Skip to main content
SpringerLink
Log in

Calculators in the Mathematics Curriculum: the Scope of Personal Computational Technology

  • Chapter
International Handbook of Mathematics Education

Part of the book series: Kluwer International Handbooks of Education ((SIHE,volume 4))

Abstract

The idea of personal computational technology in mathematics education is explored, and different portable devices, from the arithmetic calculator to the laptop computer, are described and appraised in terms of their potential as individual resources for classroom use. The relatively modest impact of calculators on mathematics education is documented, and factors which inhibit and support development are discussed: resourcing; curricular influence; public perceptions; and teacher confidence. Two examples of ways in which calculators have been integrated into classroom mathematics are sketched: one involving arithmetic calculators in the lower primary school; the other, graphic calculators at upper secondary level. Findings from research into the effects of calculator use are summarised and evaluated. Various aspects of the engraining of calculator use in processes of mathematical thinking and of teaching mathematics are identified and discussed, and emerging issues highlighted.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 789.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 999.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 999.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ainley, J. & Pratt, D.: 1994, ‘Portable Technology and Fluid Data’, in G. Wain (ed.), Research Reports from the Second British Congress on Mathematics Education, Leeds, 17–23.

    Google Scholar 

  • Barton, B., Bullock, J., Buzeika, A., Ellis, J., Graham, A. & Regan, M.: 1994, The implementation of calculators in secondary schools’, in G. Bell, B. Wright, N. Leeson and J. Geake (eds.), Proceedings of the Seventeenth Annual Conference of the Mathematics Education Research Group of Australasia, Lismore, 73–82.

    Google Scholar 

  • Bitter, G. & Hatfield, M.: 1992, Integration of the Math Explorer Calculator into the Mathematics Curriculum: The Calculator Project Report, Technology Based Learning and Research, Arizona State University, Tempe.

    Google Scholar 

  • Blume, G. & Schoen, H.: 1988, ‘Mathematical problem-solving performance of eighth-grade programmers and nonprogrammers’, Journal for Research in Mathematics Education 19 (2), 142–156.

    Article  Google Scholar 

  • Boers, M. & Jones, P.: 1992, ‘The Graphics Calculator in Tertiary Mathematics’, in B. Southwell, B. Perry and K. Owens (eds.), Proceedings of the Fifteenth Annual Conference of the Mathematics Education Research Group of Australasia, Sydney, 155–164.

    Google Scholar 

  • Boers, M. & Jones, P.: 1993, ‘Exam Performance and the Graphics Calculator in Calculus’, in B. Atweh, C. Kanes, M. Carss & G. Booker (eds.), Proceedings of the Sixteenth Annual Conference of the Mathematics Education Research Group of Australasia, Brisbane, 123–128.

    Google Scholar 

  • Bowell, B., France, S. & Redfern, S.: 1994, Portable Computers in Action, National Council for Educational Technology, Coventry.

    Google Scholar 

  • Bullock, J, Barton, B., Buzeika, A., Ellis, J., Regan, M., Thomas, M. & Tyrrell, J.: 1994, Technology in Mathematics Education, Mathematics Education Unit, University of Auckland.

    Google Scholar 

  • Cockcroft, W. (ch.): 1982, Mathematics Counts, Her Majesty’s Stationery Office, London.

    Google Scholar 

  • Cornu, B. & Ralston, A. (eds.): 1992, The influence of computers and informatics on mathematics and its teaching, UNESCO, Paris.

    Google Scholar 

  • Demana, F. & Waits, B.: 1990, ‘Enhancing Mathematics Teaching and Learning through Technology’, in T. Cooney and C. Hirsch (eds.), Teaching and Learning Mathematics in the 1990’s, National Council of Teachers of Mathematics, Reston VA, 212–222.

    Google Scholar 

  • Dick, T.: 1992, ‘Super Calculators: Implications for Calculus Curriculum, Instruction, and Assessment’, in J. Fey and C. Hirsch (eds.), Calculators in Mathematics Education, National Council of Teachers of Mathematics, Reston VA, 145–157.

    Google Scholar 

  • Dörfler, W.: 1993, ‘Computer Use and Views of the Mind’, in C. Keitel and K. Ruthven (eds.), Learning from Computers: Mathematics Education and Technology, Springer Verlag, Berlin, 159–186.

    Chapter  Google Scholar 

  • Dunham, P.: 1992, ‘Student Use of Graphing Calculators: Gender and Confidence Issues’, Paper presented at the Annual Conference of the National Council of Teachers of Mathematics, Nashville.

    Google Scholar 

  • Dunham, P. & Dick, T.: 1994, ‘Research on Graphing Calculators’, The Mathematics Teacher 87 (6), 440–445.

    Google Scholar 

  • Dunham, P. & Osborne, A.: 1991, ‘Learning to See: Students’ Graphing Difficulties’, Focus on Learning Problems in Mathematics 13 (4), 35–49.

    Google Scholar 

  • Engel, A: 1977, Elementarmathematik vom algorithmischen Standpunkt, Ernst KlettVerlag, Stuttgart.

    Google Scholar 

  • Engel, A.: 1979, ‘The role of algorithms and computers in teaching mathematics in school’, in New trends in mathematics teaching: Volume IV, UNESCO, Paris, 249–277.

    Google Scholar 

  • Fey, J. & Hirsch, C. (eds.): 1992, Calculators in Mathematics Education, National Council of Teachers of Mathematics, Reston VA.

    Google Scholar 

  • Fielker, D.: 1973, ‘Electronic Calculators’, Mathematics Teaching 64, 28–32.

    Google Scholar 

  • Fielker, D.: 1987, ‘A Calculator, A Tape Recorder, and Thou’, Educational Studies in Mathematics 18, 417–437.

    Article  Google Scholar 

  • Fitzgerald, A.: 1985, New Technology and Mathematics in Employment, Faculty of Education, University of Birmingham, Birmingham.

    Google Scholar 

  • Foxman, D., Ruddock, G., McCallum, I. & Schagen, I.: 1991, APU Mathematics Monitoring (Phase 2), National Foundation for Educational Research, Slough.

    Google Scholar 

  • Graf, K.-D., Fraser, R., Klingen, L., Stewart, J. & Winkelmann, B.: 1992, ‘The Effect of Computers on the School Mathematics Curriculum’, in B. Cornu, B. and A. Ralston (eds.), The influence of computers and informatics on mathematics and its teaching, UNESCO, Paris, 57–79.

    Google Scholar 

  • Groves, S.: 1993a, ‘The Effect of Calculator Use on Third Graders’ Solutions of Real World Division and Multiplication Problems’, in I. Hirabashi, N. Nodha, K. Shigematsu and F.-L. Lin (eds.), Proceedings of the Seventeenth International Conference for the Psychology of Mathematics Education, Tsukuba, 2, 9–16.

    Google Scholar 

  • Groves, S.: 1993b, ‘Calculators as an Agent for Change: Teachers’ Perceptions and Practice’, Paper presented at the Annual Conference of the Australian Association for Research in Education, Fremantle.

    Google Scholar 

  • Groves, S.: 1994a, ‘Calculators: A Learning Environment to Promote Number Sense’, Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans.

    Google Scholar 

  • Groves, S.: 1994b, The Effect of Calculator Use on Third and Fourth Graders’ Computation and Choice of Calculating Device’, in J. da Ponte and J. F. Matos (eds.), Proceedings of the Eighteenth International Conference for the Psychology of Mathematics Education, Lisbon, 3, 33–40.

    Google Scholar 

  • Groves, S. & Cheeseman, J.: 1993, Young Children Using Calculators [video-tape], Deakin University.

    Google Scholar 

  • Harvey, J., Waits, B., & Demana, F.: 1992, ‘The Influence of Technology on the Teaching and Learning of Algebra’, Paper presented at the Seventh International Congress on Mathematical Education, Québec.

    Google Scholar 

  • Hedren, R: 1985, ‘The Hand-Held calculator at the Intermediate Level’, Educational Studies in Mathematics, 16, 163–179.

    Article  Google Scholar 

  • Hembree, R. & Dessart, D.: 1986, ‘Effects of Hand-Held Calculators in Precollege Mathematics: A Meta-Analysis’, Journal for Research in Mathematics Education 17 (2), 83–99.

    Article  Google Scholar 

  • Hembree, R. & Dessart, D.: 1992, ‘Research on Calculators in Mathematics Education1, in J. Fey and C. Hirsch (eds.), Calculators in Mathematics Education., National Council of Teachers of Mathematics, Reston VA, 23–32.

    Google Scholar 

  • Her Majesty’s Inspectorate: 1991, Mathematics: Key Stages I and 3, Her Majesty’s Stationery Office, London.

    Google Scholar 

  • Her Majesty’s Inspectorate: 1992. Mathematics: Key Stages I, 2 and 3, Her Majesty’s Stationery Office, London.

    Google Scholar 

  • Howson, G.: 1991, National Curricula in Mathematics, The Mathematical Association, Leicester.

    Google Scholar 

  • Illich, I.: 1973, Tools For Conviviality, Calder and Boyars, London.

    Google Scholar 

  • Kaput, J.: 1989, ‘Linking Representations in the Symbol Systems of Algebra1, in S. Wagner and C. Kieran (eds.), Research Issues in the Teaching and Learning of Algebra, National Council of Teachers of Mathematics, Reston VA, 167–197.

    Google Scholar 

  • Kieran, C: 1992, ‘The Learning and Teaching of School Algebra’, in D. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning. Macmillan, New York, 390–419

    Google Scholar 

  • Kirshner, D.: 1989, ‘Critical Issues in Current Representation System Theory’, in S. Wagner and C. Kieran (eds.), Research Issues in the Teaching and Learning of Algebra, National Council of Teachers of Mathematics, Reston VA, 195–198.

    Google Scholar 

  • Lapointe, A., Mead, N. & Askew, J.: 1992. Learning Mathematics, Educational Testing Service, Princeton NJ.

    Google Scholar 

  • Meissner, H.: 1979, ‘Problem-solving with the One-Way Principle’, in D. Tall (ed.), Proceedings of the Third International Conference for the Psychology of Mathematics Education, Warwick, 157–159.

    Google Scholar 

  • Meissner, H.: 1985, ‘Self Developing Strategies with a Calculator Game’, in L. Streefland (ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education, Utrecht, 68–73.

    Google Scholar 

  • Moskowitz, S.: 1994, The Integration of the Graphing Calculator into the Algebra Classroom at the Community College. Unpublished MSc thesis, California State University Chico,

    Google Scholar 

  • Newman, D., Griffin, P. & Cole, M.: 1989, The construction zone: Working for cognitive change in school, Cambridge University Press, Cambridge.

    Google Scholar 

  • Office for Standards in Education: 1994, Science and Mathematics in Schools: A review, Her Majesty’s Stationery Office, London.

    Google Scholar 

  • Oldknow, A.: 1995, ‘On twin peaks and flat Functions’, The Mathematical Gazette 79 (484) 47–50.

    Article  Google Scholar 

  • Palumbo, D.: 1990, ‘Programming Language/Problem-Solving Research: A Review of Relevant Issues’, Review of Educational Research 60 (1), 65–89.

    Article  Google Scholar 

  • Pea, R.: 1987, ‘Cognitive technologies for mathematics education’, in A. H. Schoenfeld (ed.), Cognitive Science and Mathematics Education, Lawrence Erlbaum Associates, Hillsdale NJ, 89–122.

    Google Scholar 

  • Ponte, J., Nunes, F. & Veloso, E.: 1991, ‘Graphic calculators in mathematics teaching’, in Using Computers in Mathematics Teaching: A collection of case studies, Department of Education, Faculty of Sciences, University of Lisbon, 157–172.

    Google Scholar 

  • Primary Initiatives in Mathematics Education: 1989, The Second Year of CAN, Homerton College, Cambridge.

    Google Scholar 

  • Quesada, A. & Maxwell, M.: 1994, ‘The Effects of Using Graphic Calculators to Enhance College Students Performance in Precalculus’, Educational Studies in Mathematics 27, 205–215.

    Article  Google Scholar 

  • Reys, R., Reys, B., Nohda, N. & Emori, H.: 1995, ‘Mental Computation Performance and Strategy Use of Japanese Students in Grades 2, 4, 6, and 8’, Journal for Research in Mathematics Education 26 (4), 304–326.

    Article  Google Scholar 

  • Roberts, D. M.: 1980, ‘The Impact of Electronic Calculators on Educational Performance’, Review of Educational Research 50 (1), 71–98.

    Article  Google Scholar 

  • Rowland, T.: 1989, CAN in Suffolk: The beginnings of a calculator-aware number curriculum in three Suffolk primary schools, Homerton College, Cambridge.

    Google Scholar 

  • Ruthven, K.: 1990, ‘The Influence of Graphic Calculator Use on Translation from Graphic to Symbolic Forms’, Educational Studies in Mathematics, 21, 431–450.

    Article  Google Scholar 

  • Ruthven, K.: 1991, ‘Teacher Centred Curriculum Development’, in A. Warbecq (ed.), Proceedings of the 41st CIEAEM Meeting, Brussels, 349–352.

    Google Scholar 

  • Ruthven, K.: 1992a, Graphic Calculators in Advanced Mathematics, National Council for Educational Technology, Coventry.

    Google Scholar 

  • Ruthven, K.: 1992b, ‘Personal Technology and Classroom Change: A British Perspective’, in J. Fey and C. Hirsch (eds.), Calculators in Mathematics Education, National Council of Teachers of Mathematics, Reston VA, 91–100.

    Google Scholar 

  • Ruthven, K: 1995a, ‘Pressing on: towards considered calculator use’, in L. Burton and B. Ja-worski (eds.), Technology — a Bridge between Teaching and Learning Mathematics, Chart-well Bratt, 231–256.

    Google Scholar 

  • Ruthven, K.: 1995b, ‘Pupils’ views of number work and calculators’, Educational Research, 17(3), 229–237.

    Article  Google Scholar 

  • Schumacher, E. F.: 1973, Small is Beautiful: A Study of Economics as if People Mattered, Blond and Briggs, London.

    Google Scholar 

  • Shoaf-Grubbs, M. M.: 1994, ‘The Effect of the Graphing Calculator on Female Students’ Spatial Visualization Skills and Level-of-Understanding in Elementary Graphing and Algebra Concepts’, Issues in Mathematics Education 4, 169–194.

    Google Scholar 

  • Shuard, H.: 1992, ‘CAN: Calculator Use in the Primary Grades in England and Wales’, in J. Fey and C. Hirsch (eds.), Calculators in Mathematics Education, National Council of Teachers of Mathematics, Reston VA, 33–45.

    Google Scholar 

  • Shuard, H., Walsh, A., Goodwin, J. & Worcester, V.: 1991a, Calculators, Children and Mathematics, Simon and Schuster, London.

    Google Scholar 

  • Shuard, H., Walsh, A., Goodwin, J. & Worcester, V.: 1991b, Calculators, Children and Mathematics [video-tape], Simon and Schuster, London.

    Google Scholar 

  • Shumway, R.: 1990, ‘Supercalculators and the Curriculum’, For the Learning of Mathematics 10(2), 2–9.

    Google Scholar 

  • Shumway, R., Wheatley, G., Coburn, T., White, A., Reys R. & Schoen, H.: 1981, ‘Initial Effects of Calculators in Elementary School Mathematics’, Journal for Research in Mathematics Education 12(2), 119–141.

    Article  Google Scholar 

  • Stacey, K.: 1994, ‘Calculators in Primary Mathematics: An Analysis of Classroom Activities’, Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans.

    Google Scholar 

  • Stacey, K. & Groves, S.: 1994, ‘Calculators in Primary Mathematics’, Paper presented at the Annual Meeting of the National Council of Teachers of Mathematics, Indianapolis.

    Google Scholar 

  • Stigler, J., Chalip, L. & Miller, K.: 1986, ‘Consequences of Skill: The Case of Abacus Training in Taiwan’, American Journal of Education 94, 447–479.

    Article  Google Scholar 

  • Stradling, R., Sims, D. & Jamison, J.: 1994, Portable Computers Pilot Evaluation Report, National Council for Educational Technology, Coventry.

    Google Scholar 

  • Ter Heege, H.: 1983, ‘The Multiplication Algorithm: an Integrated Approach’, For the Learning of Mathematics 3 (3), 29–34.

    Google Scholar 

  • Van den Brink, J.: 1993, ‘Different aspects in designing mathematics education: three examples from the Freudenthal Institute’, Educational Studies in Mathematics 24, 35–64.

    Article  Google Scholar 

  • Vonder Embse, C: 1992, ‘Concept Development and Problem Solving Using Graphing Calculators in the Middle School’, in J. Fey and C. Hirsch (eds.), Calculators in Mathematics Education, National Council of Teachers of Mathematics, Reston VA, 65–78.

    Google Scholar 

  • Waits, B. & Demana, F: 1994, The Calculator and Computer Precalculus Project (C2PC): What Have We Learned in Ten Years?’, in G. Bright, H. Waxman and S.Williams (eds.) Impact of Calculators on Mathematics Instruction, University Press of America, Lanham MD, 91–110.

    Google Scholar 

  • Wheatley, C: 1980, ‘Calculator Use and Problem-Solving Performance’, Journal for Research in Mathematics Education 11 (5), 323–334.

    Article  Google Scholar 

  • Wheatley, G. & Shumway, R.: 1992, ‘The Potential for Calculators to Transform Elementary School Mathematics’, in J. Fey and C. Hirsch (eds.) Calculators in Mathematics Education, National Council of Teachers of Mathematics, Reston VA, 1–8.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Cambridge, UK

    Kenneth Ruthven

Authors
  1. Kenneth Ruthven
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Monash University, Clayton, Victoria, Australia

    Alan J. Bishop

  2. Universiti Brunei, Darussalam, Brunei

    Ken Clements

  3. Freie Universität Berlin, Germany

    Christine Keitel

  4. The University of Georgia, USA

    Jeremy Kilpatrick

  5. Université Joseph Fourier, Grenoble, France

    Colette Laborde

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Kluwer Academic Publishers

About this chapter

Cite this chapter

Ruthven, K. (1996). Calculators in the Mathematics Curriculum: the Scope of Personal Computational Technology. In: Bishop, A.J., Clements, K., Keitel, C., Kilpatrick, J., Laborde, C. (eds) International Handbook of Mathematics Education. Kluwer International Handbooks of Education, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1465-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-1465-0_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7155-0

  • Online ISBN: 978-94-009-1465-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation