Skip to main content
SpringerLink
Log in

A Framework for Assessing Statistical Knowledge for Teaching Based on the Identification of Conceptions of Variability Held by Teachers

  • Chapter
Book cover The Teaching and Learning of Statistics

Abstract

This article introduces a conceptual framework for statistical knowledge for teaching (henceforth SKT), which addresses some noted gaps identified in the research literature on statistics education. It is proposed that the use and adaptation—for the case of statistics—of the model of mathematical knowledge for teaching (henceforth MKT) developed by Ball et al. (J Teach Educ 59:389–407, 2008), as well as an extension of that model—and of almost all the few conceptualizations of SKT proposed to date—addressing some of its limitations, may help to gain a deeper insight into the knowledge needed to teach statistics effectively. In the present chapter, the components of this new framework for SKT are elicited, identified, and described through a set of tasks that examine teachers’ conceptions of variability in diverse statistical contexts (as in Shaughnessy (Second handbook of research on mathematics teaching and learning. Reston, VA: NCTM, 2007)), as well as teachers’ subject matter and pedagogical content knowledge in relation to the statistical ideas involved in such tasks.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Ball, D. L., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • Batanero, C., & Díaz, C. (2010). Training teachers to teach statistics: What can we learn from research? Statistique et Enseignement, 1(1), 5–20.

    Google Scholar 

  • Burgess, T. A. (2011). Teacher knowledge of and for statistical investigations. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education: A joint ICMI/IASE study (pp. 259–270). New York: Springer.

    Chapter  Google Scholar 

  • Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., et al. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K-12 curriculum framework. Alexandria, VA: American Statistical Association.

    Google Scholar 

  • Gal, I. (2004). Statistical literacy: Meanings, components, responsibilities. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 47–78). Dordrecht, The Netherlands: Kluwer.

    Chapter  Google Scholar 

  • Gal, I., Ginsburg, L., & Schau, C. (1997). Monitoring attitudes and beliefs in statistics education. In I. Gal & J. Garfield (Eds.), The assessment challenge in statistics education (pp. 37–51). Amsterdam, The Netherlands: Ios Press.

    Google Scholar 

  • Garfield, J., delMas, R., & Chance, B. L. (1999). Tools for Teaching and Assessing Statistical Inference. Retrieved from http://www.tc.umn.edu/~delma001/stat_tools/

  • Gattuso, L., & Ottaviani, M. G. (2011). Complementing mathematical thinking and statistical thinking in school mathematics. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education: A joint ICMI/IASE study (pp. 121–132). New York: Springer.

    Chapter  Google Scholar 

  • Godino, J. D., Ortiz, J. J., Roa, R., & Wilhelmi, M. R. (2011). Models for statistical pedagogical knowledge. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education: A joint ICMI/IASE study (pp. 271–282). New York: Springer.

    Chapter  Google Scholar 

  • González, O. (2011). Survey on Japanese elementary, middle and high school teachers’ statistical literacy: Focusing on variability (Unpublished master’s thesis). University of Tsukuba, Tsukuba.

    Google Scholar 

  • Groth, R. E. (2007). Toward a conceptualization of statistical knowledge for teaching. Journal for Research in Mathematics Education, 38, 427–437.

    Google Scholar 

  • Hand, D. J. (1998). Breaking misconceptions—Statistics and its relationship to mathematics. Journal of the Royal Statistical Society: Series D (The Statistician), 47, 245–250.

    Google Scholar 

  • Isoda, M., & González, O. (2012). 小学校・中学校・高等学校教師の統計的リテラシー に関する調査研究:「ばらつき(ちらばり)」に係る教員研修の必要性を探る [Survey on elementary, junior and high school teachers’ statistical literacy: The need for teacher training in variability]. Journal of Science Education in Japan, 36(1), 61–76.

    Google Scholar 

  • Knuth, E. (2002). Teachers’ conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5(1), 61–88.

    Article  Google Scholar 

  • Makar, K. M., & Confrey, J. (2004). Secondary teachers’ reasoning about comparing two groups. In D. Ben-Zvi & J. Garfield (Eds.), The challenges of developing statistical literacy, reasoning, and thinking (pp. 327–352). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

    Google Scholar 

  • Noll, J. A. (2011). Graduate teaching assistants’ statistical content knowledge of sampling. Statistics Education Research Journal, 10(2), 48–74.

    Google Scholar 

  • Petrou, M., & Goulding, M. (2011). Conceptualising teachers’ mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 9–25). New York: Springer.

    Chapter  Google Scholar 

  • Pfannkuch, M., & Ben-Zvi, D. (2011). Developing teachers’ statistical thinking. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education: A joint ICMI/IASE study (pp. 323–333). New York: Springer.

    Chapter  Google Scholar 

  • Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Charlotte, NC: Information Age.

    Google Scholar 

  • Pierce, R., & Chick, H. (2011). Teachers’ beliefs about statistics education. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education: A joint ICMI/IASE study (pp. 151–162). New York: Springer.

    Chapter  Google Scholar 

  • Sánchez, E., da Silva, C. B., & Coutinho, C. (2011). Teachers’ understanding of variation. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education: A joint ICMI/IASE study (pp. 211–221). New York: Springer.

    Chapter  Google Scholar 

  • Shaughnessy, J. M. (2007). Research on statistics’ reasoning and learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1009). Reston, VA: NCTM.

    Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • Trigwell, K., Prosser, M., & Waterhouse, F. (1999). Relations between teachers’ approaches to teaching and students’ approaches to learning. Higher Education, 37, 57–70.

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of International Development and Cooperation (IDEC), Hiroshima University, Hiroshima, Japan

    Orlando González

Authors
  1. Orlando González
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Orlando González .

Editor information

Editors and Affiliations

  1. Faculty of Education, University of Haifa, Haifa, Israel

    Dani Ben-Zvi

  2. School of Education, University of Queensland, St Lucia, Queensland, Australia

    Katie Makar

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

González, O. (2016). A Framework for Assessing Statistical Knowledge for Teaching Based on the Identification of Conceptions of Variability Held by Teachers. In: Ben-Zvi, D., Makar, K. (eds) The Teaching and Learning of Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-23470-0_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23470-0_37

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23469-4

  • Online ISBN: 978-3-319-23470-0

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation