Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-6bf8c574d5-86b6f Total loading time: 0 Render date: 2025-03-07T10:51:55.039Z Has data issue: false hasContentIssue false

11 - Guiding Inquiry-Based Math Learning

Published online by Cambridge University Press:  05 June 2012

By
Paul Cobb  and
Kay McClain
Edited by
R. Keith Sawyer
Paul Cobb
Affiliation:
Vanderbilt University
Kay McClain
Affiliation:
Vanderbilt University
R. Keith Sawyer
Affiliation:
Washington University, St Louis
Get access

Summary

In this chapter, we present a case study of a classroom approach whose development was inspired by learning sciences research. We conducted a sequence of classroom design experiments in urban seventh and eighth grade classrooms (see Barab, this volume, and Confrey, this volume, for discussions of design experiment methodology) focused on teaching and learning statistical data analysis. During this process, we formulated, tested, and revised specific conjectures about both the process of students' learning in the domain of statistics, and ways to scaffold that learning. The primary products of these design experiments were two sequences of instructional activities: one that focused on the analysis of univariate data and one on bivariate data, and three computer-based data analysis tools that were used in both. In this chapter, we restrict our focus to the first of the two classroom design experiments – the one focused on the analysis of univariate data.

We start by critically examining the traditional instructional goals of middle school math. Learning sciences research rejects a conception of knowledge as consisting of facts and procedures to be memorized; unfortunately, this traditional style of instruction still predominates in most mathematics classrooms. As part of this discussion, we briefly summarize recent developments in both the use of statistics in wider society and in statistics as a discipline. We then describe the initial assessments of students' statistical reasoning, and contrast them with the concluding assessments.

Type
Chapter
Information
The Cambridge Handbook of the Learning Sciences , pp. 171 - 186
Publisher: Cambridge University Press
Print publication year: 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bakker, A., & Gravemeijer, K. (2004). Learning to reason about distribution. In Ben-Zvi, D. & Garfield, J. (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 147–168). Dordrecht, Netherlands: Kluwer.CrossRefGoogle Scholar
Banks, C., & Banks, J. (1995). Equity pedagogy: An essential component of multicultural education. Theory into Practice, 34, 152–158.CrossRefGoogle Scholar
Biehler, R. (1993). Software tools and mathematics education: The case of statistics. In Keitel, C. & Ruthven, K. (Eds.), Learning from computers: Mathematics education and technology (pp. 68–100). Berlin: Springer.CrossRefGoogle Scholar
Biehler, R., & Steinbring, H. (1991). Entdeckende statistik, stenget-und Blatter, Boxplots: Konzepte, Begrundungen and Enfahrungen eines Unterrichtsversuch es [Explorations in statistics, stem-and-leaf, boxplots: Concepts, justifications, and experience in a teaching experiment]. Der Mathematikunterricht, 37(6), 5–32.Google Scholar
Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.Google Scholar
Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104, 801–823.CrossRefGoogle Scholar
Cobb, P. (1999). Individual and collective mathematical learning: The case of statistical data analysis. Mathematical Thinking and Learning, 1, 5–44.CrossRefGoogle Scholar
Cobb, P., McClain, K., & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 21, 1–78.CrossRefGoogle Scholar
Cobb, P., & Tzou, C. (2000, April). Learning about data creation. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.Google Scholar
Delpit, L. D. (1988). The silenced dialogue: Power and pedagogy in educating other people's children. Harvard Educational Review, 58, 280–298.CrossRefGoogle Scholar
Dewey, J. (1980). Democracy and education. In Boydston, J. A. (Ed.), John Dewey: The middle works, 1899 –1924, Vol. 9 (pp. 1–370). Carbondale, IL: Southern Illinois University Press.Google Scholar
Dörfler, W. (1993). Computer use and views of the mind. In Keitel, C. & Ruthven, K. (Eds.), Learning from computers: Mathematics education and technology (pp. 159–186). Berlin: Springer-Verlag.CrossRefGoogle Scholar
Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht, The Netherlands: CD-ß Press.Google Scholar
Hancock, C., Kaput, J. J., & Goldsmith, L. T. (1992). Authentic inquiry with data: Critical barriers to classroom implementation. Educational Pyschologist, 27, 337–364.CrossRefGoogle Scholar
Kaput, J. J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In Biehler, R., Scholz, R. V., Strasser, R., & Winkelmann, B. (Eds.), Didactics of mathematics as a scientific discipline (pp. 379–397). Dordrecht, Netherlands: Kluwer.Google Scholar
Konold, C., Pollatsek, A., Well, A., & Gagnon, A. (1997). Students' analyzing data: Research of critical barriers. In Garfield, J. B. & Burrill, G. (Eds.), Research on the role of technology in teaching and learning statistics: Proceedings of the 1996 International Association for Statistics Education Roundtable Conference (pp. 151–167). Voorburg, The Netherlands: International Statistics Institute.Google Scholar
Latour, B. (1987). Science in action. Cambridge, MA: Harvard University Press.Google Scholar
Lehrer, R., & Romberg, T. (1996). Exploring children's data modeling. Cognition and Instruction, 14, 69–108.CrossRefGoogle Scholar
Lehrer, R., Schauble, L., & Penner, D. (2000). The inter-related development of inscriptions and conceptual understanding. In Cobb, P., Yackel, E., & McClain, K. (Eds.), Symbolizing, mathematizing, and communicating: Perspectives on discourse, tools, and instructional design (pp. 325–360). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
McClain, K. (2002). Teacher's and students' understanding: The role of tool use in communication. Journal of the Learning Sciences, 11, 217–249.CrossRefGoogle Scholar
McClain, K., & Cobb, P. (2001). Supporting students' ability to reason about data. Educational Studies in Mathematics, 45, 103–129.CrossRefGoogle Scholar
McClain, K., Cobb, P., & Gravemeijer, K. (2000). Supporting students' ways of reasoning about data. In Burke, M. (Ed.), Learning mathematics for a new century (2001 Yearbook of the National Council of Teachers of Mathematics) (pp. 174–187). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
McGatha, M., Cobb, P., & McClain, K. (2002). An analysis of students' initial statistical understandings: Developing a conjectured learning trajectory. Journal of Mathematical Behavior, 16, 339–355.CrossRefGoogle Scholar
Meira, L. (1998). Making sense of instructional devices: The emergence of transparency in mathematical activity. Journal for Research in Mathematics Education, 29, 121–142.CrossRefGoogle Scholar
Noss, R., Pozzi, S., & Hoyles, C. (1999). Touching epistemologies: Statistics in practice. Educational Studies in Mathematics, 40, 25–51.CrossRefGoogle Scholar
Pea, R. D. (1993). Practices of distributed intelligence and designs for education. In Salomon, G. (Ed.), Distributed cognitions (pp. 47–87). New York: Cambridge University Press.Google Scholar
Roth, W. M. (1996). Where is the context in contextual word problems? Mathematical practices and products in grade 8 students' answers to story problems. Cognition and Instruction, 14, 487–527.CrossRefGoogle Scholar
Wiggins, G., & McTighe, J. (1998). Understanding by design. Washington, DC: Association for Curriculum and Supervision.Google Scholar
Wilensky, U. (1997). What is normal anyway? Therapy for epistemological anxiety. Educational Studies in Mathematics, 33, 171–202.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×