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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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.
Batanero, C., & Díaz, C. (2010). Training teachers to teach statistics: What can we learn from research? Statistique et Enseignement, 1(1), 5–20.
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.
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.
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.
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.
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.
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.
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.
Groth, R. E. (2007). Toward a conceptualization of statistical knowledge for teaching. Journal for Research in Mathematics Education, 38, 427–437.
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.
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.
Knuth, E. (2002). Teachers’ conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5(1), 61–88.
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.
National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
Noll, J. A. (2011). Graduate teaching assistants’ statistical content knowledge of sampling. Statistics Education Research Journal, 10(2), 48–74.
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.
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.
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.
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.
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.
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.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Trigwell, K., Prosser, M., & Waterhouse, F. (1999). Relations between teachers’ approaches to teaching and students’ approaches to learning. Higher Education, 37, 57–70.
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–265.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights 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)