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From Primitive Knowing to Formalising: The Role of Student-to-Student Questioning in the Development of Mathematical Understanding
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this type has the potential to call attention to the importance of providing meaningful opportunities for such student-to-student interaction.
REFERENCES
Carpenter, T.P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding.
In E. Fennema & T.A. Romberg, Eds.) Mathematics classrooms That Promote Understanding. Lawrence Erlbaum. Hillside NJ. (pp. 19-32).
Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and
collective reflection. Journal of Research in Mathematics Education, 28, 258-277.
Cobb, P. (2000). From representations to symbolizing: introductory comments on semiotics
and mathematical learning. In P. Cobb, E. Yackel, & K. McClain (Eds.) Symbolizing and communicating in mathematics classrooms. Lawrence Erlbaum, Hillside NJ. (pp. 17-36)
Doerfler, W. (2000). Means for meaning. In P. Cobb, E. Yackel, & K. McClain (Eds.)
Symbolizing and communicating in mathematics classrooms. Lawrence Erlbaum, Hillside NJ.w (pp. 99-132)
Maher, C.A. (2002). How students structure their own investigations and educate us: What
we have learned from a 14 year study. In A.D. Cockburn & E. Nardi (Eds.), 26th Annual Conference of the International Group for the Psychology of Mathematics Education: Vol. 4. Learning from Learners. (031-046), Norwich, UK: School of Education and Professional Development University of East Anglia
National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for
School Mathematics. Reston, Va.: The Council, 2000.
Pirie, S.E.B. (1988). Understanding-Instrumental, relational, formal, intuitive…, How can we
know? For the Learning of Mathematics 8(3), 2-6
Pirie, S. E.B. & Kieren, T. E. (1994). Growth in mathematical understanding: How can we
characterize it and how can we represent it? Educational Studies in Mathematics, 26, 165-190.
Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers
of Mathematics, 2000.
Schorr, R.Y. (2003). Motion, speed, and other ideas that “should be put in books”. Journal
of Mathematical Behavior. 22(4), 467-479.
Sfard, A. (2000). Symbolizing mathematical reality into being—or how mathematical
discourse and mathematical objects create each other. In P. Cobb, E. Yackel, & K. McClain (Eds.) Symbolizing and communicating in mathematics classrooms. Lawrence Erlbaum, Hillside NJ. (pp. 37-98)
Shafer, M.K., & Romberg, T. (1999). Assessment in classrooms that promote understanding.
In E. Fennema & T.A. Romberg, Eds.) Mathematics classrooms That Promote Understanding. Lawrence Erlbaum. Hillside NJ. (pp. 159-184).
Warner, L.B., Coppolo Jr., J. & Davis, G.E. (2002). Flexible mathematical thought. In A.D.
Cockburn & E. Nardi (Eds.), 26th Annual Conference of the International Group for the Psychology of Mathematics Education: Vol. 4. Learning from Learners. (31-46), Norwich, UK: School of Education and Professional Development University of East Anglia
Warner, L.B., Alcock, L. J., Coppolo Jr., J. & Davis, G. E. (2003). "How does Flexible
Mathematical Thinking Contribute to the Growth of Understanding?" In N.A. Pateman, B.J. Dougherty & J. Zillox (eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25
th
Conference of PME-NA , July 13 – 18, 2003, Honolulu, Hawaii (Vol. 4, pp.371-
378).
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| | Authors: Warner, Lisa. and Schorr, Roberta. |
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this type has the potential to call attention to the importance of providing meaningful
opportunities for such student-to-student interaction.
REFERENCES
Carpenter, T.P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding.
In E. Fennema & T.A. Romberg, Eds.) Mathematics classrooms That Promote
Understanding. Lawrence Erlbaum. Hillside NJ. (pp. 19-32).
Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and
collective reflection. Journal of Research in Mathematics Education, 28, 258-277.
Cobb, P. (2000). From representations to symbolizing: introductory comments on semiotics
and mathematical learning. In P. Cobb, E. Yackel, & K. McClain (Eds.) Symbolizing and
communicating in mathematics classrooms. Lawrence Erlbaum, Hillside NJ. (pp. 17-36)
Doerfler, W. (2000). Means for meaning. In P. Cobb, E. Yackel, & K. McClain (Eds.)
Symbolizing and communicating in mathematics classrooms. Lawrence Erlbaum, Hillside
NJ.w (pp. 99-132)
Maher, C.A. (2002). How students structure their own investigations and educate us: What
we have learned from a 14 year study. In A.D. Cockburn & E. Nardi (Eds.), 26th Annual
Conference of the International Group for the Psychology of Mathematics Education:
Vol. 4. Learning from Learners. (031-046), Norwich, UK: School of Education and
Professional Development University of East Anglia
National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for
School Mathematics. Reston, Va.: The Council, 2000.
Pirie, S.E.B. (1988). Understanding-Instrumental, relational, formal, intuitive…, How can we
know? For the Learning of Mathematics 8(3), 2-6
Pirie, S. E.B. & Kieren, T. E. (1994). Growth in mathematical understanding: How can we
characterize it and how can we represent it? Educational Studies in Mathematics, 26, 165-
190.
Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers
of Mathematics, 2000.
Schorr, R.Y. (2003). Motion, speed, and other ideas that “should be put in books”. Journal
of Mathematical Behavior. 22(4), 467-479.
Sfard, A. (2000). Symbolizing mathematical reality into being—or how mathematical
discourse and mathematical objects create each other. In P. Cobb, E. Yackel, & K.
McClain (Eds.) Symbolizing and communicating in mathematics classrooms. Lawrence
Erlbaum, Hillside NJ. (pp. 37-98)
Shafer, M.K., & Romberg, T. (1999). Assessment in classrooms that promote understanding.
In E. Fennema & T.A. Romberg, Eds.) Mathematics classrooms That Promote
Understanding. Lawrence Erlbaum. Hillside NJ. (pp. 159-184).
Warner, L.B., Coppolo Jr., J. & Davis, G.E. (2002). Flexible mathematical thought. In A.D.
Cockburn & E. Nardi (Eds.), 26th Annual Conference of the International Group for the
Psychology of Mathematics Education: Vol. 4. Learning from Learners. (31-46),
Norwich, UK: School of Education and Professional Development University of East
Anglia
Warner, L.B., Alcock, L. J., Coppolo Jr., J. & Davis, G. E. (2003). "How does Flexible
Mathematical Thinking Contribute to the Growth of Understanding?" In N.A. Pateman,
B.J. Dougherty & J. Zillox (eds.), Proceedings of the 27th Conference of the
International Group for the Psychology of Mathematics Education held jointly with the
25
th
Conference of PME-NA , July 13 – 18, 2003, Honolulu, Hawaii (Vol. 4, pp.371-
378).
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