Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Mathematics Teacher Education Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Aiken, L. R. (1970). Attitudes toward mathematics. Review of Educational Research, 40, 551–596.

    Article  Google Scholar 

  • Aiken, L. R. (1980). Attitudes measurement research. In D. A. Payne (Ed.), Recent developments in affective measurement (pp. 1–24). San Francisco: Jossey-Bass.

  • 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. www.stat.auckland.ac.nz/~iase/publications. Accessed 10 September 2011.

  • 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.

    Article  Google Scholar 

  • 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 

  • Ben-Zvi, D., & Garfield, J. (2004). The challenge of developing statistical literacy, reasoning and thinking. The Netherlands: Kluwer.

    Google Scholar 

  • 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 

  • 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 

  • Carnell, L. J. (2008). The effect of a student-designed data collection project on attitudes toward statistics. Journal of Statistics Education, 16(1). www.amstat.org/publications/jse/v16n1/carnell.html. Accessed 10 Sept 2011.

  • Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. The American Mathematical Monthly, 104(9), 801–823.

    Article  Google Scholar 

  • 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. http://redeabe.org.br/ICOTS7/Proceedings/PDFs/ContributedPapers/C216.pdf. Accessed 24 May 2013.

  • 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. http://www.stat.auckland.ac.nz/~iase/serj/SERJ6(2)_delMas.pdf. Accessed 15 Sept 2011.

  • 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 

  • 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.

    Chapter  Google Scholar 

  • 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. www.stat.auckland.ac.nz/~iase/publications. Accessed 1 Sept 2011.

  • Evans, B. (2007). Student attitudes, conceptions, and achievement in introductory undergraduate college statistics. The Mathematics Educator, 17(2), 24–30.

    Google Scholar 

  • 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. http://www.stat.auckland.ac.nz/~iase/publications/isi56/CPM80_Fabrizio.pdf. Accessed 30 Aug 2011.

  • 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 

  • Gal, I., & Ginsburg, L. (1994). The role of beliefs and attitudes in learning statistics : Towards an assessment framework. Journal of Statistics Education, 2(2) www.amstat.org/publications/jse/. Accessed 10 Sept 2011.

  • 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 

  • Garfield, J. (2001). Evaluating the impact of educational reform in statistics: A survey of introductory statistics courses. Final report for NSF Grant REC-9732404.

  • Garfield, J., & Ben-Zvi, D. (2005). A framework for teaching and assessing reasoning about variability. Journal of Statistics Education, 4(1) http://www.stat.auckland.ac.nz/~iase/serj/SERJ4(1)_Garfield_BenZvi.pdf. Accessed 25 Aug 2011.

  • Garfield, J., delMas, R., & Chance, B. (2002a). The assessment resource tools for improving statistical thinking (ARTIST) project. NSF CCLI grant ASA-0206571. https://app.gen.umn.edu/artist/. Accessed 13 Sept 2011.

  • Garfield, J., & Everson, M. (2009). Preparing teachers of statistics: a graduate course for future teachers. Journal of Statistics Education 17(2) http://www.amstat.org/publications/jse/v17n2/garfield.html. Accessed 14 Sept 2011.

  • 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). http://www.amstat.org/publications/jse/v10n2/garfield.html. Accessed August 20 2011.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Leavy, A. M. (2004). Indexing distributions of data: Preservice teachers’ notions of representativeness. School Science and Mathematics, 104(3), 119–134.

    Article  Google Scholar 

  • 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. http://www.stat.auckland.ac.nz/~iase/serj/SERJ5(2)_Leavy.pdf. Accessed 12 Sept 2011.

  • 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.

    Article  Google Scholar 

  • Leavy, A. M., & Sloane, F. (2010). Developing statistical literacy in primary level mathematics. Dublin: Stationery Office.

    Google Scholar 

  • 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 

  • 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 

  • Moore, D. S. (1997). New pedagogy and new content: the case of statistics. International Statistical Review, 65, 123–137.

    Google Scholar 

  • 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 

  • 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 

  • 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). www.amstat.org/publications/jse/. Accessed 14 Sept 2011.

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. From http://standards.nctm.org/document/index.htm. Accessed 24 Aug 2011.

  • NiRiordain, M., & Hannigan, A. (2011). Who teaches mathematics at second level in Ireland? Irish Educational Studies, 30(3), 289–304.

    Article  Google Scholar 

  • 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 

  • Olson, J. M., & Zanna, M. P. (1993). Attitude and attitude change. Annual Review of Psychology, 44, 117–154.

    Article  Google Scholar 

  • Onwuegbuzie, A. J. (1998). Statistics anxiety: A function of learning style? Research in School, 5(1), 43–52.

    Google Scholar 

  • Onwuegbuzie, A. J. (2000). Statistics anxiety and the role of self perceptions. Journal of Educational Research, 93(5), 323–335.

    Article  Google Scholar 

  • Peters, S. A. (2011). A robust understanding of variation. Statistics Education Research Journal, 10(1), 52–88.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Roberts, D. M., & Saxe, J. E. (1982). Validity of a statistics attitude survey: A follow-up study. Educational and Psychological Measurement, 42, 907–912.

    Article  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • Smith, G. (1998). Learning statistics by doing statistics. Journal of Statistics Education, 6(3). http://www.amstat.org/publications/jse/v6n3/smith.html. Accessed 10 Sept 2011.

  • Snee, R. D. (1993). What’s missing in statistical education? The American Statistician, 47(2), 149–154.

    Google Scholar 

  • 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 

  • 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. http://www.stat.auckland.ac.nz/~iase/serj/SERJ11%281%29_Tintle.pdf. Accessed 10 Nov 2012.

  • 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 

  • Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical inquiry. International Statistical Review, 67(3), 223–265.

    Google Scholar 

  • Wise, S. L. (1985). The development and validation of a scale measuring attitudes toward statistics. Educational and Psychological Measurement, 45, 401–405.

    Google Scholar 

  • 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 

Download references

Author information

Authors and Affiliations

  1. Graduate Entry Medical School, University of Limerick, Limerick, Ireland

    Ailish Hannigan

  2. Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland

    Olivia Gill

  3. Mary Immaculate College, South Circular Road, Limerick, Ireland

    Aisling M. Leavy

Authors
  1. Ailish Hannigan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Olivia Gill
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aisling M. Leavy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ailish Hannigan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hannigan, A., Gill, O. & Leavy, A.M. An investigation of prospective secondary mathematics teachers’ conceptual knowledge of and attitudes towards statistics. J Math Teacher Educ 16, 427–449 (2013). https://doi.org/10.1007/s10857-013-9246-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-013-9246-3

Keywords

Search

Navigation