Alternatives to traditional algorithms in elementary mathematics instruction
DOI:
https://doi.org/10.7146/nomad.v4i2-3.146428Abstract
The purpose of the research project has been to find out what changes ought to take place in elementary mathematics teaching, if we want to consider the changing need of mathematical knowledge and skill in a society with calculators and computers.
The project is and will be carried out in one class followed through years 2 - 5. The children are now (May 1996) in year 3. Traditional algorithms for the four arithmetic operations are not taught, instead the children are encouraged to invent their own methods for written computation and, besides, to use mental arithmetic and estimation whenever appropriate. Each child has also access to a calculator of her/ his own.
The project is mainly evaluated by qualitative methods, e. g. clinical interviews and observations of groups of children. The results that are discussed, are mainly from year 3. They show that the children, when given the chance, invent a lot of different methods to cope with exercises in addition and subtraction, and in so doing they exhibit signs of increasing number sense. However, many children still have difficulties with regrouping in subtraction.
References
Beishuizen, M. (1993). Mental Strategies and Materials or Models for Addition and Subtraction up to 100 in Dutch Second Grades. Journal for Research in Mathematics Education 24(4), 294 - 323. https://doi.org/10.2307/749464
Björkqvist, O. (1993). Social konstruktivism som grund för matematikundervisning [Social Constructivism as a Foundation for the Teaching of Mathematics]. Nordic Studies in Mathematics Education 7(1), 8 - 17.
Cobb, P. (1994). Where Is the Mind? Constructivist and Sociocultural Perspectives on Mathematical Development. Educational Researcher 23(7), 13-20. https://doi.org/10.3102/0013189X023007013
Curriculum and Evaluation Standards for School Mathematics (1989). Reston, Va (USA): National Council of Teachers of Mathematics.
Davis, R. B., Maher, C. A., & Noddings, N. (Eds.) (1990). Constructivist Views on the Teaching and Learning of Mathematics. Journal for Research in Mathematics Education. Monograph No. 4. Reston, Va (USA): National Council of Teachers of Mathematics. https://doi.org/10.2307/749908
Ernest, P. (1991a). Constructivism, the Psychology of Learning, and the Nature of Mathematics: Some Critical Issues. In F. Furinghetti (Ed.), Proceedings of the Fifteenth International Conference of Psychology of Mathematics Education. Vol II (pp. 25 - 32). Genova (Italy): Università di Genova.
Ernest, P. (1991b). The Philosophy of Mathematics Education. London (UK): The Falmer Press.
Ernest, P. (1994). Varieties of Constructivism: Their Metaphors, Epistemologies and Pedagogical Implications. Hiroshima Journal of Mathematics Education Vol.2,1-14.
Glaserfeld, E. von (1990). An Exposition of Constructivism: Why Some Like It Radical. In Constructivist Views on the Teaching and Learning of Mathematics. Journalfor Research in Mathematics Education. Monograph No. 4 (pp. 19 - 29). Reston, Va (USA): National Council of Teachers of Mathematics. https://doi.org/10.2307/749910
Glaserfeld, E. von (Ed.) (1991). Radical Constructivism in Mathematics Education. Dordrecht (Netherlands): Kluwer Academic Publishers.
Greenes, C, Schulman, L., & Spungin, R. (1992/93). Developing Sense about Numbers. Arithmetic Teacher 40(5), 279-284. https://doi.org/10.5951/AT.40.5.0279
Harz, W. (1993). Regning uden standardalgoritmer. Mimeo.
Hedrén, R. (1995a). Miniräknaren eller algoritmer i den elementära matematikundervisningen. Högskolan Falun Borlänge (Sweden): Forskning. Sektionen för humaniora och beteendevetenskap. Rapport 1995:2.
Hedrén, R. (1995b). How Pupils Think when they Are Allowed to Develop their Own Calculation Methods. In E. Cohors-Fresenborg (Ed.), European Research Conference on the Psychology of Mathematics Education. Abstracts (pp. 26 - 30). University of Osnabrück (Germany), FB Mathematik-Informatik.
Kamii, C. (1985). Young Children Reinvent Arithmetic. Implications of Piaget's Theory. New York (USA): Teachers College Press.
Kamii, C. (1989). Young Children Continue to Reinvent Arithmetic. 2nd Grade. Implications of Piaget's Theory. New York (USA): Teachers College Press.
Kamii, C. (1994). Young Children Continue to Reinvent Arithmetic. 3rd Grade. Implications of Piaget's Theory. New York (USA): Teachers College Press.
Kamii, C , Lewis, B. A., & Livinston, S. Jones (1993/94). Primary Arithmetic: Children Inventing Their Own Procedures. Arithmetic Teacher 41(4), 200-203. https://doi.org/10.5951/AT.41.4.0200
Koyama, M. (1994). Research Into Relationship Between the Computational Estimation Ability and Strategy and the Mental Computation Ability: Analysis of a Survey of the Fourth, Fifth, and Sixth Graders in Japan. Hiroshima Journal of Mathematics Education Vol.2,35-44.
Krauthausen, G. (1993). Kopfrechnen, halbschriftliches Rechnen, schriftliche Normalverfahren, Taschenrechner: Für eine Neubestimmung des Stellenwertes der vier Rechenmethoden. Journal für Mathematikdidaktik 14(3/4), 189-219. https://doi.org/10.1007/BF03338792
Kursplanerför grundskolan (1994). Stockholm (Sweden): Utbildningsdepartementet.
Ljung, B.-O., & Pettersson, A. (1990). Matematiken i nationell utvärdering. Kunskaper och färdigheter i årskurserna 2 och 5. Rapportfrån PRIM-gruppen nr 5. Stockholm (Sweden): Högskolan för lärarutbildning.
McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A Proposed Framework for Examining Basic Number Sense. For the Learning of Mathematics 72(3), 2-8,44.
Murray, H., Olivier, A., & Human, P. (1991). Young Children's Division Strategies. In F. Furinghetti (Ed.), Proceedings of the Fifteenth International Conference of Psychology of MathematicsEducation VolIII(pp.49-56).
Narode, R., Board, J., & Davenport, L. (1993). Algorithms Supplant Understanding: Case Studies of Primary Students' Strategies for Double-Digit Addition and Subtraction. In J. R. Becker,. & J. B. Pence (Eds.), Proceedings of the Fifteenth Annual Meeting, North American Chapter of the International Group for the Psychology of Mathematics Education Vol I. Pacific Groves, CA (USA).
Olivier, A. (1988). The Future of Pencil-and-Paper Algorithms in the Arithmetic Curriculum. Pythagoras No. 77 (May, 1988).
Olivier, A., Murray, H., & Human, P. (1990). Building on Young Children's Informal Arithmetical Knowledge. In Proceedings of the Fourteenth International Conference of Psychology of Mathematics Education Vol III (pp.297-304).
Plunkett, S. (1979). Decomposition and All that Rot. Mathematics in School 8(2), 2-5.
Reys, B. J. (1991). Developing Number Sense in the Middle Grades. Curriculum and Evaluation Standards for School Mathematics. Addenda Series Grades 5-8. Reston, Va (USA): National Council of Teachers of Mathematics.
Reys, B. J. (1994). Promoting Number Sense. Mathematics Teaching in the Middle School 7(2), 114-120. https://doi.org/10.5951/MTMS.1.2.0114
Reys, B. J., Reys R. E. & Emanuelsson, G. (1995). Meningsfulla tal. Nämnaren 22(4), 8-12.
Shuard, H. et al. (1991). Prime. Calculators, Children and Mathematics. London (UK): Simon & Schuster.
Sowder, J. (1992). Estimation and Number Sense. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 371 -389). New York (USA): Macmillan Publishing Company.
Sullivan, P. (1990). Calculations in the Classroom: Implications for Teaching and Learning. Journal of Science and Mathematics Education in S. E. Asia 73(1), 7 - 1 3 .
Thompson, I. (1994). Young Children's Idiosyncratic Written Algorithms for Addition. Educational Studies in Mathematics, 26(4), 323-345. https://doi.org/10.1007/BF01279519
Unenge, J., Sandahl, A. & Wyndhamn, J. (1994). Lära matematik. Lund: Studentlitteratur.
Vygotsky, L. S. (1978). Mind in Society. Cambridge, Ma (USA): Harvard University Press.
Wheatley, G. H. & Shumway, R. (1992). The Potential for Calculators to Transform Elementary School Mathematics. In J. T. Fey, & C. R. Hirsch (Eds.), Calculators in Mathematics Education. 1992 Yearbook (pp. 1 - 8). Reston, Va (USA): National Council of Teachers of Mathematics.
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