Personal Experiences And Beliefs In Probabilistic Reasoning: Implications For Research

Sashi Sharma

doi:10.29333/iejme/170

Full Text (PDF)

Sashi Sharma

More Detail

Abstract

Concerns about students' difficulties in statistical thinking led to a study which explored form five (14 to 16 year olds) students’ ideas in this area. The study focussed on probability, descriptive statistics and graphical representations. This paper presents and discusses the ways in which students made sense of probability concepts used in individual interviews. The findings revealed that many of the students used strategies based on beliefs, prior experiences (everyday and school) and intuitive strategies. From the analysis, I identified a four category rubric that could be considered for describing how students construct meanings for probability questions. While students showed competence with theoretical interpretation, they were less competent on tasks involving frequentist definition of probability. This could be due to instructional neglect of this viewpoint or linguistic problems. The paper concludes by suggesting some implications for further research.

Keywords

Probabilistic Reasoning
High School Students
Interviews
Intuitive Strategies
Beliefs
Experiences
Culture
Contexts

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2006, Volume 1, Issue 1, 35-54

https://doi.org/10.29333/iejme/170

Publication date: 10 Oct 2006

Article Views: 2623

Article Downloads: 2086

Open Access References How to cite this article

References

Amir, G. & Williams, J. (1999). Cultural Influences on Children’s Probabilistic Thinking. Journal of Mathematical Behavior, 18(10), 85-107.
Amir, G. & Williams, J. (1994). The influence of children's culture on their probabilistic Thinking. In J. da Ponte & J. Matos (eds.), Proceedings of the Eighteenth International Conference for the Psychology of Mathematics Education, 29 July-3 August, 1994, Vol. II (pp. 24-31). Lisbon, Portugal, The Program Committee of the 18th PME Conference.
Australian Education Council. (1991). A National Statement on Mathematics for Australian Schools, Canberra, Curriculum Corporation.
Barnes, M. (1998). Dealing with misconceptions about probability. Australian Mathematics Teacher, 54(10), 17-20.
Barton, B. (1996). Making sense of ethno-mathematics: ethno-mathematics is making sense. Educational Studies in Mathematics, 31, 201-133.
Carraher, D. & Schliemann A. (2002). Modeling Reasoning. In K. Gravemeijer, R. Lehrer, B. V. Oers & L. Verschaffel (eds.), Symbolizing, Modeling and Tool Use in Mathematics Education (pp. 295-304). Dordrecht: Kluwer Academic Publishers.
Cobb, P. (1994).’Where is the mind? Constructivist and sociocultural perspectives on mathematical development’ Educational Research, 23(7), 13-20.
Cooper, B. and Dunne, M. (1999). Assessing Children’s Mathematical Ability. Buckingham, Open University Press.
Fijian Ministry of Education, Women, Culture, Science and Technology (1994). Primary Mathematics Prescriptions. Suva: Curriculum Development Unit.
Fischbein, E., Nello, M. S. & Marino, M. S. (1991). Factors affecting probabilistic judgements in children and adolescents’. Educational Studies in Mathematics, 22, 523-549.
Fischbein, E. & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28, 96-105.
Garfield, J. B. (1995). How students learn statistics, International Statistical Review, 63(1), 25–34.
Holmes, P. (1994). Teaching statistics at school level in some European countries, in L. Brunelli and G. Cicchutelli (eds.), Proceedings of the First Scientific Meeting (pp. 3-11), University of Perugia,
Lajioe, S. P. and Romberg, T. A.: 1998: ‘ Identifying an agenda for statistics instruction and assessment in K-12’. In S.P. Lajoie (ed.), Reflections on Statistics: Learning, Teaching, and Assessment in Grades K-12..Mahwah NJ, Lawrence Erlbaum Associates.
Lave, J. (1991). Cognition in practice; Mind, mathematics and culture in everyday life. New York: Cambridge University Press.
Lecoutre, M. (1992). Cognitive models and problem spaces in purely random situations. Educational Studies in Mathematics, 23, 557-568.
Metz, K. E. (1997). Dimensions in the assessment of students’ understanding and application of Chance. In I. Gal and J. B. Garfield (eds.), The Assessment Challenge in Statistics Education (pp. 223-238). Amsterdam: The Netherlands, IOS Press,
Meyer, M. R, Dekker, T. & Querelle, N. (2001). Context in mathematics curricula. Mathematics Teaching in the Middle School, 6(9), 522-527.
Mills, J. D. (2003). A theoretical framework for teaching statistics. Teaching Statistics, 25(2), 56-58.
Ministry of Education. (1992). Mathematics in the New Zealand Curriculum. Wellington: Ministry of Education.
Nicolson, C. P. (2005). Is chance fair? One student’s thoughts on probability. Teaching Children Mathematics. 12(2), 83-89.
Shaughnessy, J. M. (1997). Missed opportunities in research on the teaching and learning of data and chance. In F. Biddulph & K. Carr (eds.), People in mathematics education. Mathematics Education Beyond 2000 (pp. 6-22). Proceedings of the 20d Annual Conference of the Mathematics Education Research Group of Australasia. Hamilton, MERGA INC,
Shaughnessy, J.M. & Zawojewski, J. S. (1999). Secondary students’ performance on data and chance in the 1996 NAEP. The Mathematics Teacher, 92(8), 713-718.
Sullivan, P., Zevenbergen, R., & Mousley, J. (2002). Contexts in Mathematics teaching: snakes or ladders? In B. Barton, K. C. Irwin, M. Pfannncuch and M. Thomas (eds.), Mathematics Education in the South Pacific (pp 649-656). Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia. Auckland.
Truran, K. M. (1994). Children’s understandings of random generators. In C. Beesey &D. Rasmussen (eds.), Mathematics Without Limits, Proceedings of the 31st Annual Conference of the Mathematical Association of Victoria (pp. 356-362). Melbourne: Mathematics Association of Victoria.
Tversky, A. & Kahneman, D. (1974). Judgement under uncertainty: Heuristics and biases. Science, 185, 1124-1131.
Von Glasersfeld, E. (1993). Questions and answers about radical constructivism. In K. Tobin (ed.), The practice of constructivism in science education (pp. 24-38). Washington: American Association for the Advancement of Science.
Watson, J. M. & Callingham R. (2003). Statistical literacy: A complex hierarchical construct. Statistics Education Research Journal, 2(2), 3-46.

How to cite this article

APA

Sharma, S. (2006). Personal Experiences And Beliefs In Probabilistic Reasoning: Implications For Research. International Electronic Journal of Mathematics Education, 1(1), 35-54. https://doi.org/10.29333/iejme/170

Vancouver

Sharma S. Personal Experiences And Beliefs In Probabilistic Reasoning: Implications For Research. INT ELECT J MATH ED. 2006;1(1):35-54. https://doi.org/10.29333/iejme/170

AMA

Sharma S. Personal Experiences And Beliefs In Probabilistic Reasoning: Implications For Research. INT ELECT J MATH ED. 2006;1(1), 35-54. https://doi.org/10.29333/iejme/170

Chicago

Sharma, Sashi. "Personal Experiences And Beliefs In Probabilistic Reasoning: Implications For Research". International Electronic Journal of Mathematics Education 2006 1 no. 1 (2006): 35-54. https://doi.org/10.29333/iejme/170

Harvard

Sharma, S. (2006). Personal Experiences And Beliefs In Probabilistic Reasoning: Implications For Research. International Electronic Journal of Mathematics Education, 1(1), pp. 35-54. https://doi.org/10.29333/iejme/170

MLA

Sharma, Sashi "Personal Experiences And Beliefs In Probabilistic Reasoning: Implications For Research". International Electronic Journal of Mathematics Education, vol. 1, no. 1, 2006, pp. 35-54. https://doi.org/10.29333/iejme/170