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Part of the book series: Mathematics Education Library ((MELI,volume 12))

Abstract

This chapter is concerned with the impact of computers on probability in general secondary education. Mathematics educators have been producing ideas for using computers and calculators in probability education for two decades. Although there are many teaching suggestions, empirical research on this topic is uncommon and critical reports of practical experience rarely go beyond an enthusiastic description. A critical review of ideas, software and experience which would be helpful for further research and development is the major objective of this chapter. We will deal with pedagogical aspects, the subject matter and its change, and the role of changing technology. Various approaches will be reviewed; computers used as general mathematical utilities, simulation as a scientific method, and simulation for providing an empirical background for probability. Graphical methods may enhance the idea of visualization. The emphasis is on general orientation in the field.

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Bibliography

  • Alvord, L.L.: 1985, Probability in APL: A Model for Using Executable Language, Ph.D.thesis, Rutgers University, New Brunswick.

    Google Scholar 

  • Atkinson, D.T.: 1975, A Comparison of the Teaching of Statistical Inference by Monte Carlo and Analytic methods, Ph.D.thesis, University of Illinois, Urbana Champaign.

    Google Scholar 

  • Bar-On, E. and R. Or-Bach: 1988, ‘Programming Mathematics: A New Approach in Introducing Probability to Less Able Pupils’, International Journal for Mathematical Education in Science and Technology 19, 281–297.

    Article  Google Scholar 

  • Bauersfeld, H.: 1984, ‘The Disparity of Computer Experience — a Case for Orienting the Syllabus for Elementary Education?’, in J.D. Tinsley (ed.), Informatics in Elementary Education, North Holland, Amsterdam, 199–206.

    Google Scholar 

  • Becker, R.A., J.M. Chambers and A.R. Wilks: 1988, The New S Language, Wadsworth and Brooks, Pacific Grove.

    Google Scholar 

  • Biehler, R.: 1982, Explorative Datenanalyse — Eine Untersuchung aus der Perspektive einer deskriptiv — empirischen Wissenschaftstheorie, Materialien und Studien 24, IDM, Bielefeld.

    Google Scholar 

  • Biehler, R.: 1985, ‘Interrelations between Computers, Statistics and Teaching Mathematics’, in Commission Internationale de L’ Enseignement Mathématique (ed.), The Influence of Computers and Informatics on Mathematics and Its Teaching, Supporting Papers, IREM, Strasbourg, 209–214.

    Google Scholar 

  • Biehler, R.: 1991, ‘Fortschritte der Software und die Tradition der Schulmathematik’, in W. Dörfler, W. Peschek, and E. Schneider (eds.), Mensch-Computer-Mathematik, Hölder-Pichler-Tempsky, Wien.

    Google Scholar 

  • Biehler, R. and W. Rach: 1990, Softwaretools zur Statistik und Datenanalyse: Beispiele, Anwendungen und Konzepte aus didaktischer Sicht, Soester Verlagskontor, Soest.

    Google Scholar 

  • Bright, G.W.: 1985, ‘What Research Says: Teaching Probability and Estimation of Length and Angle Measurement through Microcomputer Instructional Games’, School Science and Mathematics 85, 513–522.

    Article  Google Scholar 

  • Collis, B.: 1983, ‘Teaching Descriptive and Inferential Statistics Using a Classroom Microcomputer’, Mathematics Teacher 76(5), 318–322

    Google Scholar 

  • diSessa, A.: 1986, ‘Artificial Worlds and Real Experience’, Instructional Science 14, 207–227.

    Article  Google Scholar 

  • Dreyfus, T.: 1986, ‘Cognitive Effects of Microworlds: Learning about Probability’, Proceedings Second Intern. Conf. Logo and Math. Educ, London, 172–179.

    Google Scholar 

  • Efron, B.: 1979, ‘Computers and the Theory of Statistics: Thinking the Unthinkable’, SIAM Review 21, 460–480.

    Article  Google Scholar 

  • Engel, A.: 1975, ‘Computing and Probability’, in L. Råde (ed.), Statistics at School Level, Proc. Third ISI Round Table Conference on the Teaching of Statistics, Wiley, New York, 95–120.

    Google Scholar 

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

    Google Scholar 

  • Engel, A.: 1985, ‘Algorithmic Aspects of Stochastics’, in Commission Internationale de L’ Enseignement Mathématique (ed.), The Influence of Computers and Informatics on Mathematics and Its Teaching, Supporting Papers, IREM, Strasbourg, 215–222.

    Google Scholar 

  • Engel, A.: 1986, ‘statistik mit programmierbaren Taschenrechnern (PTR) und Tischrechnern’, Didaktik der Mathematik 14, 243–263.

    Google Scholar 

  • Engel, A.: 1987, Stochastik, Klett, Stuttgart.

    Google Scholar 

  • Feller, W.: 1968, An Introduction to Probability Theory and its Applications, Wiley, New York.

    Google Scholar 

  • Fraser, R.: 1989, ‘Role of Computers for Application and Modelling. The ITMA Approach’, in W. Blum, J. Berry, R. Biehler, I. Huntley, G. Kaiser-Messmer and L. Profke (eds.), Applications and Modelling in Learning and Teaching Mathematics, Ellis Horwood, Chichester, 373–380.

    Google Scholar 

  • Fraser, R., H. Burkhardt, J. Coupland, R. Phillips, D. Pimm and J. Ridgway: 1988, ‘Learning Activities and Classroom Roles with and without Computers’, Journal of Mathematical Behavior 6, 305–338.

    Google Scholar 

  • Freiberger, W. and U. Grenander: 1971, A Course in Computational Probability and Statistics, Springer, New York.

    Book  Google Scholar 

  • Freudenthal, H.: 1974, ‘The Crux of Course Design in Probability’, Educational Studies in Mathematics 5, 261–277.

    Article  Google Scholar 

  • Freudenthal, H.: 1975, Wahrscheinlichkeit und Statistik 3rd. ed., Oldenbourg, München.

    Google Scholar 

  • Gnanadesikan, M., R.L. Schaeffer, and J. Swift: 1987, The Art and Technique of Simulation, Dale Seymour, Palo Alto.

    Google Scholar 

  • Harten, G. von, H.N. Jahnke, T. Mormann, M. Otte, F. Seeger, H. Steinbring, and H. Stellmacher: 1986, Funktionsbegriff und funktionales Denken, Aulis, Köln.

    Google Scholar 

  • Holmes, A. H.: 1968, Teaching the Logic of Statistical Inference by the Monte Carlo Approach, Ph.D.thesis, Univ. Illinois, Urbana.

    Google Scholar 

  • Holmes, P.: 1985, ‘Using Micro Computers to Extend and Supplement Existing Material for Teaching Statistics’, in L. Råde and T. Speed (eds.), Teaching of Statistics in the Computer Age. Proceedings of the 6th ISI Round Table Conference on Teaching of Statistics, Chartwell Bratt Ltd., Bromley, 87–104.

    Google Scholar 

  • Howson, A.G. and J.P. Kahane (eds.): 1986, The Influence of Computers and Informatics on Mathematics and Its Teaching, Cambridge Univ. Press, Cambridge.

    Google Scholar 

  • Inhelder, W.: 1981, ‘solving Probability Problems through Computer Simulation’, in A.P. Shulte and J.R. Smart (eds.), Teaching Statistics and Probability, NCTM Yearbook 1981, National Council of Teachers of Mathematics, Reston VA, 220–234.

    Google Scholar 

  • Jäger, J. and H. Schupp: 1983, Curriculum Stochastik in der Hauptschule, Schöningh, Paderborn.

    Google Scholar 

  • Johnson, N.C.: 1986, Using a Microcomputer to Teach a Statistical Concept, Ph.D.thesis, Univ. Minnesota.

    Google Scholar 

  • Kaput, J.J.: 1986, ‘Information Technology and Mathematics. Opening New Representational Windows’, Journal of Mathematical Behavior 5, 187–207.

    Google Scholar 

  • Kaput, J.J.: 1988, Looking Back From the Future. A History of Computers in Mathematics Education, 1978-1998, Unpublished Manuscript, Educational Technology Center, Cambridge MA.

    Google Scholar 

  • Klingen, L.H.: 1977, ‘Zusammenhang und Reichweite modularer Algorithmen in der Schulmathematik’, in Informatik im Unterricht der Sekundarstufe II. Grundfragen, Probleme und Tendenzen mit Bezug auf allgemeinbildende und berufsqualifizierende Ausbildungsgänge, Schriftenreihe des IDM 16, IDM, Bielefeld, 3–33.

    Google Scholar 

  • Konoid, G: 1991, One Son, Coincidences, Coin Flipping, Random vs. Mixed up, Building Box Models, Pilot student materials from the Computer Based Curriculum for Probability and Statistics Project, Univ. Massachusetts, Amherst MA.

    Google Scholar 

  • Konoid, C., M. Sutherland, and J. Lochhead: 1989, A Computer Based Curriculum for Probability and Statistics, Project Proposal, Univ. Massachusetts, Amherst MA.

    Google Scholar 

  • Landwehr, J.M., J. Swift, and A.E. Watkins: 1987, Exploring Surveys and Information from Samples, Dale Seymour, Palo Alto.

    Google Scholar 

  • Lunn, D.: 1985, ‘Computer Animation: A Powerful Way of Teaching Concept of Probability and Statistics’, in L. Råde and T. Speed (eds.), Teaching of Statistics in the Computer Age. Proceedings of the 6th ISI Round Table Conference on Teaching of Statistics, Chartwell Bratt Ltd., Bromley, 114–125.

    Google Scholar 

  • Moore, D.S.: 1990, ‘Uncertainty’, in L.A. Steen (ed.), On the Shoulders of Giants, National Academy Press, Washington D.C., 95–137.

    Google Scholar 

  • O’Shea, T. and J. Self: 1983, Learning and Teaching with Computers, Harvester, Brighton.

    Google Scholar 

  • Pollak, H.O.: 1989, ‘Recent Applications of Mathematics and their Relevance for Teaching’, in W. Blum, J. Berry, R. Biehler, I. Huntley, G. Kaiser-Messmer and L. Profke (eds.), Applications and Modelling in Learning and Teaching Mathematics, Ellis Horwood, Chichester, 32–36.

    Google Scholar 

  • Rach, W., R. Biehler, and B. Winkelmann: 1988, ‘Teacher Interfaces in Software for Mathematics Education: Different Requirements of Software from the Perspectives of Learners and Teachers’, in A. Vermandel (ed.), Theory of Mathematics Education. Proceedings of the Third International Conference, Univ. Antwerpen, Antwerpen, 149–156.

    Google Scholar 

  • Råde, L.: 1977, ‘Probability, Simulation, and Programmable Calculators’, in W. Dörfler and R. Fischer (eds.), Anwendungsorientierte Mathematik in der Sek. II, Hölder-Pichler-Tempsky, Wien, 163–177.

    Google Scholar 

  • Råde, L.: 1981, ‘statistics, Simulation, and Statistical Data Analysis at the School Level’, in W. Dörfler and R. Fischer (eds.), Stochastik im Schulunterricht, Hölder-Pichler-Tempsky, Wien, 165–178.

    Google Scholar 

  • Råde, L.: 1981a, ‘Random Digits and the Programmable Calculator’, in A.P. Shulte and J.R. Smart (eds.), Teaching Statistics and Probability, NCTM Yearbook 1981, National Council of Teachers of Mathematics, Reston, 118–125.

    Google Scholar 

  • Råde, L.: 1983, ‘stochastics at the School Level in the Age of Computer’, in D.R. Grey, P. Holmes, V. Barnett, and G.M. Constable (eds.), Proceedings First Intern. Conf. Teach. Statistics vol. 1, Teaching Statistics Trust, Sheffield, 19–33.

    Google Scholar 

  • Riemer, W.: 1985, Neue Ideen zur Stochastik, Bibliographisches Institut, Mannheim.

    Google Scholar 

  • Sanders, W.J.: 1971, Teaching Statistical Decision Making to Junior High School Students, Ph.D.diss, Univ. Illinois.

    Google Scholar 

  • Shevokas, C: 1974, Using a Computer-Oriented Monte Carlo Approach to Teach Probability and Statistics in a Community College General Mathematics Course, Ph.D.diss, Univ. Illinois.

    Google Scholar 

  • Simon, J.L., D.T. Atkinson, and C. Shevokas: 1976, ‘Probability and Statistics. Experimental Results of a Radically Different Teaching Method’, American Mathematical Monthly, 83, 733–739.

    Article  Google Scholar 

  • Simon, J.L. and D. Weidenfeld: 1973, Simple. A Radical Teaching and Computer Program for Statistics , Univ. Illinois.

    Google Scholar 

  • Steinbring, H.: 1985, ‘Wie verteilen sich die Kugeln beim Galton-Brett wirklich?’, mathematik lehren 12, 31–38.

    Google Scholar 

  • Swets, J.A., A. Rubin, and W. Feuerzeig: 1987, Cognition, Computers, and Statistics. Software Tools for Curriculum Design, Progress Report-Year 1, BBN Laboratories, Cambridge.

    Google Scholar 

  • Tall, D. and B. Winkelmann: 1988, ‘Plotting Function Graphs and Teaching Hidden Algorithms’, Bulletin of the IMA. 24(7/8), 111–115.

    Google Scholar 

  • Travers, K.: 1981, ‘Using Monte Carlo Methods to Teach Probability and Statistics’, in A.P. Shulte and J.R. Smart (eds.), Teaching Statistics and Probability, NCTM Yearbook 1981, National Council of Teachers of Mathematics, Reston, 210–219.

    Google Scholar 

  • Travers, K.J., W.F. Stout, J.H. Swift, and J. Sextro: 1985, Using Statistics, Addison Wesley, Menlo Park.

    Google Scholar 

  • Tukey, J.W.: 1962, ‘The Future of Data Analysis’, Annals of Mathematical Statistics 33, 1–67.

    Article  Google Scholar 

  • Watkins, A.E.: 1981, ‘Monte Carlo Simulation: Probability the Easy Way’, in nr]A.P. Shulte and J.R. Smart (eds.), Teaching Statistics and Probability, NCTM Yearbook 1981, National Council of Teachers of Mathematics, Reston, 203–209.

    Google Scholar 

  • Watson, F.R.: 1980, A Simple Introduction to Simulation. Part I+II, Keele Mathematical Education Publications, Keele.

    Google Scholar 

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Biehler, R. (1991). Computers in Probability Education. In: Kapadia, R., Borovcnik, M. (eds) Chance Encounters: Probability in Education. Mathematics Education Library, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3532-0_6

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  • DOI: https://doi.org/10.1007/978-94-011-3532-0_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5563-5

  • Online ISBN: 978-94-011-3532-0

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