Skip to main content
SpringerLink
Log in
Book cover

Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education pp 223–234Cite as

Teachers’ Knowledge of Distribution

  • Chapter
  • First Online:

Part of the book series: New ICMI Study Series ((NISS,volume 14))

Abstract

To teach statistics effectively teachers need to have a well-developed knowledge of distribution. As a key concept in an intricate web of statistical knowledge, distribution depends on, and is depended on by many other statistical concepts. Various frameworks have been developed as researchers strive to describe the cognitive development of knowledge of distribution. Considering the professional learning continuum that a teacher needs to traverse, research studies are reported that have focused, from the perspective of teachers as learners, on the development of teacher knowledge of distribution both before teaching and while teaching. Recommendations are made for teacher learning and future research into teachers’ knowledge of distribution.

This is a preview of subscription content, 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   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
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

Learn about institutional subscriptions

References

  • Afamasaga-Fuata’i, K., & Reading, C. (2007). Using concept maps to assess pre-service teachers’ understanding of connections between statistical concepts. In B. Phillips & L. Weldon (Eds.), Assessing student learning in statistics: Proceedings of the IASE/ISI Satellite Conference on Statistical Education. Voorburg, The Netherlands: International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications

  • Bakker, A. (2004). Reasoning about shape as a pattern in variability. Statistics Education Research Journal, 3(2), 64–83. Online: www.stat.auckland.ac.nz/serj/

    Google Scholar 

  • Bakker, A., & Gravemeijer, K. P. E. (2004). Learning to reason about distribution. 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 

  • Batanero, C., Burrill, G., Reading, C., & Rossman, A. (Eds.). (2008). Joint ICMI/IASE Study: Teaching Statistics in School Mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey: International Commission on Mathematical Instruction and International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications

  • Batanero, C., Tauber, L. M., & Sanchez, V. (2004). Students’ reasoning about the normal distribution. In D. Ben-Zvi & J. Garfield (Eds.), The challenges of developing statistical literacy, reasoning, and thinking (pp. 257–276). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Canada, D. (2008). Conceptions of distribution held by middle school students and preservice teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Canada, D., & Ciancetta, M. (2007). Elementary preservice teachers’ informal conceptions of distribution. In T. Lamberg & L. Wiest (Eds.), Proceedings of the 29th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 960–967). Lake Tahoe, NV: University of Nevada, Reno.

    Google Scholar 

  • Chance, B., delMas, R., & Garfield, J. (2004). Reasoning about sampling distributions. In D. Ben-Zvi & J. Garfield (Eds.), The challenges of developing statistical literacy, reasoning, and thinking (pp. 295–323). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Ciancetta, M. (2007). Students’ reasoning when comparing distributions of data. Unpublished Ph.D. dissertation, Portland State University, Portland.

    Google Scholar 

  • Franklin, C. A., & Garfield, J. (2006). The GAISE Project: Developing statistical education guidelines for grades pre-K-12 and college courses. In G. F. Burrill (Ed.), Thinking and reasoning with chance and data: 68th NCTM Yearbook (2006) (pp. 345–375). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Friel, S. N., O’Connor, W., & Mamer, J. D. (2006). More than “meanmodemedian” and a bar graph: What’s needed to have a statistical conversation? In G. F. Burrill (Ed.), Thinking and reasoning with chance and data: 68th NCTM Yearbook (2006) (pp. 117–137). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Garfield, J. B., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. New York: Springer.

    Google Scholar 

  • Hammerman, J., & Rubin, A. (2004). Strategies for managing statistical complexity with new software tools. Statistics Education Research Journal, 3(2), 17–41. Online: www.stat.auckland.ac.nz/serj/

    Google Scholar 

  • Kadijevich, D. (2008). Towards a suitably designed instruction on statistical reasoning: Understanding sampling distribution through technology. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Leavy, A. (2006). Using data comparisons to support a focus on distribution: Examining preservice teachers’ understandings of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 27–45. Online: www.stat.auckland.ac.nz/serj/

    Google Scholar 

  • Madden, S. (2008). High school mathematics teachers’ evolving understanding of comparing distributions. Unpublished Ph.D. dissertation, Western Michigan University, Kalamazoo.

    Google Scholar 

  • Makar, K., & Canada, D. (2005). Pre-service teachers’ conceptions of variation. In H. Chick & J. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (pp. 273–280). Melbourne, Australia: University of Melbourne.

    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 

  • McClain, K. (2008). The evolution of teachers’ understandings of distribution. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Mickelson, W., & Heaton, R. (2004). Primary teachers’ statistical reasoning about data. 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 

  • Pfannkuch, M. (2006). Comparing box plot distributions: A teacher’s reasoning. Statistics Education Research Journal, 5(2), 27–45. Online: www.stat.auckland.ac.nz/serj/

    Google Scholar 

  • Pfannkuch, M., & Reading, C. (2006). Reasoning about distribution: A complex process. Statistics Education Research Journal, 5(2), 4–9. Online: www.stat.auckland.ac.nz/serj/

    Google Scholar 

  • Prodromou, T., & Pratt, D. (2006). The role of causality in the co-ordination of two perspectives on distribution within a virtual simulation. Statistics Education Research Journal, 5(2), 69–88. Online: www.stat.auckland.ac.nz/serj/

    Google Scholar 

  • Reading, C., & Reid, J. (2006). An emerging hierarchy of reasoning about distribution: From a variation perspective. Statistics Education Research Journal, 5(2), 46–68. Online: www.stat.auckland.ac.nz/serj/

    Google Scholar 

  • Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1010). Greenwich, CT: Information Age Publishing and National Council of Teachers of Mathematics.

    Google Scholar 

  • Watson, J. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education, 1(2), 1–33.

    Google Scholar 

  • Wild, C. (2006). The concept of distribution. Statistics Education Research Journal, 5(2), 10–26. Online: www.stat.auckland.ac.nz/serj/

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SiMERR National Centre, University of New England, Education Building, Armidale, NSW, 2351, Australia

    Chris Reading

  2. Department of Mathematics, Eastern Washington University, Cheney, WA, 99004, USA

    Dan Canada

Authors
  1. Chris Reading
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dan Canada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chris Reading .

Editor information

Editors and Affiliations

  1. Fac. Ciencias de la Educación, Universidad de Granada, Granada, 18071, Spain

    Carmen Batanero

  2. Dept. Counseling,, Educational Psychology &, Michigan State University, Erickson Hall 240, East Lansing, 48824, Michigan, USA

    Gail Burrill

  3. SiMERR National Centre, University of New England, Armidale, 2350, New South Wales, Australia

    Chris Reading

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Reading, C., Canada, D. (2011). Teachers’ Knowledge of Distribution. In: Batanero, C., Burrill, G., Reading, C. (eds) Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education. New ICMI Study Series, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1131-0_23

Download citation

Publish with us

Policies and ethics

Search

Navigation