Abstract
The Problem-Solving Cycle (PSC) model of mathematics Professional Development (PD) seeks to enhance teachers’ knowledge and skills in a variety of domains. In this paper we consider how participating in the PSC program, with a specific focus on algebra, impacted one teachers’ instructional practice. We explore the nature of change in the teacher’s classroom, as well as the connection between these changes, the focus of our PD, and the teacher’s intentions. Our analyses are based on a set of videotaped classroom lessons collected over two years, along with interviews and written reflections. We conclude that there was a close match between the teacher’s personal goals for improvement and our program goals, and notable shifts in his algebra instruction that was likely to have supported his students’ algebraic reasoning.
The Professional Development program featured in this chapter is one component of a larger research project entitled Supporting the Transition from Arithmetic to Algebraic Reasoning (STAAR). STAAR is supported by NSF Proposal No. 0115609 through the Interagency Educational Research Initiative (IERI). The views shared in this chapter are ours, and do not necessarily represent those of IERI. Portions of this chapter were presented at the American Educational Research Association Annual Meeting, San Francisco, 2006. The authors would like to acknowledge Eric Eiteljorg’s role in our many years of discussions about this case study, and his early efforts to get these analyses off the ground. We also thank Ken Bryant for his enthusiastic participation in our PD, and his unwavering commitment to improving mathematics teaching and learning. This chapter is a revised version of an article published in ZDM—International Reviews on Mathematical Education, 37(1), 43–52. DOI 10.1007/BF02655896.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the Learning Profession: Handbook of Policy and Practice (pp. 3–32). San Francisco: Jossey-Bass.
Ball, D. L., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of Research on Teaching (4th ed.). New York: Macmillan.
Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412–446.
Borko, H., Frykholm, J. A., Pittman, M. E., Eiteljorg, E., Nelson, M., Jacobs, J. K., Clark, K. K., & Schneider, C. (2005). Preparing teachers to foster algebraic thinking. Zentralblatt für Didaktik der Mathematik: International Reviews on Mathematical Education, 37(1), 43–52.
Borko, H., Jacobs, J., Eiteljorg, E., & Pittman, M. E. (2008). Video as a tool for fostering productive discourse in mathematics professional development. Teaching and Teacher Education, 24, 417–436.
Clark, K. K., Jacobs, J., Pittman, M., & Borko, H. (2005). Strategies for building mathematical communication in the middle school classroom: Modeled in professional development, implemented in the classroom. Current Issues in Middle Level Education, 11(2), 1–12.
Cnop, I., & Grandsard, F. (1998). Teaching abstract algebra concepts using small group instruction. International Journal of Mathematical Education in Science & Technology, 29(6), 843–851.
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.
Design-Based Research Collective (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5–8.
Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide for Teachers, Grades 6–10. New York: Heinemann.
Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24, 94–116.
Ferrinni-Mundy, J., & Schram, T. (1997). Recognizing and Recording Reform in Mathematics Education: Issues and Implications. Reston, VA: National Council of Teachers of Mathematics. Journal for Research in Mathematics Education Monograph, no 8.
Greeno, J. G. (2003). Situative research relevant to standards for school mathematics. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics (pp. 304–332). Reston, VA: National Council of Teachers of Mathematics.
Grossman, P., Hammerness, K., & McDonald, M. (2009). Refining teaching, re-imagining teacher education. Teachers and Teaching: Theory and Practice, 15(2), 273–289.
Hadjidemetriou, C., & Williams, J. (2002). Teachers’ pedagogical content knowledge: Graphs from a cognitivist to a situated perspective. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 57–64). Norwich, UK.
Jacobs, J., Hiebert, J., Givvin, K. B., Hollingsworth, H., Garnier, H., & Wearne, D. (2006). Does eighth-grade teaching in the United States align with the NCTM Standards? Results from the TIMSS 1995 and 1999 Video Studies. Journal for Research in Mathematics Education, 37(1), 5–32.
Jacobs, J., Borko, H., Koellner, K., Schneider, C., Eiteljorg, E., & Roberts, S. A. (2007). The problem-solving cycle: A model of mathematics professional development. Journal of Mathematics Education Leadership, 10(1), 42–57.
Kaput, J. J. (2007). What is algebra? What is algebraic reasoning. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades. London: Taylor & Francis.
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. K. Lester Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics (Vol. 2, pp. 707–752). Charlotte, NC: Information Age Publishing.
Koellner, K., Jacobs, J., Borko, H., Schneider, C., Pittman, M., Eiteljorg, E., Bunning, K., & Frykholm, J. (2007). The problem-solving cycle: A model to support the development of teachers’ professional knowledge. Mathematical Thinking and Learning, 9(3), 271–303.
Lampert, M. (2001). Teaching Problems and the Problems of Teaching. New Haven: Yale University Press.
Lave, J., & Wenger, E. (1991). Situated Learning: Legitimate Peripheral Participation. Cambridge, UK: Cambridge University Press.
Learning Mathematics for Teaching (LMT). (2006). A coding rubric for measuring the quality of mathematics in instruction (Technical Report LMT1.06). Ann Arbor, MI: University of Michigan, School of Education.
Miles, M. B., & Huberman, A. M. (1994). An Expanded Sourcebook: Qualitative Data Analysis. Thousand Oaks, CA: Sage.
Moses, R. P., & Cobb, C. (2001). Organizing algebra: The need to voice a demand. Social Policy, 31(4), 4–12.
Nathan, M. J., & Koedinger, K. R. (2000). Teachers’ and researchers’ beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31, 168–190.
National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
National Mathematics Advisory Panel (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
National Research Council (1998). The Nature and Role of Algebra in the K-14 Curriculum: Proceedings of a National Symposium. Washington, DC: National Academy Press.
Putnam, R., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4–15.
Shulman, L. S. (1983). Autonomy and obligation: The remote control of teaching. In L. S. Shulman & G. Sykes (Eds.), Handbook of Teaching and Policy (pp. 484–504). New York: Longman.
Winicki-Landman, G. (2001). Shhh… Let them think… Let them talk!. Australian Senior Mathematics Journal, 15(2), 30–38.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Koellner, K., Jacobs, J., Borko, H., Roberts, S., Schneider, C. (2011). Professional Development to Support Students’ Algebraic Reasoning: An Example from the Problem-Solving Cycle Model. In: Cai, J., Knuth, E. (eds) Early Algebraization. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17735-4_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-17735-4_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17734-7
Online ISBN: 978-3-642-17735-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)