Teachers’ Construction of Learning Environments for Conditional Probability and Independence

Randall E. Groth

doi:10.29333/iejme/248

Full Text (PDF)

Randall E. Groth

More Detail

Abstract

Although literature on challenges to students’ learning of data analysis and probability has steadily accumulated over the past few decades, research on challenges encountered in teaching the content area is in its beginning stages. The present study aims to help build this area of research by identifying some knowledge elements necessary for teaching conditional probability and independence. Artifacts of classroom practice, including written plans and lesson video, were used to identify challenges encountered by teachers in establishing productive learning environments for students first learning the concepts. It is proposed that enhanced common and specialized content knowledge may help teachers address the challenges identified. Some salient aspects include knowledge of: distinctions among major concepts, data displays with pedagogical value, and the roles of fractions and combinatorial ideas in the psychology of learning conditional probability and independence. The discussion of these and other relevant knowledge aspects is drawn upon to propose potentially productive directions for teacher education efforts and future research.

Keywords

conditional probability
statistical independence
learning environments
mathematical knowledge for teaching

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 5, Issue 1, January 2010, 32-35

https://doi.org/10.29333/iejme/248

Publication date: 04 Apr 2010

Article Views: 2910

Article Downloads: 3324

Open Access References How to cite this article

References

American Statistical Association. (2005). Guidelines for assessment and instruction in statistics education (GAISE) college report. Retrievedfrom http://www.amstat.org/education/GAISE/GAISECollege.htm.
Amir, G. S., & Williams, J. S. (1999). Cultural influences on children’s probabilistic thinking. The Journal of Mathematical Behavior, 18, 85-107. doi:10.1016/S0732- 3123(99)00018-8
Ancker, J. S. (2006). The language of conditional probability. Journal of Statistics Education, 14 (2).
Ball, D. L., Hill, H. C., & Bass, H. (2005, Fall). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29, 14-22.
Bright, G. W., Frierson, D. Jr., Tarr, J. E., & Thomas, C. (2003). Navigating through probability in grades 6-8. Reston, VA: National Council of Teachers of Mathematics.
Clement, L. L., & Bernhard, J. Z. (2005). A problem-solving alternative to using key words. Mathematics Teaching in the Middle School, 10, 360-365.
Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers. Providence, Rhode Island: American Mathematical Society.
Curcio, F. (2002). A user’s guide to Japanese Lesson Study: Ideas for improving mathematics teaching. Reston, VA: National Council of Teachers of Mathematics.
Falk, R. (1986). Conditional probabilities: Insights and difficulties. In R. Davidson & J. Swift (Eds.), Proceedings of the Second International Conference on Teaching Statistics, Victoria, B.C.: University of Victoria (pp. 292-297). Voorburg, The Netherlands: International Statistical Institute.
Franklin, C. A., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K–12 curriculum framework. Alexandria, VA: American Statistical Association.
Glesne, C. (1999). Becoming qualitative researchers: An introduction (2nd ed.). New York: Longman.
Groth, R. E. (2007). Toward a conceptualization of statistical knowledge for teaching. Journal for Research in Mathematics Education, 38, 427-437.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524-549. doi:10.2307/749690
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematical knowledge for teaching. Elementary School Journal, 105, 11–30. doi:10.1086/428763
Jones, G. A., Langrall, C. W., & Mooney, E. S. (2007). Research in probability: Responding to classroom realities. In F.K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 909-955). Charlotte, NC: NCTM and Information Age Publishing.
Kelly, I. W., & Zwiers, F. W. (1986, August). Introducing disjoint and independent events in probability. Paper presented at the Second International Conference on Teaching Statistics, Victoria, Canada.
Konold, C., & Miller, C. D. (2005). TinkerPlots: Dynamic data exploration. [Computer software]. Emeryville, CA: Key Curriculum Press.
Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S., & Phillips, E. D. (1997). Connected mathematics: What do you expect? Menlo Park, CA: Dale Seymour Publications.
Maryland State Department of Education. (2004). Voluntary state curriculum – mathematics grades 3-8. Retrieved from http://mdk12.org/share/vsc/vsc_mathematics_gr38.pdf.
Maxwell, J. A. (2005). Qualitative research design: An interactive approach. Thousand Oaks, CA: Sage.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd ed.). Thousand Oaks, CA: Sage Publications.
National Center for Research in Mathematical Sciences Education & Freudenthal Institute (Eds.). (1997-1998). Mathematics in context. Chicago, IL: Encyclopaedia Brittanica.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
National Research Council. (2000). How people learn: Brain, mind, experience, and school. Washington, D.C.: National Academy Press.
Perkowski, D. A., & Perkowski, M. (2006). Data analysis and probability connections: Mathematics for middle school teachers. New York: Pearson.
Richardson, L., & St. Pierre, E. A. (2005). Writing: A method of inquiry. In N.K. Denzin & Y.S. Lincoln (Eds.), The Sage handbook of qualitative research (3rd ed.) (pp. 959-978). Thousand Oaks, CA: Sage.
Russell, S. J., Schifter, D., & Bastable, V. (2002). Developing mathematical ideas: Working with data. Parsippany, NJ: Dale Seymour Publications.
Scheaffer, R., Smith, W. B. (2007). Using statistics effectively in mathematics education research: A report from a series of workshops organized by the American Statistical Association with funding from the National Science Foundation. Alexandria, VA: American Statistical Association.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). Reston, VA: NCTM.
Schwarz, C. V., & Gwekwerere, Y. N. (2007). Using a guided inquiry and modeling instructional framework (EIMA) to support preservice K-8 science teaching. Science Education, 91, 158-186.
Shaugnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465-494). Reston, VA: National Council of Teachers of Mathematics.
Shaughnessy, J. M. (2003). Research on students’ understandings of probability. In J. Kilpatrick, W.G. Martin, & D. Schifter (Eds.), A research companion to Principles and standards for school mathematics (pp. 216-226). Reston, VA: NCTM.
Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A.E. Kelly & R.A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267-306). Mahwah, NJ: Erlbaum.
Stipek, D., Salmon, J. M., Givvin, K. B., Kazemi, E., Saxe, G., & MacGyvers, V. L. (1998). The value (and convergence) of practices suggested by motivation research and promoted by mathematics education reformers. Journal for Research in Mathematics Education, 29, 465-488.
Stohl, H. (2005). Probability in teacher education and development. In G.A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 345-366). New York: Springer.
Tarr, J. E. (1997). Using middle school students’ thinking in conditional probability and independence to inform instruction (Doctoral dissertation). Available from Dissertation & Theses database. (Publication No. AAT 9803741).
Tarr, J. E., & Jones, G. A. (1997). A framework for assessing middle school students’ thinking in conditional probability and independence. Mathematics Education Research Journal, 9, 39-59.
Tarr, J. E., & Lannin, J. K. (2005). How can teachers build notions of conditional probability and independence? In G.A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 215-238). New York: Springer. doi:10.1007/0-387-24530- 8_10
Watson, J. M. (1995). Conditional probability: Its place in the mathematics curriculum. Mathematics Teacher, 88, 12-17.
Watson, J. M. (1997). Chance and data for luddites. Australian Mathematics Teacher, 53(3), 24-29.
Watson, J. M. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education, 4, 305-337.
Watson, J. M., & Moritz, J. B. (2002). School students’ reasoning about conjunction and conditional events. International Journal of Mathematical Education in Science and Technology, 33, 59-84.
Wood, T. (1998). Alternative patterns of communication in mathematics classes: Funneling or focusing? In H. Steinbring, M.B. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167-178). Reston, VA: National Council of Teachers of Mathematics.

How to cite this article

APA

Groth, R. E. (2010). Teachers’ Construction of Learning Environments for Conditional Probability and Independence. International Electronic Journal of Mathematics Education, 5(1), 32-35. https://doi.org/10.29333/iejme/248

Vancouver

Groth RE. Teachers’ Construction of Learning Environments for Conditional Probability and Independence. INT ELECT J MATH ED. 2010;5(1):32-5. https://doi.org/10.29333/iejme/248

AMA

Groth RE. Teachers’ Construction of Learning Environments for Conditional Probability and Independence. INT ELECT J MATH ED. 2010;5(1), 32-35. https://doi.org/10.29333/iejme/248

Chicago

Groth, Randall E.. "Teachers’ Construction of Learning Environments for Conditional Probability and Independence". International Electronic Journal of Mathematics Education 2010 5 no. 1 (2010): 32-35. https://doi.org/10.29333/iejme/248

Harvard

MLA

Groth, Randall E. "Teachers’ Construction of Learning Environments for Conditional Probability and Independence". International Electronic Journal of Mathematics Education, vol. 5, no. 1, 2010, pp. 32-35. https://doi.org/10.29333/iejme/248