A longitudinal study of student understanding of chance and data
 Jane Watson,
 Ben Kelly,
 John Izard
 … show all 3 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
This study uses Partial Credit Rasch analysis to study a complex data set of student responses to survey items relating to chance and data. The items were administered in the classroom and collected from 1993 to 2003 in the Australian state of Tasmania. Data were collected from a total of 5514 individual students across Grades 3 to 11 over the decade and of these students 896 provided at least one repeated measure. As students completed a core of common items, Rasch analysis could be performed and all students were subsequently placed on the same logit scale for comparison. The purpose of the analysis is to consider average cohort change over time and trends in performance during the first 10 years after the curriculum was introduced in Tasmania. Implications for the education system and curriculum implementation are considered.
 Australian Education Council. (1991).A national statement on mathematics for Australian schools. Melbourne: Author.
 Biggs, J. B., & Collis, K. F. (1982).Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.
 Cai, J. (1998). Exploring students’ conceptual understanding of the averaging algorithm.School Science and Mathematics, 98, 93–98. CrossRef
 Callingham, R. A., & Watson, J. M. (2005). Measuring statistical literacy.Journal of Applied Measurement, 6(1), 19–47.
 Cohen, J. (1969).Statistical power analysis for the behavioural sciences. New York: Academic Press.
 Department of Education Tasmania. (2002).Essential learnings framework 1. Hobart: Author.
 Department of Education and the Arts. (1993).Mathematics guidelines K8. Hobart: Curriculum Services Branch.
 Fischbein, E. (1975).The intuitive sources of probabilistic thinking in children. Dordrecht, The Netherlands: D. Reidel.
 Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? An exploratory research study.Educational Studies in Mathematics, 15, 1–24. CrossRef
 Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications.Journal for Research in Mathematics Education, 32, 124–158. CrossRef
 Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities.International Statistical Review, 70, 1–51. CrossRef
 Goodchild, S. (1988). School pupils’ understanding of average.Teaching Statistics, 10, 77–81. CrossRef
 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 (Vol. 2, pp. 766–783). Sheffield, UK: Teaching Statistics Trust.
 Green, D. R. (1986). 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, BC: The Organizing Committee, ICOTS2.
 Green, D. (1993). Data analysis: What research do we need? In L. PereiraMendoza (Ed.),Introducing data analysis in the schools: Who should teach it? (pp. 219–239). Voorburg, The Netherlands: International Statistical Institute.
 Holmes, P. (1980).Teaching statistics 11–16. Slough, UK: Schools Council and Foulsham Educational.
 Izard, J. F. (2004, March).Best practice in assessment for learning. Paper presented at the Third Conference of the Association of Commonwealth Examinations and Accreditation Bodies on Redefining the Roles of Educational Assessment, South Pacific Board for Educational Assessment, Nadi, Fiji.
 Jacobs, V.R. (1999). How do students think about statistical sampling before instruction?Mathematics in the Middle School, 5(4), 240–263.
 Kelly, B. A., & Watson, J. M. (2002). Variation in a chance sampling setting: The lollies task. In B. Barton, K. C. Irwin, M. Pfannkuch, & M. O. J. Thomas (Eds.),Mathematics education in the South Pacific (Proceedings of the 26th annual Conference of the Mathematics Education Research Group of Australasia, Auckland, NZ, Vol. 2, pp. 366–373). Sydney: MERGA.
 Lehrer, R., & Romberg, T. (1996). Exploring children’s data modeling.Cognition and Instruction, 14(1), 69–108. CrossRef
 Masters, G. N. (1982). A Rasch model for partial credit scoring.Psychometrika, 47, 149–174. CrossRef
 Mevarech, Z. (1983). A deep structure model of students’ statistical misconceptions.Educational Studies in Mathematics, 14, 415–429. CrossRef
 Moore, D. S. (1990). Uncertainty. In L. S. Steen (Ed.),On the shoulders of giants: New approaches to numeracy (pp. 95–137). Washington, DC: National Academy Press.
 National Council of Teachers of Mathematics. (1989).Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
 Piaget, J., & Inhelder, B. (1975).The origin of the idea of chance in children (L. Leake Jr., P. Burrell, & H. D. Fishbein, Trans.). New York: W.W. Norton. (Original work published 1951)
 Rasch, G. (1980).Probabilistic models for some intelligence and attainment tests. Chicago: University of Chicago Press. (Original work published 1960)
 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 (Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 6–22). Waikato, NZ: MERGA.
 Shaughnessy, J. M. (2003). Research on students’ understandings of probability. In J. Kilpatrick, W.G. Martin, & D. Schifter (Eds.),A research companion to Principles and Standards for School Mathematics (pp. 216–226). Reston, VA: National Council of Teachers of Mathematics.
 Strauss, S., & Bichler, E. (1988). The development of children’s concept of the arithmetic average.Journal for Research in Mathematics Education, 19, 64–80. CrossRef
 Wallman, K. K. (1993). Enhancing statistical literacy: Enriching our society.Journal of the American Statistical Association, 88, No 421, 1–8. CrossRef
 Watson, J. M. (1994). Instruments to assess statistical concepts in the school curriculum. In National Organizing Committee (Ed.),Proceedings of the 4th International Conference on Teaching Statistics (Vol. 1, pp. 73–80). Rabat, Morocco: National Institute of Statistics and Applied Economics.
 Watson, J. M. (1997). Assessing statistical literacy using the media. In I. Gal & J. B. Garfield (Eds.),The assessment challenge in statistics education (pp. 107–121). Amsterdam: IOS Press and The International Statistical Institute.
 Watson, J. M. (2006).Statistical literacy at school: Growth and goals. Mahwah, NJ: Lawrence Erlbaum.
 Watson, J. M., & Callingham, R. A. (2003). Statistical literacy: A complex hierarchical construct.Statistics Education Research Journal, 2(2), 3–46.
 Watson, J. M., & Callingham, R. A. (2005). Statistical literacy: From idiosyncratic to critical thinking. In G. Burrill & M. Camden (Eds.),Curricular Development in Statistics Education. International Association for Statistical Education (IASE) Roundtable, Lund, Sweden, 2004 (pp. 116–162). Voorburg, The Netherlands: International Statistical Institute.
 Watson, J. M., & Kelly, B. A. (2002). Grade 5 students’ appreciation of variation. In A. Cockburn & E. Nardi (Eds),Proceedings of the 26th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 385–392). Norwich, UK: PME.
 Watson, J. M., & Kelly, B. A. (2004a). Expectation versus variation: Students’ decision making in a chance environment.Canadian Journal of Science, Mathematics and Technology Education, 4, 371–396. CrossRef
 Watson, J. M., & Kelly, B. A. (2004b). A twoyear study of students’ appreciation of variation in the chance and data curriculum. In I. Putt, R. Faragher, & M. McLean (Eds.),Mathematics education for the third millennium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia, Townsville, Vol. 2, pp. 573–580). Sydney, NSW: MERGA.
 Watson, J. M., & Kelly, B. A. (2005). The winds are variable: Student intuitions about variation.School Science and Mathematics, 105, 252–269. CrossRef
 Watson, J. M., Kelly, B. A., Callingham, R. A., & Shaughnessy, J. M. (2003). The measurement of school students’ understanding of statistical variation.International Journal of Mathematical Education in Science and Technology, 34, 1–29. CrossRef
 Watson, J. M., Kelly, B. A., & Izard, J. F. (2004, December). Student change in understanding of statistical variation after instruction and after two years: An application of Rasch analysis.Proceedings of the 2004 annual conference of the Australian Association for Research in Education. Available at http://www.aare.edu.au/04pap/wat04867.pdf
 Watson, J. M., Kelly, B. A., & Izard, J. F. (2005). Statistical literacy over a decade. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.),Building connections: Theory, research and practice (Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia, Melbourne, Vol. 2., pp. 775–782). Sydney: MERGA.
 Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry.International Statistical Review, 67, 223–265. CrossRef
 Title
 A longitudinal study of student understanding of chance and data
 Journal

Mathematics Education Research Journal
Volume 18, Issue 2 , pp 4055
 Cover Date
 20061001
 DOI
 10.1007/BF03217435
 Print ISSN
 10332170
 Online ISSN
 2211050X
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Authors

 Jane Watson ^{(1)}
 Ben Kelly ^{(1)}
 John Izard ^{(2)}
 Author Affiliations

 1. Faculty of Education, University of Tasmania, Private Bag 66, 7001, Hobart, TAS
 2. RMIT University, GPO Box 2476V, 3001, Melbourne, VIC