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Mathematics teachers' abilities to use and make sense of drawn representations

Published: 24 June 2008 Publication History

Abstract

This qualitative study considers middle grades' mathematics teachers' abilities to make sense of drawn representations of fraction and decimal operations. Our interest was in understanding how teachers interpret these drawings and whether they can flexibly move within and between the various drawings. Our findings focus issues of relevant mathematics that emerged as well as teachers' abilities to move between and within the various drawings of interest. The conclusions tie our findings to the need for more professional development to support teachers in using drawn representations.

References

[1]
Ball, D. (2003). What mathematical knowledge is needed for teaching mathematics? Secretary's Summit on Mathematics, U.S. Department of Education, February 6, 2003; Washington, D.C. Retrieved October 13, 2007 from http://www.ed.gov/inits/mathscience
[2]
Ball, D., 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., pp. 433-456). New York: Macmillan.
[3]
Behr, M. J., Khoury, H. A., Harel, G., Post, T., & Lesh, R. (1997). Conceptual units analysis of preservice elementary school teachers' strategies on a rational number as operator task. Journal for Research in Mathematics Education, 28(1), 48-69.
[4]
Coffey, A., & Atkinson, P. (1996). Making sense of qualitative data. Thousand Oaks, CA: Sage Publications, Inc.
[5]
Denzin, N. K. (1989). The research act: A theoretical introduction to sociological methods. Englewood Cliffs, NJ: Prentice Hall.
[6]
Dreyfus, T. & Eisenberg, T. (1996). On different facets of mathematical thinking. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking, (pp. 253-284). Mahwah, NJ: Erlbaum.
[7]
Gagatsis, A. & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645-657.
[8]
Goldin, G. (2002). Representation in mathematical learning and problem solving. In L. English (Ed.), Handbook of international research in mathematics education (pp. 197-218). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.
[9]
Hall, R. (2000). Videorecording as theory. In Kelly, A. E., & Lesh, R. A. (Eds.) Handbook of research design in mathematics and science education (pp. 647-664). Mahwah, NJ: Erlbaum.
[10]
Hill, H. C., Rowan, B., & Ball, D. L. (2004). Developing measures of teachers' mathematics knowledge for teaching. Elementary School Journal, 105(1), 11.
[11]
Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26, 95-143.
[12]
Izsák, A., Tillema, E., & Tunçç-Pekkan, Z. (2008). Teaching and learning fraction addition on number lines. Journal for Research in Mathematics Education, 39(1), 33-62.
[13]
Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N. & Phillips, E. D. (2002). Connected mathematics program. Glenview, IL: Prentice Hall.
[14]
Lesh, R. (1987). The evolution of problem representations in the presence of powerful conceptual amplifiers. In C. Janvier (Ed.), Problems of representation in teaching and learning mathematics (pp. 197-206). Hillsdale, NJ: Erlbaum.
[15]
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.) Problems on representation in the teaching and learning of mathematics (pp. 33-40). London: Lawrence Erlbaum Associates, Publishers.
[16]
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
[17]
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
[18]
Kilpatrick, Swafford, & Findell (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
[19]
Rider, R. (2004). The effect of multi-representational methods on students' knowledge of function concepts in developmental college mathematics. Doctoral Dissertation, North Carolina State University.
[20]
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
[21]
SII/LMT (Study of Instructional Improvement/Learning Mathematics for Teaching) (2004). Learning mathematics for teaching. Ann Arbor, MI: Consortium for Policy Research in Education.
[22]
Sowder, J., Philipp, R., Armstrong, B., & Schappelle, B. (1998). Middle-grade teachers' mathematical knowledge and its relationship to instruction: A research monograph. New York: State University of New York Press.
[23]
Steffe, L. P. (2002). A new hypothesis concerning children's fractional knowledge. Journal of Mathematical Behavior, 102, 1-41.
[24]
Strauss, A. & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Thousand Oaks, CA: Sage.

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        ICLS'08: Proceedings of the 8th international conference on International conference for the learning sciences - Volume 2
        June 2008
        523 pages

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        International Society of the Learning Sciences

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        Published: 24 June 2008

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