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Experiential models of students' geometry thinking: Case studies of two secondary mathematics teachers
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children. These learning trajectories are a valuable resource for teachers, but are not yet readily or easily available for teachers’ use. Practicing teachers develop their own trajectories based on their years of planning activities and interacting with students. These trajectories are not as detailed or refined as the ones created by researchers, but they can provide powerful insights for teacher education. As researchers continue to develop learning trajectories of childrens’ mathematics I think it would also be valuable to examine teachers created learning trajectories.
References
Carpenter, T. P., Fennema, E., Peterson, P. L., Chaing, C. & Loef, M. (1989). Using knowledge of
childrens’ mathematical thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499–532.
Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A
longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403–434.
Gravemeijer, K. (2004, April). Local instruction theories as means of support for teachers in
reform mathematics education. Paper presented at the annual meeting of American Educational Research Association, San Diego.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning
in second-grade arithmetic. American Educational Research Journal, 30, 393–425.
Jackiw, N. (1991). Geometer’s Sketchpad [Computer software]. Berkeley, CA: Key Curriculum
Press.
Lubinski, C. A., & Jaberg, P. A. (1997). Teacher change and mathematics K-4: Developing a
theoretical perspective. In E. Fennama & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 223–254). Mahwah, NJ: Lawrence Erlbaum Associates.
Merriam, S. B. & Associates. (2002). Qualitative research in Practice: Examples for discussion
and analysis. San Francisco, CA: Jossey-Bass.
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective.
Journal for Research in Mathematics Education, 26, 114–145.
Steffe, L. P. (2004). On the construction of learning trajectories: The case of commensurate
fractions. Mathematical Thinking and Learning, 6(2), 129–163.
Lamberg, T., & Wiest, L. R. (Eds.). (2007). Proceedings of the 29
th
annual meeting of the North
American Chapter of the International Group for the Psychology of Mathematics Education, Stateline (Lake Tahoe), NV: University of Nevada, Reno.
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125
children. These learning trajectories are a valuable resource for teachers, but are not yet readily or
easily available for teachers’ use. Practicing teachers develop their own trajectories based on their
years of planning activities and interacting with students. These trajectories are not as detailed or
refined as the ones created by researchers, but they can provide powerful insights for teacher
education. As researchers continue to develop learning trajectories of childrens’ mathematics I
think it would also be valuable to examine teachers created learning trajectories.
References
Carpenter, T. P., Fennema, E., Peterson, P. L., Chaing, C. & Loef, M. (1989). Using knowledge of
childrens’ mathematical thinking in classroom teaching: An experimental study. American
Educational Research Journal, 26, 499–532.
Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A
longitudinal study of learning to use children's thinking in mathematics instruction. Journal
for Research in Mathematics Education, 27, 403–434.
Gravemeijer, K. (2004, April). Local instruction theories as means of support for teachers in
reform mathematics education. Paper presented at the annual meeting of American Educational
Research Association, San Diego.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning
in second-grade arithmetic. American Educational Research Journal, 30, 393–425.
Jackiw, N. (1991). Geometer’s Sketchpad [Computer software]. Berkeley, CA: Key Curriculum
Press.
Lubinski, C. A., & Jaberg, P. A. (1997). Teacher change and mathematics K-4: Developing a
theoretical perspective. In E. Fennama & B. S. Nelson (Eds.), Mathematics teachers in
transition (pp. 223–254). Mahwah, NJ: Lawrence Erlbaum Associates.
Merriam, S. B. & Associates. (2002). Qualitative research in Practice: Examples for discussion
and analysis. San Francisco, CA: Jossey-Bass.
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective.
Journal for Research in Mathematics Education, 26, 114–145.
Steffe, L. P. (2004). On the construction of learning trajectories: The case of commensurate
fractions. Mathematical Thinking and Learning, 6(2), 129–163.
Lamberg, T., & Wiest, L. R. (Eds.). (2007). Proceedings of the 29
th
annual meeting of the North
American Chapter of the International Group for the Psychology of Mathematics Education,
Stateline (Lake Tahoe), NV: University of Nevada, Reno.
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