Skip to main content
SpringerLink
Log in
Book cover

Exploring Probability in School pp 65–92Cite as

An Overview of Research into the Teaching and Learning of Probability

  • Chapter

Part of the book series: Mathematics Education Library ((MELI,volume 40))

This is a preview of subscription content, 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   89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Amir, G. S., & Williams, J. S. (1999). Cultural influences on children's probabilistic thinking. Journal of Mathematical Behaviour, 18(1), 85–107.

    Article  Google Scholar 

  • Austin, J. D. (1974). An experimental study of the effects of three instructional methods in basic probability and statistics. Journal for Research in Mathematics Education, 5, 146–154.

    Article  Google Scholar 

  • Australian Education Council. (1991). A national statement on mathematics for Australian schools. Carlton, VIC: Curriculum Corporation.

    Google Scholar 

  • Australian Education Council. (1994). Mathematics: A curriculum profile for Australian schools. Carlton, VIC: Curriculum Corporation.

    Google Scholar 

  • Batanero, C., Estepa, A., Godino, J. D., Green, D. R. (1996). Intuitive strategies and preconceptions about association in contingency tables. Journal for Research in Mathematics Education, 27, 151–169.

    Article  Google Scholar 

  • Batanero, C. & Serrano, L. (1999). The meaning of randomness for secondary students. Journalfor Research in Mathematics Education, 30, 558–567.

    Article  Google Scholar 

  • Batanero, C., Serrano, L., & Garfield, J. B. (1990). Heuristics and biases in secondary school students' reasoning about probability. In L. Puig and A. Gutiérrez (Eds.), Proceedings of the 20 th conference of the International Group for the Psychology of Mathematics Education (Vol.2, pp. 51–58). University of Valencia, Spain.

    Google Scholar 

  • Batanero, C., Serrano, L, & Green, D. R. (1998). Randomness, its meanings and educational implications. International Journal for Mathematics Education in Science and Technology, 29(1), 11–123.

    Google Scholar 

  • Batanero, C., Tauber, L., & Sanchez, L. (in press). Students' reasoning about the normal distribution. In D. Ben Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking. Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Begg, A. & Edwards, R. (1999, December). Teachers' ideas about teaching statistics. Paper presented at the combined annual meeting of the Australian Association for Research in Education and the New Zealand Association for Research in Education. Melbourne.

    Google Scholar 

  • Benson, C. T. (2000). Assessing students' thinking in modeling probability contexts. Unpublished doctoral dissertation, Illinois State University, Normal.

    Google Scholar 

  • Benson, C. T., & Jones, G. A. (1999). Assessing students' thinking in modeling probability contexts. The Mathematics Educator, 4(2), 1–21.

    Google Scholar 

  • Biehler, R. (1991). Computers in probability education. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 169–211). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Biehler, R. (1993). Software tools and mathematics education. In C. Keitel & K. Ruthven (Eds.), Learning through computers: Mathematics and educational technology (pp. 68–100). Berlin: Springer Verlag.

    Google Scholar 

  • Bloom, B. (1968). Learning for mastery. UCLA-CSEIP Evaluation Comment, 1(2). Los Angeles: Center for the Study of Evaluation of Instructional Programs.

    Google Scholar 

  • Bright, G. W., & Friel, S. N. (1998). Teacher development in statistics education. In S. P. Lajoie (Ed.), Reflections on statistics: Learning, teaching and assessment in Grades K-12 (pp. 56–74). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Brousseau, G., Brousseau, N., & Warfield, V. (2002). An experiment on the teaching of statistics and probability. Journal of Mathematical Behavior, 20, 363–411.

    Article  Google Scholar 

  • Burgess, T. (2002). Investigating the "data sense" of preservice teachers. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on the Teaching of Statistics(On CD). Hawthorn, VIC: International Statistical Institute.

    Google Scholar 

  • Cambridge Conference on School Mathematics. (1963). Goals for school mathematics. Boston: Houghton Mifflin.

    Google Scholar 

  • Carlson, J. S. (1970). The development of probabilistic thinking in children: A comparison of two methods of assessment. Journal of Genetic Psychology, 116: 263–269.

    Google Scholar 

  • Castro, C. S. (1998). Teaching probability for conceptual change. Educational Studies in Mathematics, 35, 233–254.

    Article  Google Scholar 

  • Chance, B. (2002). Concepts of statistical thinking and implications for instruction and assessment. Journal of Statistics Education, 10(3). [Online:www.amstat.org/publications/jse/v10n3/chance.html]

    Google Scholar 

  • Clemen, R., & Gregory, R. (2000). Preparing adult students to be better decision makers. In I. Gal (Ed.), Adult numeracy development: Theory, research, and practice. Cresskill, NJ: Hampton Press.

    Google Scholar 

  • Cobb, P. & Bauersfeld, H. (1995). The emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M. (1991). Assessment of aproblem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22, 3–29.

    Article  Google Scholar 

  • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education, (pp. 307–334). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Cohen, J. (1960). Chance, skill, and luck: The psychology of guessing and gambling. Baltimore, MD: Penguin Books.

    Google Scholar 

  • Dessart, D. J. (1995). Randomness: A connection to reality. In P. A. House (Ed.), Connecting mathematics across the curriculum: 1995 Yearbook (pp. 177–181). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Department of Education and Science and the Welsh Office. (1991). National curriculum: Mathematics for ages 5 to 16. York, UK: Central Office of Information.

    Google Scholar 

  • Engel, A. (1966). Initiation la theorie des probabilities. In New trends in mathematics teaching (Vol. 1, pp. 159–174). Paris: UNESCO.

    Google Scholar 

  • Evans, J. (2000). Adults' mathematical thinking and emotions: A study of numerate practices. Routledge-Falmer, London.

    Google Scholar 

  • Falk, R. (1981). The perception of randomness. In Proceedings of the fifth conference of the International Group for the Psychology of Mathematics Education (pp. 222–229). Grenoble, France: University of Grenoble.

    Google Scholar 

  • Falk, R. (1988). Conditional probabilities: Insights and difficulties. In R. Davidson & J. Swift (Eds.), Proceedings of the Second International Conference on Teaching Statistics (pp. 714–716). Victoria, BC: University of Victoria.

    Google Scholar 

  • Falk, R. (1989). The judgement of coincidences: Mine versus yours. American Journal of Psychology, 102, 417–493.

    Article  Google Scholar 

  • Falk, R. & Konold, C. (1997). Making sense of randomness. Implicit encoding as a basis for judgment. Psychological Review, 104, 301–318.

    Article  Google Scholar 

  • Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht, The Netherlands: Reidel.

    Google Scholar 

  • Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, The Netherlands: Reidel.

    Google Scholar 

  • Fischbein, E., Ileana, B., & Minzat, I. (1971). Primary and secondary intuitions in the introduction of probability. Educational Studies in Mathematics, 4, 264–280.

    Article  Google Scholar 

  • Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics, 15, 1–24.

    Article  Google Scholar 

  • Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgments in children in adolescence. Educational Studies in Mathematics, 22, 523–549.

    Article  Google Scholar 

  • Fischbein, E., Pampu, I., & Manzat, I. (1969). Initiation aux probabilities a l'ecole elementaire. Educational Studies in Mathematics, 2, 16–31.

    Article  Google Scholar 

  • Fischbein, E., Pampu, I., & Manzat, I. (1970a). Comparisons of ratios and the chance concept in children. Child Development, 41, 377–389.

    Google Scholar 

  • Fischbein, E., Pampu, I., & Manzat, I. (1970b). Effects of age and instruction on combinatory ability in children. The British Journal of Experimental Psychology, 40, 261–270.

    Google Scholar 

  • Fischbein, E. & Schnarch, D. (1997). The evolution, with age of probabilistic, intuitively-based misconceptions. Journal for Research in Mathematics Education, 28, 96–105.

    Article  Google Scholar 

  • Freudenthal, H. (1970). The aims of teaching probability. In L. Rade (Ed.), The teaching of probability and statistics (pp. 151–168). Stockholm: Almqvist & Wiksell.

    Google Scholar 

  • Gal, I (2000). Adult numeracy development: Theory, research, practice. Cresskill, NJ: Hampton Press.

    Google Scholar 

  • Gal, I (2002). Adult statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1–25.

    Google Scholar 

  • Garfield, J. & Ahlgren, A. (1988). Difficulties in learning basic concepts of probability and statistics: Implications for research. Journal for Research in Mathematics Education, 19, 44–63.

    Article  Google Scholar 

  • Garfield, J., & delMas, R. (1989). Reasoning about chance events: Assessing and changing students' conceptions of probability. In C. Maher, G. Goldin, & B. Davis (Eds.), Proceedings of the 13 th conference of the International Group for the Psychology of Mathematics Education (Vol. 2, 189–195). Rutgers, NJ: Rutgers University Press.

    Google Scholar 

  • Gratch, G. (1959). The development of the expectation of the non-independence of random events in children. Child Development, 30, 217–227.

    Google Scholar 

  • Green, D. R. (1979). The chance and probability concepts project. Teaching Statistics, 1(3), 66–71.

    Google Scholar 

  • Green, D. R. (1983). A survey of probability concepts in 3000 pupils aged 11–16 years, In D. R. Grey, P. Holmes, V. Barnett, & G. M. Constable (Eds.), Proceedings of the First International Conference on Teaching Statistics (pp. 766–783). Sheffield, UK: Teaching Statistics Trust.

    Google Scholar 

  • Green, D. R. (1988). Children's understanding of randomness: Report of a survey of 1600 children aged 7–11 years. In R. Davidson & J. Swift (Eds.), Proceedings of the Second International Conference on Teaching Statistics (pp. 287–291). Victoria, B.C.: University of Victoria.

    Google Scholar 

  • Grouws, D. A. (Ed.). (1992). Handbook of research on mathematics teaching and Learning. New York: Macmillan.

    Google Scholar 

  • Hancock, C. (1988). Hands on data: Direct manipulation environments for data organization and analysis. Proposal funded by the National Science Foundation. Cambridge, MA: TERC.

    Google Scholar 

  • Hacking, I. (1975). The emergence of probability. Cambridge, MA: Cambridge University Press.

    Google Scholar 

  • Haller, S. K. (1997). Adopting probability curricula: The content and pedagogical content knowledge of middle grades teachers. Unpublished doctoral dissertation, University of Minnesota.

    Google Scholar 

  • Hawkins, A. (1990). Training teachers to teach statistics. Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Hoemann, H. W., & Ross, B. W. (1971). Children's understanding of probability concepts. Child Development, 42, 221–236.

    Google Scholar 

  • Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence (A. Parsons & S. Milgram, Trans.). New York: Basic Books.

    Google Scholar 

  • Jolliffe, F. (1997). Issues in constructing assessment items for the classroom. In I. Gal & J. B. Garfield (Eds.), The assessment challenge in statistics education (pp. 191–204). Amsterdam, The Netherlands: IOS Press.

    Google Scholar 

  • Jones, G. A. (1974). The performances offirst, second, and thirdgrade children on five concepts of probability and the effects of grade, I.Q., and embodiments on their performance. Unpublished doctoral dissertation, Indiana University, Bloomington.

    Google Scholar 

  • Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1997). Framework for assessing and nurturing young children's thinking in probability. Educational Studies in Mathematics, 32, 101–125.

    Article  Google Scholar 

  • Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Students' probabilistic thinking in instruction. Journal for Research in Mathematics Education, 30, 487–519.

    Article  Google Scholar 

  • Jones, G. A., Thornton, C. A., Langrall, C. W., & Tarr, J. E. (1999). Understanding students' probabilistic reasoning. In L. V. Stiff & F. R. Curcio (Eds.), Developing mathematical reasoning in Grades K-12: 1999 Yearbook (pp. 146–155) Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Kahneman, D., & Tversky, A. (1972). Subjective Probability: A judgement of representativeness. Cognitive Psychology, 3, 430–454.

    Article  Google Scholar 

  • Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases. Cambridge: Cambridge University Press.

    Google Scholar 

  • Kipp, W. E. (1975). An investigation of the effects of integrating topics of elementary algebra with those of probability within a unit of mathematics prepared for college basic mathematics students. Unpublished doctoral dissertation, University of Minnesota, Minneapolis.

    Google Scholar 

  • Konold, C. (1983). Conceptions about probability: Reality between a rock and a hard place. Unpublished doctoral dissertation, University of Massachusetts, Boston.

    Google Scholar 

  • Konold, C. (1989a). Informal conceptions of probability. Cognition and Instruction, 6, 59–98.

    Article  Google Scholar 

  • Konold, C. (1989b). An outbreak of belief in independence? In C. Maher, G. Goldin, & B. Davis (Eds.), Proceedings of the 13 th conference of the International Group for the Psychology of Mathematics Education (Vol. 2, 203–209). Rutgers, NJ: Rutgers University Press.

    Google Scholar 

  • Konold, C. (1991). Understanding students' beliefs about probability. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 139–156). Dordrecht, Netherlands: Kluwer.

    Google Scholar 

  • Konold, C. (1995). Issues in assessing conceptual understanding in probability and statistics. Journal of Statistics Education (Online), 3(1).

    Google Scholar 

  • Konold, C., Pollatsek, A., Well, A., Lohmeier, J., & Lipson, A. (1993). Inconsistencies in students' reasoning about probability. Journal for Research in Mathematics Education, 24, 392–414.

    Article  Google Scholar 

  • Kosonen, P. & Whinne, P. H. (1995). Effects of teaching statistical laws on reasoning about everyday problems. Journal of Educational Psychology, 87(1), 33–46.

    Article  Google Scholar 

  • Kvatinsky, T. & Even, R. (2002). Framework for teacher knowledge and understanding of probability. Proceedings of the Sixth International Conference on the Teaching of Statistics (On CD), Hawthorn, VIC: International Statistical Institute.

    Google Scholar 

  • Lecoutre, M. P. (1992). Cognitive models and problem spaces in "purely random" situations. Educational Studies in Mathematics, 23, 557–568.

    Article  Google Scholar 

  • Leffin, W. W. (1971). A study of three concepts of probability possessed by children in the fourth, fifth, sixth, and seventh grades. Unpublished doctoral dissertation, University of Wisconsin, Madison.

    Google Scholar 

  • Li, J., & Pereira-Mendoza, L. (2002). Misconceptions in probability. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics (On CD), Hawthorn, VIC: International Statistical Institute.

    Google Scholar 

  • Maher, C. A. & Speiser, R. (2002). The complexity of learning to reason probabilistically. Working group at the 25 th annual meeting of North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 103–108). Athens, GA.

    Google Scholar 

  • Maher, C. A., Speiser, R., Friel, S., & Konold, C. (1998). Learning to reason probabilistically. In S. B. Berenson, K. R. Dawkins, M. Blanton, W. N. Coulombe, J. Kolb, K. Norwood, L. Stiff (Eds.), Proceedings of the 20 th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 82–87). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

    Google Scholar 

  • Metz, K. E. (1997). Dimensions in the assessment of students' understanding and application of chance. In I. Gal & J. B. Garfield (Eds.). The assessment challenge in statistics education (pp. 223–238). Amsterdam, The Netherlands: IOS Press.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Offenbach, S. I. (1965). Studies of children's probability learning behavior II: Effect of method and event frequency. Child Development, 36, 952–961.

    Google Scholar 

  • Page, D. (1959) Probability. In P. S. Jones (Ed.), The growth of mathematical ideas, Grades K-12: 24th Yearbook (pp. 229–271). Washington, DC: National Council of Teachers of Mathematics.

    Google Scholar 

  • Paparistodemou, E., Noss, R., & Pratt, D. (2002). Developing young children's knowledge of randomness. In B. Phillips (Ed.), Proceedings of the sixth International Conference on the Teaching of Statistics (On CD). Hawthorn, VIC: International Statistical Institute.

    Google Scholar 

  • Peard, R. (1995). The effect of social background on the development of probabilistic reasoning. In A. J. Bishop (Ed.), Regional collaboration in mathematics education (pp. 561–570). Melbourne, VIC: Monash University.

    Google Scholar 

  • Pereira-Mendoza, L. (2002). Would you allow your accountant to perform surgery? Implications for the education of primary teachers. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on the Teaching of Statistics(On CD). Hawthorn, VIC: International Statistical Institute.

    Google Scholar 

  • Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in students (L. Leake, Jr., P. Burrell, & H. D. Fischbein, Trans). New York: Norton (Original work published 1951).

    Google Scholar 

  • Polaki, M. V. (2002a). Using instruction to identify key features of Basotho elementary students' growth in probabilistic thinking. Mathematical Thinking and Learning, 4, 285–314.

    Article  Google Scholar 

  • Polaki, M. V. (2002b). Using instruction to identify mathematical practices associated with Basotho elementary students' growth in probabilistic reasoning. Canadian Journal of Science, Mathematics and Technology Education, 2, 357–370.

    Google Scholar 

  • Pratt, D. (1998). The coordination of meanings for randomness. For the Learning of Mathematics, 18(3), 2–11.

    Google Scholar 

  • Pratt, D. (2000). Making sense of the total of two dice. Journal of Research in Mathematics Education, 31, 602–625.

    Article  Google Scholar 

  • Pratt, D. & Noss, R. (2002). The microevolution of mathematical knowledge: The case of randomness. Journal of the Learning Sciences, 11(4), 453–488.

    Article  Google Scholar 

  • Resnick, L. B. (1983). Towards a cognitive theory of instruction. In S. G. Paris & G. M. Olson, & W. H. Stevenson (Eds.), Learning and motivation in the classroom (pp. 5–38). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Sanchez, E. S. (2002). Teachers' beliefs about usefulness of simulations with the educational software Fathom for developing probability concepts in statistics classroom. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on the Teaching of Statistics (On CD). Hawthorn, VIC: International Statistical Institute.

    Google Scholar 

  • Scheaffer, R. L., Watkins, A. E., & Landwehr, J. M. (1998). What every high school graduate should know about statistics. In S. P. Lajoie, (Ed.), Reflections on statistics: Learning, teaching, and assessment in grades K-12 (pp. 3–31). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Scholttmann, A. (2001). Children's probability intuitions: Understanding the expected value ofcomplex gambles. Child Development, 72, 103–122.

    Article  Google Scholar 

  • School Mathematics Study Group (1966). Probability for primary grades: Teachers' commentary. Pasadena, CA: A. C. Vroman.

    Google Scholar 

  • School Mathematics Study Group (1966). Probability for intermediate grades: Teachers' commentary. Pasadena, CA: A. C. Vroman.

    Google Scholar 

  • Siegel, S. & Andrews, J. M. (1962). Magnitude of reinforcement and choice behavior in children. Journal of Experimental Psychology, 63, 337–341.

    Google Scholar 

  • Simon, M. A. (1995). Reconstructing mathematics from a constructivist pedagogy. Journal for Research in Mathematics Education, 26, 146–149.

    Article  Google Scholar 

  • Shaughnessy, J. M. (1977). Misconceptions of probability: An experiment with a small-group, activity-based, model building approach to introductory probability at the college level. Educational Studies in Mathematics, 8, 285–316.

    Article  Google Scholar 

  • Shaughnessy, J. M. (1992). Research in probability and statistics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465–494). New York: Macmillan.

    Google Scholar 

  • Shaughnessy, J. M., Watson, J. D., Moritz, J. B., & Reading, C. (1999, April). School mathematics students' acknowledgment of statistical variation. Paper presented at the Research Presession, 77th annual meeting of the National Council of Teachers of Mathematics, San Francisco, CA.

    Google Scholar 

  • Shepler, J. L. (1970). Parts of a systems approach to the development of a unit in probability and statistics for the elementary school. Journal for Research in Mathematics Education, 1, 197–205.

    Article  Google Scholar 

  • Slovic, P. & Lichtenstein, S. (1971). Comparison of Bayesian and regression approaches to the study of information processing in judgment. Organizational Behavior and Human Performance, 6, 649–744.

    Article  Google Scholar 

  • Speiser, R. & Walter, C. (2001). Two dice, two sample spaces. In L. Pereira-Mendoza (Ed.), Proceedings of the Fifth International Conference on Teaching Statistics (pp. 61–66). Singapore: International Statistical Institute.

    Google Scholar 

  • Steffe, L. P. (1983, July). The teaching experiment methodology in a constructivist research program. Paper presented at the Fourth International Congress on Mathematical Education, Boston.

    Google Scholar 

  • Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In E. von Glassersfeld (Ed.), Radical constructivism in mathematics education (pp. 177–194). Dordercht, The Netherlands: Kluwer.

    Google Scholar 

  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267–306). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Steinbring, H. (1991). The theoretical nature of probability in the classroom. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 135–168). Amsterdam, The Netherlands: Kluwer.

    Google Scholar 

  • Steinbring, H. (1984). Mathematical concepts in didactical situations as complex systems: The case of probability. In H. Steiner & N. Balacheff (Eds.), Theory of mathematics education (TME: ICME 5): Occasional paper 54 (pp. 56–88). Bielefeld: IDM.

    Google Scholar 

  • Stevenson, H., W., & Zigler, E. F. (1958). Probability learning in children. Journal of Experimental Psychology, 56, 185–192

    Google Scholar 

  • Tarr, J. E. (1997). Using research-based knowledge of students' thinking in conditional probability and independence to inform instruction. Unpublished doctoral dissertation, Illinois State University, Normal.

    Google Scholar 

  • Tarr, J. E. (2002). The confounding effects of “50–50 chance” in making conditional probability judgments, Focus on Learning Problems in Mathematics, 24, 35–53.

    Google Scholar 

  • Tarr, J. E., & Jones, G. A. (1997). A framework for assessing middle school students' thinking in conditional probability and independence. Mathematics Education Research Journal, 9, 39–59.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76, 105–110.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124–1131.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1982). Causal schemas in judgments under uncertainty. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 117–128). Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgement. Psychological Review, 90, 293–315.

    Article  Google Scholar 

  • Varga, T. (1969a). Combinatorials and probability for the young (Part 1). Journal for Structural Learning, 1, 49–99.

    Google Scholar 

  • Varga, T. (1969b). Combinatorials and probability for the young (Part 2). Journal for Structural Learning, 1, 139–161.

    Google Scholar 

  • Volkova, T. (2003). Assessing Russian children's thinking in probability. Unpublished master's thesis, Illinois State University, Normal.

    Google Scholar 

  • Vygotsky, L. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Watson, J. M. (2001). Profiling teachers' competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education 4, 305–337.

    Article  Google Scholar 

  • Watson, J. M., Collis, K. F., & Moritz, J. B. (1997). The development of chance measurement. Mathematics Education Research Journal, 9, 60–82.

    Google Scholar 

  • Watson, J. D., & Moritz, J. B. (1998). Longitudinal development of chance measurement. Mathematics Education Research Journal, 10, 103–127.

    Google Scholar 

  • Watson, J. D., & Moritz, J. B. (2002). School students' reasoning about conjunction and conditional events. International Journal of Mathematics Education in Science and Technology, 33(1), 59–84.

    Article  Google Scholar 

  • Watson, J. D. & Moritz, J. B. (2003a). Fairness of dice: A longitudinal study of students' beliefs and strategies for making judgments. Journalfor Research in Mathematics Education, 34, 270–304.

    Article  Google Scholar 

  • Watson, J. D. & Moritz, J. B. (2003b). The development of comprehension of chance language: evaluation and interpretation. School Science and Mathematics, 103, 65–80

    Google Scholar 

  • Way, J. (2003). The development of children's notions of probability. Unpublished doctoral dissertation, University of Western Sydney.

    Google Scholar 

  • Zimmermann, G. M. (2002). Using research-based knowledge of students' thinking in simulation to inform instruction. Unpublished doctoral dissertation, Illinois State University, Normal.

    Google Scholar 

  • Zimmerman, G. M., & Jones, G. A. (2002). Probability simulation: What meaning does it have for high school students? Canadian Journal of Science, Mathematics, and Technology Education, 2, 221–237.

    Article  Google Scholar 

Download references

Authors
  1. Graham A. Jones
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carol A. Thornton
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Griffith University, Gold Coast Campus, Australia

    Graham A. Jones

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

Jones, G.A., Thornton, C.A. (2005). An Overview of Research into the Teaching and Learning of Probability. In: Jones, G.A. (eds) Exploring Probability in School. Mathematics Education Library, vol 40. Springer, Boston, MA. https://doi.org/10.1007/0-387-24530-8_4

Download citation

Publish with us

Policies and ethics

Search

Navigation