Sample, Random and Variation: The Vocabulary of Statistical Literacy

  • Jane M. WatsonEmail author
  • Ben A. Kelly


This paper considers the development of school students’ ability to define three terms that are fundamental to statistical literacy: sample, random, and variation. A total of 738 students in grades 3, 5, 7, and 9 were asked in a survey to define and give an example for the word “sample.” Of these, 379 students in grades 7 and 9 were also asked about the words “random” and “variation.” Responses were used to describe developmental levels overall and to document differences across grades on the understanding of these terms. Changes in performance were also monitored after lessons on chance and data, emphasizing variation for 335 students. After 2 years, 132 of these students and a further 209 students who were surveyed originally but did not take part in specialized lessons, were surveyed again. The difference after 2 years between the performance of students who experienced the specialized lessons and those who did not was considered, revealing no differences in performance longitudinally. For students in grades 7 and 9, the association of performance on the three terms was explored. Implications for mathematics and literacy educators are discussed.

Key words

random sample school students statistical literacy variation vocabulary 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arzarello, F. (1998). The role of natural language in prealgebraic and algebraic thinking. In H. Steinbring, M.G. Bartoline Bussi & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 249–261). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  2. Bereska, C., Bolster, C.H., Bolster, L.C. & Schaeffer, R. (1999). Exploring statistics in the elementary grades. Book two (grades 4–8). White Plains, NY: Dale Seymour.Google Scholar
  3. Biggs, J.B. & Collis, K.F. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.Google Scholar
  4. Cohen, J. (1969). Statistical power analysis for the behavioral sciences. New York: Academic Press.Google Scholar
  5. Corwin, R.B. & Friel, S.N. (1990). Statistics: Prediction and sampling: A unit of study for grades 5–6. [Used numbers: Real data in the classroom] Palo Alto, CA: Dale Seymour Publications.Google Scholar
  6. Department of Education Tasmania (2002). Essential learnings framework 1. Hobart: Author.Google Scholar
  7. Durkin, K. & Shire, B. (1991). Lexical ambiguity in mathematical contexts. In K. Durkin & B. Shire (Eds.), Language in mathematical education: Research and practice (pp. 71–84). Milton Keynes, UK: Open University Press.Google Scholar
  8. Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70, 1–51.CrossRefGoogle Scholar
  9. Luke, A. & Freebody, P. (1997). Shaping the social practices of reading. In S. Musprati, A. Luke & P. Freebody (Eds.), Constructing critical literacies: Teaching and learning textual practice (pp. 185–225). St. Leonards, NSW: Allen and Unwin.Google Scholar
  10. Madison, B.L. & Steen, L.A. (2003). Quantitative literacy: Why numeracy matters for schools and colleges. Princeton, NJ: The National Council on Education and the Disciplines.Google Scholar
  11. Malone, J. & Miller, D. (1993). Communicating mathematical terms in writing: Some influential variables. In M. Stephens, A. Waywood, D. Clarke & J. Izard (Eds.), Communicating mathematics: Perspectives from classroom practice and current research (pp. 177–190). Hawthorn, VIC: The Australian Council for Educational Research Ltd.Google Scholar
  12. Mason, J. & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277–289.CrossRefGoogle Scholar
  13. Miller, L.D. (1993). Making the connection with language. Arithmetic Teacher, 40, 311–316.Google Scholar
  14. 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.Google Scholar
  15. Moritz, J.B., Watson, J.M. & Pereira-Mendoza, L. (1996). The language of statistical understanding: An investigation in two countries. A paper presented at the Joint ERA/AARE Conference, Singapore., November.
  16. New South Wales Board of Studies (2002). Mathematics: Years 7–10 syllabus. Sydney: Author.Google Scholar
  17. Orr, D.B. (1995). Fundamentals of applied statistics and surveys. New York: Chapman & Hall.Google Scholar
  18. Pimm, D. (1987). Speaking mathematically. London: Routledge & Kegan Paul.Google Scholar
  19. Pirie, S.E.B. (1998). Crossing the gulf between thought and symbol: Language as (slippery) stepping-stones. In H. Steinbring, M.G. Bartoline Bussi & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 7–29). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  20. Reading, C. & Shaughnessy, M. (2004). Reasoning about variation. In J. Garfield & D. Ben-Zvi (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 201–226). Dordrecht: Kluwer Academic Publishers.Google Scholar
  21. Tall, D. & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169.CrossRefGoogle Scholar
  22. Wallman, K.K. (1993). Enhancing statistical literacy: Enriching our society. Journal of the American Statistical Association, 88(421), 1–8.CrossRefGoogle Scholar
  23. Watson, J.M. (1994). Instruments to assess statistical concepts in the school curriculum. In National Organizing Committee (Ed.), Proceedings of the fourth international conference on teaching statistics. Volume 1 (pp. 73–80). Rabat, Morocco: National Institute of Statistics and Applied Economics.Google Scholar
  24. Watson, J.M. & Moritz, J.B. (2000). Development of understanding of sampling for statistical literacy. Journal of Mathematical Behavior, 19, 109–136.CrossRefGoogle Scholar
  25. Watson, J.M. & Kelly, B.A. (2002a). Can grade 3 students learn about variation? In B. Phillips (Ed.), Developing a statistically literate society (CD of the Proceedings of the sixth international conference on teaching statistics, Cape Town). Voorburg, The Netherlands: International Statistical Institute.Google Scholar
  26. Watson, J.M. & Kelly, B.A. (2002b). Variation as part of chance and data in grades 7 and 9. 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, pp. 682–689). Sydney: MERGA.Google Scholar
  27. Watson, J.M., Collis, K.F. & Moritz, J.B. (1993). Assessment of statistical understanding in Australian schools. A paper presented at the Statistics ’93 conference, Wollongong, NSW, September.Google Scholar
  28. 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.CrossRefGoogle Scholar

Copyright information

© National Science Council, Taiwan 2007

Authors and Affiliations

  1. 1.University of TasmaniaHobartAustralia

Personalised recommendations