Committee (1973) The role of electronic computers and calculators. In Instructional Aids in Mathematics-Thirty-fourth Yearbook, E. Berger (ed), NCTM, Reston (Virginia).
Neill, H. (1994) (Gen. ed), Nuffield Advanced Mathematics-Book 1, Longman Group Ltd, Harlow, Essex.
Neuwirth, E. (1995) Visualizing structural and formal relationships with spreadsheets. The Design of Computational Media to Support Exploratory Learning, A. diSessa, C. Hoyles and R. Noss (eds), Springer-Verlag: New York, p. 155-174.
Neuwirth, E. (1998) Spreadsheets: just smart calculators or a new paradigm for thinking about mathematical structures? Information and Communications Technologies in School Mathematics, D. Tinsley and D.C. Johnson (eds), Chapman & Hall, London, p. 77-88.
Noss, R. (1985) Creating a Mathematical Environment through Programming: A Study of Young Pupils Learning Logo. Institute of Education, University of London, UK.
Noss, R. & Hoyles, C. (1996) Windows on Mathematical Meanings: Learning Cultures and Computers. Kluwer Academic Publishers, Dordrecht.
O'Reilly, D. (1998) School programming as literacy: the case for BOXER. Journal of Computer Assisted Learning, 14, 51-58.
Papert, S. (1980) Mindstorms: Children, Computers, and Powerful Ideas. Basic Books, New York.
Papert, S. (1998) Child Power: Key to the New Learning of the Digital Century. The Eleventh Colin Cherry Memorial Lecture on Communication, 2 June 1998, www.connectedfamily.com.
Pea, R. and Kurland, M. (1984) On the cognitive effects of learning computer programming. New Ideas in Psychology, 2(2), 137-168.
Pendley Manor Working Group (1985) Mathematics and microcomputers: a Pendley Manor report. Mathematics in School, March, 26-28.
Ralston, A. and Reilly Jr., E. (1993) Encyclopedia of Computer Science, Third Edition. Van Nostrand Reinhold, New York.
Sfard, A. and Leron, U. (1996) Just give me a computer and I will move the Earth: programming as a catalyst of a cultural revolution in the mathematics classroom. International Journal of Computers for Mathematical Learning, 1, 189-195.
Sparkes, R. (1995) An investigation of Year 7 pupils learning Control LOGO. Journal of Computer Assisted Learning, 11, 182-191.
Thompson, P. (1991) To experience is to conceptualize: a discussion of epistemology and mathematical experience. In Epistemological Foundations of Mathematical Experience, L. Steffe (ed), Springer-Verlag, New York, p. 260-281.
Watson, D. (ed) (1993) The ImpacT Report: An Evaluation of the Impact of Information Technology on Children's Achievements in Primary and Secondary Schools. Department for Education=King's College London, UK.
Weir, S. (1987) Cultivating Minds: A Logo Casebook. Harper & Row, New York.
Yackel, E. and Cobb, P. (1996) Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458-477.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Johnson, D.C. Algorithmics and programming in the school mathematics curriculum: support is waning - is there still a case to be made?. Education and Information Technologies 5, 201–214 (2000). https://doi.org/10.1023/A:1009658802970
Issue Date:
DOI: https://doi.org/10.1023/A:1009658802970