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

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.

[1]  Jean-Marie Laborde.  Intelligent Microworlds and Learning Environments , 1996 .

[2]  Adrian Oldknow.  On Twin Peaks and Flat Functions , 1995 .

[3]  Kaye Stacey,et al.  Calculators in Primary Mathematics: An Analysis of Classroom Activities. , 1994 .

[4]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[5]  David S. Fielker.  A calculator, a tape recorder, and thou , 1987 .

[6]  T Rojano,et al.  A Spreadsheet Approach to Solving Algebra Problems. , 1993 .

[7]  Paolo Boero.  The Crucial Role of Semantic Fields in the Development of Problem Solving Skills in the School Environment , 1992 .

[8]  Etienne Wenger,et al.  Artificial Intelligence and Tutoring Systems , 1987 .

[9]  Anthony Ralston,et al.  The Influence of Computers and Informatics on Mathematics and Its Teaching. Science and Technology Education Series, 44. , 1986 .

[10]  Antonio R. Quesada,et al.  The effects of using graphing calculators to enhance college students' performance in precalculus , 1994 .

[11]  Kenneth Ruthven.  Pupils’ views of number work and calculators , 1995 .

[12]  Michèle Artigue,et al.  Le Logiciel ‘Derive’ comme revelateur de phenomenes didactiques lies a l'utilisation d'environnements informatiques pour l'apprentissage , 1997 .

[13]  Nicolas Balacheff.  Treatment of Refutations: Aspects of the Complexity of a Constructivist Approach to Mathematics Learning , 1991 .

[14]  Anthony Kaye,et al.  Collaborative Learning Through Computer Conferencing , 1992, NATO ASI Series.

[15]  Christian R Hirsch,et al.  Calculators in mathematics education , 1992 .

[16]  Franklin Demana,et al.  The influence of technology on the teaching and learning of algebra , 1995 .

[17]  James T. Sandefur.  Technology, Linear Equations, and Buying a Car , 1992 .

[18]  John Seely Brown,et al.  An Investigation of Computer Coaching for Informal Learning Activities. , 1978 .

[19]  Stellan Ohlsson.  Sense and Reference in the Design of Interactive Illustrations for Rational Numbers. , 1986 .

[20]  David B. Palumbo,et al.  Programming Language/Problem-Solving Research: A Review of Relevant Issues , 1990 .

[21]  Robert B. Davis,et al.  Computers and Curriculum Change in Mathematics , 1993 .

[22]  Colette Laborde,et al.  The Computer as Part of the Learning Environment: The Case of Geometry , 1993 .

[23]  Mark Elsom-Cook.  Guided discovery tutoring : a framework for ICAI research , 1990 .

[24]  Tak-Wai Chan.  Some techniques for building mathematical intelligent tutoring systems , 1991, Intell. Tutoring Media.

[25]  John Seely Brown,et al.  Process versus Product: A Perspective on Tools for Communal and Informal Electronic Learning , 1985 .

[26]  Carolyn Kieran.  The learning and teaching of school algebra. , 1992 .

[27]  Jan Van Den Brink.  Different aspects in designing mathematics education: Three examples from the Freudenthal Institute , 1993 .

[28]  Daniel Chazan,et al.  Quasi-empirical views of mathematics and mathematics teaching , 1990 .

[29]  Celia Hoyles.  Thematic Chapter: Exploratory Software, Exploratory Cultures? , 1995 .

[30]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[31]  Joao Pedro Ponte.  Using Computers in Mathematics Teaching. A Collection of Case Studies. , 1991 .

[32]  Nicolas Balacheff.  Advanced Educational Technology: Knowledge Revisited , 1996 .

[33]  James J. Kaput,et al.  Technology in Mathematics Education Research: The First 25 Years in the JRME , 1994 .

[34]  Denis Newman,et al.  The Construction Zone: Working for Cognitive Change in School , 1989 .

[35]  Rosamund Sutherland,et al.  Connecting theory and practice: Results from the teaching of Logo , 1993 .

[36]  Bert Bredeweg,et al.  Student Modelling: The Key to Individualized Knowledge-Based Instruction , 2010, NATO ASI Series.

[37]  Rosamund J Sutherland.  Technology - a bridge between teaching and learning mathematics , 1995 .

[38]  Joel Hillel.  Computer Algebra Systems as Cognitive Technologies: Implication for the Practice of Mathematics Education , 1993 .

[39]  A. Schoenfeld.  Cognitive Science and Mathematics Education , 1987 .

[40]  Celia Hoyles.  Microworlds/Schoolworlds: The Transformation of an Innovation , 1993 .

[41]  P. Thompson.  Notations, Conventions, and Constraints: Contributions to Effective Uses of Concrete Materials in Elementary Mathematics. , 1992 .

[42]  Lynn Arthur Steen,et al.  On the shoulders of giants: new approaches to numeracy , 1990 .

[43]  Jana Trgalová.  Jana Trgalova. Étude historique et épistémologique des coniques et leur implémentation informatique dans le logiciel Cabri-géomètre. Thèse de l'université Joseph Fourier - Grenoble, 31 octobre 1995 , 1996 .

[44]  Jere Confrey,et al.  Chapter 1: A Review of the Research on Student Conceptions in Mathematics, Science, and Programming , 1990 .

[45]  Thomas J. Cooney,et al.  Teaching and learning mathematics in the 1990s , 1990 .

[46]  R. Hembree,et al.  Effects of Hand-Held Calculators in Precollege Mathematics Education: A Meta-Analysis. , 1986 .

[47]  Kaye Stacey,et al.  Calculators in Primary Mathematics. , 1994 .

[48]  Harold L. Schoen,et al.  Mathematical Problem-Solving Performance of Eighth-Grade Programmers and Nonprogrammers. , 1988 .

[49]  John Seely Brown,et al.  Diagnostic Models for Procedural Bugs in Basic Mathematical Skills , 1978, Cogn. Sci..

[50]  B. White.  ThinkerTools: Causal Models, Conceptual Change, and Science Education , 1993 .

[51]  David Tall.  Proceedings of the third International Conference for the Psychology of Mathematics Education , 1979 .

[52]  Daniel Chazan,et al.  How to Use Conjecturing and Microcomputers to Teach Geometry , 1989 .

[53]  George W. Bright,et al.  Impact of Calculators on Mathematics Instruction , 1993 .

[54]  C. Hoyles,et al.  A pedagogy for mathematical microworlds , 1992 .

[55]  Robert L. Devaney,et al.  A First Course in Chaotic Dynamical Systems , 2020 .

[56]  Bernard Parzysz.  “Knowing” vs “seeing”. problems of the plane representation of space geometry figures , 1988 .

[57]  Robert E. Reys,et al.  Mental Computation Performance and Strategy Use of Japanese Students in Grades 2, 4, 6, and 8. , 1995 .

[58]  James T. Fey,et al.  Technology and mathematics education: A survey of recent developments and important problems , 1989 .

[59]  John R. Anderson,et al.  The Geometry Tutor , 1985, IJCAI.

[60]  Nicolas Balacheff,et al.  Epistemological domain of validity of microworlds: the case of LOGO and Cabri-Géomètre , 1993, Lessons from Learning.

[61]  Jeremy Kilpatrick,et al.  Didactic Transposition in Mathematics Textbooks. , 1992 .

[62]  Salima Tahri.  Salima Tahri. Modélisation de l'interaction didactique : un tuteur hybride sur Cabri-géomètre pour l'analyse de décisions didactiques. Thèse de doctorat de l'université Joseph Fourier - Grenoble I, 25 octobre 1993 , 1995 .

[63]  Derek H. Sleeman.  Inferring (Mal) Rules from Pupil's Protocols , 1982, ECAI.

[64]  Rolf Biehler,et al.  Software Tools and Mathematics Education: The Case of Statistics , 1993 .

[65]  E. F. Schumacher,et al.  Small is Beautiful: A Study of Economics as if People Mattered , 1974 .

[66]  Laurent Trilling,et al.  Tuteurs Intelligents et Intelligence Artificielle: problèmes posés en construction de figures géométriques , 1992, Intelligent Tutoring Systems.

[67]  James W. Stigler,et al.  Consequences of Skill: The Case of Abacus Training in Taiwan , 1986, American Journal of Education.

[68]  Arthur Engel.  Elementarmathematik vom algorithmischen Standpunkt , 1977 .

[69]  I. Illich.  Tools for Conviviality , 1973 .

[70]  F. Bellemain,et al.  Specificite de l'organisation d'une sequence d'enseignement lors de l'utilisation de l'ordinateur , 1992 .

[71]  Alan R. Osborne,et al.  Learning How to See: Students Graphing Difficulties. , 1991 .

[72]  Seymour Papert.  Uses of Technology to Enhance Education , 1973 .

[73]  Harold Abelson,et al.  Turtle geometry : the computer as a medium for exploring mathematics , 1983 .

[74]  Paul E. Ceruzzi.  Electronic calculators , 1990 .

[75]  Jean-François Nicaud.  A General Model of Algebraic Problem Solving for the Design of Interactive Learning Environments , 1992 .

[76]  James J. Kaput,et al.  Authentic Inquiry With Data: Critical Barriers to Classroom Implementation , 1992 .

[77]  Nicolas Balacheff,et al.  Teacher's role and reproducibility of didactical situations , 1992 .

[78]  James T. Sandefur,et al.  Discrete dynamical systems - theory and applications , 1990 .

[79]  Patrick W Thompson,et al.  Quantitative reasoning, complexity, and additive structures , 1993 .

[80]  Gary G. Bitter,et al.  Integration of the Math Explorer Calculator into the Mathematics Curriculum: The Calculator Project Report. , 1993 .

[81]  John R. Anderson,et al.  Cognitive Modeling and Intelligent Tutoring , 1990, Artif. Intell..

[82]  James Taylor Fey.  Computing and mathematics : the impact on secondary school curricula : report of a conference , 1984 .

[83]  Dennis M. Roberts.  The Impact of Electronic Calculators on Educational Performance , 1980 .

[84]  Martial Vivet.  Uses of ITS: Which Role for the Teacher? , 1992 .

[85]  Tommy Dreyfus.  Didactic Design of Computer-based Learning Environments , 1993 .

[86]  Kenneth Ruthven.  The influence of graphic calculator use on translation from graphic to symbolic forms , 1990 .

[87]  Charlotte L. Wheatley.  Calculator Use and Problem-Solving Performance. , 1980 .

[88]  M. Ann Dirkes.  GCT Review: The Geometric Supposer: Triangles , 1987 .

[89]  A. Howson.  National curricula in mathematics , 1991 .

[90]  Richard Shumway.  Supercalculators and the Curriculum. , 1990 .

[91]  Mitchel Resnick,et al.  Turtles, termites, and traffic jams - explorations in massively parallel microworlds , 1994 .

[92]  Barbara Y. White,et al.  Progressions of Qualitative Models as a Foundation for Intelligent Learning Environments. Report No. 6277. , 1986 .

[93]  Nicolas Balacheff,et al.  Artificial Intelligence and Real Teaching , 1993 .

[94]  H. G. Steiner,et al.  New Trends in Mathematics Teaching, Volume IV. , 1978 .

[95]  Rolf Hedren,et al.  The hand-held calculator at the intermediate level , 1985 .

[96]  W. Dörfler.  Computer Use and Views of the Mind , 1993 .