Fostering Teacher Learning of Conjecturing, Generalising and Justifying through Mathematics Studio

Authors

  • Kristin Lesseig Washington State University Vancouver

Abstract

Calls to advance students’ ability to engage in mathematical reasoning practices including conjecturing, generalizing and justifying (CGJ) place significant new demands on teachers.  This case study examines how Mathematics Studio provided opportunities for a team of U.S. middle school teachers to learn about these practices and ways to promote them in the classroom.  Findings demonstrate how CGJ readings and focused discussions, coupled with repeated cycles of collaborative lesson planning, observation and debrief, supported the development of teacher knowledge, professional community, and teaching resources.  In addition, this paper explores the role school leadership played in facilitating Math Studio to ensure these learning opportunities were realized.  Documenting how Math Studio features and participants contributed to teachers’ ability to implement CGJ focused lessons not only provides insights into the difficulties teachers have shifting instruction, but also adds to our understanding of school-embedded professional development more generally.

Author Biography

Kristin Lesseig, Washington State University Vancouver

Assistant Professor Mathematics Education

References

Alston, A. S., Pedrick, L., Morris, K. P., & Basu, R. (2011). Lesson study as a tool for developing teachers’ close attention to students’ mathematical thinking. In Lesson Study Research and Practice in Mathematics Education (pp. 135-151). Springer Netherlands.

Bieda, K.N., (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41, 351-382.

Cochran-Smith, M., & Lytle, S. L. (1999). Relationships of knowledge and practice: Teacher learning in communities. Review of research in education, 249-305.

Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association for Best Practices and the Council of Chief State School Officers.

DuFour, R. (2004). What is a "professional learning community"? Educational leadership, 61(8), 6-11.

DuFour, R., Eaker, R., & Many, T. (2010). Learning by doing: A handbook for professional learning communities at work. Bloomington, IN: Solution Tree Press.

Easton, L. B. (2009). Protocols for professional learning. Association for Supervision and Curriculum Development.

Emerson, R. M., Fretz, R. I., & Shaw, L. L. (1995). Writing ethnographic fieldnotes. Chicago, IL: University of Chicago Press.

Ermeling, B. A. (2010). Tracing the effects of teacher inquiry on classroom practice. Teaching and Teacher Education, 26(3), 377-388.

Fernandez, C. (2005). Lesson Study: A Means for Elementary Teachers to Develop the Knowledge of Mathematics Needed for Reform-Minded Teaching? Mathematical thinking and learning 7(4). 265-289.

Fernandez, C., Cannon, J., & Chokshi, S. (2003). A US–Japan lesson study collaboration reveals critical lenses for examining practice. Teaching and Teacher Education, 19(2), 171-185.

Fernandez, C., & Yoshida, M. (2004). Lesson Study: A case of a Japanese approach to improving instruction through school-based teacher development. Mahwah, NJ: Lawrence Erlbaum Associates.

Fogarty, R., & Pete, B. (2010). Professional Learning 101 A Syllabus of Seven Protocols. Phi Delta Kappan, 91(4), 32-34.

Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for research in mathematics education, 35 (4), 258-291.

Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. Second handbook of research on mathematics teaching and learning, 2, 805-842.

Hart, L. C., Alston, A. S., & Murata, A. (2011) Lesson Study Research and Practice in Mathematics Education: Learning Together. New York: Springer.

Hess, K. K., Jones, B. S., Carlock, D., & Walkup, J. R. (2009). Cognitive rigor: Blending the strengths of Bloom's Taxonomy and Webb's Depth of Knowledge to enhance classroom-level processes. National Center for the Improvement of Education Assessment, NH.

Hunter, J., & Back, J. (2011). Facilitating Sustainable Professional Development through Lesson Study. Mathematics Teacher Education & Development, 13(2), 94-114.

Jacobs, J., Hiebert, J., Givvin, K., Hollingsworth, H., Garnier, H., & Wearne, D. (2006). Does eighth-grade mathematics 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, 36, 5–32.

Kane, T. J., & Staiger, D. O. (2012). Gathering Feedback for Teaching: Combining High-Quality Observations with Student Surveys and Achievement Gains. Research Paper. MET Project. Bill & Melinda Gates Foundation.

Kazemi, E. (1998). Discourse That Promotes Conceptual Understanding. Teaching Children Mathematics, 4(7), 410-14.

Lannin, J.K., Ellis, A.B., Elliott, R. (2011). Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-Grade 8. R.M. Zbiek, (Ed.). Reston, VA: National Council of Teachers of Mathematics.

Lave, J., & Wenger, E. (1999). Legitimate peripheral participation in communities of practice. Learning and knowledge, 21-35.

Lewis, C. (2009). What is the nature of knowledge development in lesson study? Educational action research, 17(1), 95-110.

Lewis, C.C, Perry, R.R., & Hurd. J. (2009). Improving mathematics instruction through lesson study: A theoretical model and North American case. Journal of Mathematics Teacher Education, 12, 285-304.

Lewis, C., Perry, R., Friedkin, S., & Roth, J. (2012). Improving teaching does improve teachers: Evidence from lesson study. Journal of Teacher Education (63) 368-375.

Little, J. W. (2002). Locating learning in teachers’ communities of practice: Opening up problems of analysis in records of everyday work. Teaching and teacher education, 18(8), 917-946.

Little, J.W. & Curry, M.W. (2009). Structuring talk about teaching and learning: The use of evidence in protocol-based conversation. In L.M. Earl & H. Timperley (Eds.), Professional Learning Conversations: Challenges in using evidence for improvement (pp. 29-42). Netherlands: Springer.

Marrongelle, K., Sztajn, P., & Smith, M. (2013). Scaling up professional development in an era of common state standards. Journal of Teacher Education, 64(3), 202-211.

Murata, A., Bofferding, L., Pothen, B. E., Taylor, M. W., & Wischnia, S. (2012). Making connections among student learning, content, and teaching: Teacher talk paths in elementary mathematics lesson study. Journal for Research in Mathematics Education, 43(5), 616-650.

National Mathematics Advisory Panel. (2008). The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.

Perry, R., & Lewis, C. (2009). What is successful adaptation of lesson study in the US? Journal of Educational Change, 10(4), 365–391.

Robinson, N., & Leikin, R. (2012). One Teacher, Two Lessons: The Lesson Study Process. International Journal of Science and Mathematics Education, 10(1), 139–161.

Saldaña, J. (2012). The coding manual for qualitative researchers (No. 14). Sage.

Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25(2-3), 161–217.

Staples, M. (2008). Exploring the feasibility and value of a shared language of mathematics pedagogy. Paper presented at the annual meeting of the American Educational Research Association, New York.

Staples, M. & Truxaw, M. (2007). Words, thoughts and actions: Examining the potential impact of a shared language of mathematics pedagogy. In T. de Silva Lamberg & L. R. Wiest (Eds.), Proceedings of the twenty-ninth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Lake Tahoe, CA: University of Nevada, Reno

Stigler, J., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: The Free Press.

Stoll, L., Bolam, R., McMahon, A., Wallace, M., & Thomas, S. (2006). Professional learning communities: A review of the literature. Journal of educational change, 7(4), 221-258.

Stylianides, G. J., & Stylianides, A. J. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 314-352.

Supovitz, J. A. (2002). Developing communities of instructional practice. Teachers College Record, 104(8), 1591–1626.

Supovitz, J. A., & Christman, J. B. (2003). Developing communities of instructional practice: Lessons for Cincinnati and Philadelphia. CPRE Policy Briefs pp. 1–9. Pennsylvania: University of Pennsylvania.

Tepylo, D. H., & Moss, J. (2011). Examining change in teacher mathematical knowledge through lesson study. In L.C. Hart, A.S. Alston & A. Murata (Eds.), Lesson study research and practice in mathematics education (pp. 59-77). Springer Netherlands.

Vescio, V., Ross, D., & Adams, A. (2008). A review of research on the impact of professional learning communities on teaching practice and student learning. Teaching and Teacher education, 24(1), 80-91.

Weiss, I. R., Pasley, J. D., Smith, P. S., Banilower, E. R., & Heck, D. J. (2003). Looking inside the classroom. Chapel Hill, NC: Horizon Research Inc.

Yoshida, M. (2008). Exploring ideas for a mathematics teacher educator's contribution to lesson study. In D. Tirosh & T. Woods (Eds.), Tools and Processes in Mathematics Teacher Education, The International Handbook of Mathematics Teacher Education 2 (pp. 85-106) The Netherlands: Sense Publishers.

Yin, R. K. (2009). Case study research: Design and methods (Vol. 5). Thousand Oaks, CA: SAGE Publications.

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Published

2016-05-17

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