Journal of Mathematics Teacher Education

, Volume 16, Issue 6, pp 427–449 | Cite as

An investigation of prospective secondary mathematics teachers’ conceptual knowledge of and attitudes towards statistics

  • Ailish HanniganEmail author
  • Olivia Gill
  • Aisling M. Leavy


The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of statistics and are willing to give more relevance to the teaching of statistics; however, many mathematics teachers do not consider themselves well prepared to teach statistics. The aims of this study were to investigate the conceptual understanding of statistics of prospective secondary mathematics teachers; the nature of their attitudes towards statistics and if there was a relationship between attitude towards statistics and conceptual understanding of statistics. Conceptual understanding was measured using a standard assessment instrument (comprehensive assessment of outcomes in a first statistics course) which allows comparison across other disciplines. Despite being very mathematically able and confident, the prospective mathematics teachers in this study do no better in the assessment than students from other (mostly non-quantitative) disciplines. This, perhaps, gives further evidence that statistical thinking is different from mathematical thinking and that a strong background in mathematics does not necessarily translate to statistical thinking. Conceptual knowledge was poor in some fundamental areas of statistics such as being able to properly describe the distribution of a quantitative variable and data production. The attitudes of these teachers towards statistics were measured using a widely used instrument (survey of attitudes towards statistics). The results indicate generally positive attitudes but an acknowledgement that statistics is not a subject quickly learned by everyone and requires discipline to learn. No strong correlation was found between attitudes and conceptual knowledge. It is recommended that in order to improve teacher knowledge, teacher education programmes must include tailored modules in statistics and highlight the differences between mathematical and statistical thinking.


Teacher knowledge Affect Difficulty Value Interest Attitudes Statistics Conceptual understanding 


  1. Aiken, L. R. (1970). Attitudes toward mathematics. Review of Educational Research, 40, 551–596.CrossRefGoogle Scholar
  2. Aiken, L. R. (1980). Attitudes measurement research. In D. A. Payne (Ed.), Recent developments in affective measurement (pp. 1–24). San Francisco: Jossey-Bass.Google Scholar
  3. Arnold, P. (2008). Developing new statistical content knowledge with secondary school mathematics teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman. (Eds.), Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey: Mexico. Accessed 10 September 2011.
  4. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.CrossRefGoogle Scholar
  5. Batanero, C., Burrill, G., & Reading, C. (Eds.). (2011). Teaching statistics in school mathematics-challenges for teaching and teacher education: The 18th ICMI study. The Netherlands: Springer.Google Scholar
  6. Ben-Zvi, D., & Garfield, J. (2004). The challenge of developing statistical literacy, reasoning and thinking. The Netherlands: Kluwer.Google Scholar
  7. Boero, P., Dapueto, C., & Parenti, L. (1996). Didactics of mathematics and the professional knowledge of teachers. In A. J. Bishop, et al. (Eds.), International handbook of mathematics education: Part 2 (pp. 1097–1121). Holland: Kluwer Academic Publications.Google Scholar
  8. Brophy, J. E. (1991). Conclusion to advances in research on teaching, vol 2: Teachers’ knowledge of subject matter as it relates to their teaching practice. In J. E. Brophy (Ed.), Advances in research in teaching: Teachers’ subject matter knowledge and classroom instruction (Vol. 2, pp. 347–362). Greenwich, CT: JAI Press.Google Scholar
  9. Carnell, L. J. (2008). The effect of a student-designed data collection project on attitudes toward statistics. Journal of Statistics Education, 16(1). Accessed 10 Sept 2011.
  10. Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. The American Mathematical Monthly, 104(9), 801–823.CrossRefGoogle Scholar
  11. Da Silva, C., & de Queiroz e Silva Coutinho, C. (2006). The variation concept: a study with secondary school mathematics teachers. In A.Rossman & B. Chance (Eds.), Working cooperatively in statistics education: Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. [CDROM]. Voorburg, The Netherlands: International Statistical Institute. Accessed 24 May 2013.
  12. delMas, R., Garfield, J., Ooms, A., & Chance, B. (2007). Assessing students’ conceptual understanding after a first course in statistics. Statistics Education Research Journal, 6(2), 28–58. Accessed 15 Sept 2011.
  13. Estrada, A., Batanero, C., Fortuny, J. M., & Diaz, C. (2005). A structural study of future teachers’ attitudes towards statistics. In M. Bosch (Ed.), Proceedings of the fourth congress of the European society for research in mathematics education (pp. 508–517). Barcelona: IQS Fundemi.Google Scholar
  14. Estrada, A., Batanero, C., & Lancaster, S. (2011). Teacher’s attitudes towards statistics. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education: The 18th ICMI Study (pp. 163–174). The Netherlands: Springer.CrossRefGoogle Scholar
  15. Estrada, A. & Batenero, C. (2008). Explaining teacher’s attitudes towards statistics. In C. Batanero, G. Burrill, C. Reading, and A. Rossman (Eds.) Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey: Mexico. Accessed 1 Sept 2011.
  16. Evans, B. (2007). Student attitudes, conceptions, and achievement in introductory undergraduate college statistics. The Mathematics Educator, 17(2), 24–30.Google Scholar
  17. Fabrizio, M., Lopez, M. V., & Plencovich, M. V. (2007). Statistics in teacher training colleges in Beunos Aires, Argentina: Assessment and challenges. Proceedings of the 56th Session of the International Statistics Institute. Lisbon: Portugal. Accessed 30 Aug 2011.
  18. Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Groews (Ed.), Handbook of research on mathematics teaching and learning (pp. 147–164). New York: Macmillan.Google Scholar
  19. Gal, I., & Ginsburg, L. (1994). The role of beliefs and attitudes in learning statistics : Towards an assessment framework. Journal of Statistics Education, 2(2) Accessed 10 Sept 2011.
  20. Gal, I., Ginsburg, L., & Schau, C. (1997). Monitoring attitudes and beliefs in statistics education. In I. Gal & J. B. Garfield (Eds.), The assessment challenge in statistics education (pp. 37–51). The Netherlands: IOS.Google Scholar
  21. Garfield, J. (2001). Evaluating the impact of educational reform in statistics: A survey of introductory statistics courses. Final report for NSF Grant REC-9732404.Google Scholar
  22. Garfield, J., & Ben-Zvi, D. (2005). A framework for teaching and assessing reasoning about variability. Journal of Statistics Education, 4(1) Accessed 25 Aug 2011.
  23. Garfield, J., delMas, R., & Chance, B. (2002a). The assessment resource tools for improving statistical thinking (ARTIST) project. NSF CCLI grant ASA-0206571. Accessed 13 Sept 2011.
  24. Garfield, J., & Everson, M. (2009). Preparing teachers of statistics: a graduate course for future teachers. Journal of Statistics Education 17(2) Accessed 14 Sept 2011.
  25. Garfield, J., Hogg, B., Schau, C., & Whittinghill, D. (2002b). First courses in statistical science: the status of educational reform efforts. Journal of Statistics Education, 10(2). Accessed August 20 2011.
  26. Hilton, S. C., Schau, C., & Olsen, J. A. (2004). Survey of attitudes toward statistics: Factor structure invariance by gender and by administration time. Structural Equation Modeling, 11(1), 92–109.CrossRefGoogle Scholar
  27. Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., et al. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716–725.CrossRefGoogle Scholar
  28. Leavy, A. M. (2004). Indexing distributions of data: Preservice teachers’ notions of representativeness. School Science and Mathematics, 104(3), 119–134.CrossRefGoogle Scholar
  29. Leavy, A. M. (2006). Using data comparison to support a focus on distribution: Examining preservice teacher’s understandings of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 89–114. Accessed 12 Sept 2011.
  30. Leavy, A. M., & O’Loughlin, N. (2006). Moving beyond the arithmetic average: Preservice teachers understanding of the mean. Journal of Mathematics Teacher Education, 9(1), 53–90.CrossRefGoogle Scholar
  31. Leavy, A. M., & Sloane, F. (2010). Developing statistical literacy in primary level mathematics. Dublin: Stationery Office.Google Scholar
  32. Lester, F. K., McCormick, K., & Kapusuz, A. (2004). Pre-service teachers’ beliefs about the nature of mathematics. In B. Clarke, D. M. Clarke, G. Emanuelsson, B. Johansson, D. V. Lambdin, F. K. Lester, A. Wallby, & K. Wallby (Eds.), International perspectives on learning and teaching mathematics (pp. 555–567). National Centre for Mathematics Education, Goteborg University: Goteborg.Google Scholar
  33. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  34. Moore, D. S. (1997). New pedagogy and new content: the case of statistics. International Statistical Review, 65, 123–137.Google Scholar
  35. Moore, D. S. (2004). Foreword. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. ix–x). Dordrecht: Kluwer Academic Publishers.Google Scholar
  36. Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., Gregory, K. D., Garden, R. A., O’Connor, K. M., et al. (2000). TIMSS 1999 international mathematics report: Findings from IEA’s repeat of the Third International Mathematics and Science Study at eighth grade. Chestnut Hill, MA: Boston College.Google Scholar
  37. Nasser, F. M. (2004). Structural model of the effects of cognitive and affective factors on the achievement of Arabic-speaking prospective teachers in introductory statistics. Journal of Statistics Education, 12(1). Accessed 14 Sept 2011.
  38. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. From Accessed 24 Aug 2011.
  39. NiRiordain, M., & Hannigan, A. (2011). Who teaches mathematics at second level in Ireland? Irish Educational Studies, 30(3), 289–304.CrossRefGoogle Scholar
  40. O’ Meara, N., O’Donoghue, J., & Gill, O. (2011). Improving mathematics teaching at second Level through the design of a model of teacher knowledge and an intervention aimed at developing teachers’ knowledge, PhD. Limerick: University of Limerick.Google Scholar
  41. Olson, J. M., & Zanna, M. P. (1993). Attitude and attitude change. Annual Review of Psychology, 44, 117–154.CrossRefGoogle Scholar
  42. Onwuegbuzie, A. J. (1998). Statistics anxiety: A function of learning style? Research in School, 5(1), 43–52.Google Scholar
  43. Onwuegbuzie, A. J. (2000). Statistics anxiety and the role of self perceptions. Journal of Educational Research, 93(5), 323–335.CrossRefGoogle Scholar
  44. Peters, S. A. (2011). A robust understanding of variation. Statistics Education Research Journal, 10(1), 52–88.Google Scholar
  45. Philippou, G. N., & Christou, C. (1998). The effects of a preparatory mathematics program in changing prospective teachers attitudes toward mathematics. Educational Studies in Mathematics, 35, 189–206.CrossRefGoogle Scholar
  46. Ponte, J. P., & Chapman, O. (2008). Preservice mathematics teachers’ knowledge and development. In L. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 225–263). New York, NY: Routledge.Google Scholar
  47. Roberts, D. M., & Saxe, J. E. (1982). Validity of a statistics attitude survey: A follow-up study. Educational and Psychological Measurement, 42, 907–912.CrossRefGoogle Scholar
  48. Schau, C. (2003, August). Students’ attitudes: The other important outcome in statistics education. Paper presented at the Joint Statistical Meeting of the American Statistical Association, San Francisco, CA.Google Scholar
  49. Schau, C., Stevens, J., Dauphine, T., & del Vecchio, A. (1995). The development and validation of the survey of attitudes towards statistics. Educational and Psychological Measurement, 55(5), 868–875.CrossRefGoogle Scholar
  50. Schultz, K. S., & Koshino, H. (1998). Evidence of reliability and validity for Wise’s attitude toward statistics scale. Educational and Psychological Measurement, 82, 27–31.Google Scholar
  51. Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research on mathematical teaching and learning (pp. 465–494). New York: McMillan.Google Scholar
  52. Smith, G. (1998). Learning statistics by doing statistics. Journal of Statistics Education, 6(3). Accessed 10 Sept 2011.
  53. Snee, R. D. (1993). What’s missing in statistical education? The American Statistician, 47(2), 149–154.Google Scholar
  54. Tempelaar, D. T., Schim van der Loeff, S., & Gijselaers, W. H. (2007). A structural equation model analyzing the relationship of students’ attitudes toward statistics, prior reasoning abilities, and course performance. Statistics Education Research Journal, 6(2), 78–102.Google Scholar
  55. Tintle, N., Topliff, K., Vanderstoep, J., Holmes, V., & Swanson, T. (2012). Retention of statistical concepts in a preliminary randomization-based introductory statistics curriculum. Statistics Education Research Journal, 11(1), 21–40. Accessed 10 Nov 2012.
  56. Tremblay, P. F., Gardner, R. C., & Heipel, G. (2000). A model of the relationships among measures of affect, aptitude, and performance in introductory statistics. Canadian Journal of Behavioural Science, 32(1), 40–48.Google Scholar
  57. Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical inquiry. International Statistical Review, 67(3), 223–265.Google Scholar
  58. Wise, S. L. (1985). The development and validation of a scale measuring attitudes toward statistics. Educational and Psychological Measurement, 45, 401–405.Google Scholar
  59. Zientek, L. R., Carter, T. A., Taylor, J. M., & Capraro, R. M. (2011). Preparing prospective teachers: An examination of attitudes toward statistics. Journal of Mathematical Sciences and Mathematics Education, 5(1), 25–38.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Ailish Hannigan
    • 1
    Email author
  • Olivia Gill
    • 2
  • Aisling M. Leavy
    • 3
  1. 1.Graduate Entry Medical SchoolUniversity of LimerickLimerickIreland
  2. 2.Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland
  3. 3.Mary Immaculate CollegeLimerickIreland

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