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International Journal of Mathematics Trends and Technology

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Volume 1 | Issue 1 | Year 2011 | Article Id. IJMTT-V1I1P6 | DOI : https://doi.org/10.14445/22315373/IJMTT-V1I1P6

Teaching through Mathematics Problems: Redesigned for a Focus on Mathematics


Immaculate K. Namukasa, Elena Polotskaia
Abstract

Recent research on problem solving explores its potential as a pedagogical practice. This emphasis rejuvenates the interest in problem solving as a learning activity. This paper presents the practice of using a selected problem together with its variants in a single lesson. The practice was implemented in middle school classroom settings with gifted students and with mixed ability students as well as in teacher education classrooms. Experiences from practice are used to illustrate that the use of a set of closely related problems is likely to make students more eager to share their solutions, to generate several solution strategies, and to show various connections among the ideas involved. The shift toward exploring multiple math strategies and representations, and big ideas is at the center of innovative and successful approaches to teaching mathematics. The paper is guided by an evaluation of literature that considers teaching through problem solving and of literature on complex professional tasks.

Keywords
Problem solving, pedagogy, middle school, gifted students, strategies, innovative approaches, complex professional tasks.
References

[1] ZDM, “The International Journal on Mathematics Education (2007). A special issue on Problem solving around the world: Summing up the state of the art,”. ZDM, vol. 39, pp. 5-6, 2007.
[2] A. H. Schoenfeld, “Problem Solving in the United States, 1970-2008: Research and theory, practice and politics,” ZDM Mathematics Education, vol. 39, pp. 537-551, 2007.
[3] D. Clarke, M. Goos, and W. Morony, “Problem solving and working mathematically: An Australian perspective,” ZDM Mathematics Education, vol. 39, pp. 475-490, 2007.
[4] F. K. Lester, and R. L. Charles, Teaching mathematics through problem solving: Prekindergarten-grade 6. Reston, VA: NCTM, 2003).
[5] S. Crespo, and N. Sinclair, “What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems,” Journal of Mathematics Teacher Education, vol.11, pp. 395-415, 2008.
[6] G. Brousseau, and P. Gibel, “Didactical handling of students’ reasoning processes in problem solving situations,” Educational Studies in Mathematics, vol. 59, pp. 13-58, 2005.
[7] Y. Bar-Yam, Dynamics of complex systems, Reading, MA: AddisonWesley, 1997.
[8] E. Simmt, “Mathematical knowing in action,” Unpublished doctoral dissertation, University of Alberta, 2000.
[9] G., Gadanidis, J. Hughes, R. Scucuglia, and S. Tolley, “Low floor, high ceiling: performing mathematics across grades 2-8,” In Swars, D. W. Stinson, and S. Lemons-Smith, (Eds.), Proceedings of the 31st annual meeting of the North American Chapter ofthe International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University, 2009.
[10] G. Polya, How to solve it: A new aspect of mathematics, 2nd ed, New Jersey: Princeton University Press, 1945/1973
[11] G. Flewelling,, and W. Higginson, Realizing a vision of tomorrow’s mathematics classroom: A handbook on rich learning tasks. Kingston: MSTE, 2001.
[12] A. Sfard, “On the dual nature of mathematical conceptions: Reflections on process and objects as different sides of the same coin,” Educational Studies in Mathematics, vol. 22, pp. 1-36, 1991.
[13] M. Lampert, Connecting mathematical teaching and learning, E. Fennema, T. P. Carpenter, and A. J. Lamon, Eds. Integrating research on teaching and learning mathematics (pp. 121-152). Albany: State University of New York, 1991.
[14] C. T. Fosnot, and M. Dolk, Mathematicians at Work: Constructing Multiplication and Division. Portsmouth, NH: Heinemann, 2001.
[15] I. K. Namukasa, and G. Gadanidis, (2010) Mathematical tasks as experiential therapy for elementary pre-service teachers. International Journal for Mathematics Teaching and Learning. [Online]. Available: http://www.cimt.plymouth.ac.uk/journal/default.htm.
[16] C. Fernandez, “Lesson study: A means for elementary teachers to develop the knowledge of mathematics needed for reform-minded teaching?,” Mathematical Thinking and Learning, vol.7, pp. 265-289, 2005.
[17] T. P. Carpenter, E. Fennema, M. L. Franke, L. Levi,, and S. B. Empson, Children’s mathematics: Cognitively guided instructions.Portsmouth: Heinemann, 1999. [18] OECD: The PISA 2003 Assessment Framework. Mathematics, Reading, Science and Problem Solving Knowledge and Skills. Paris: OECD, 2003.
[19] English, L. D. Integrating complex systems within the mathematics curriculum. Teaching Children Mathematics, 15(1), 38, 2008.
[20] Nelson, Nelson Mathematics Grade 6 by Kelleher, H., Kubota-Zarivnij, K., Milot, P., Morris, B., and Super, Doug. Thomson, 2005.
[21] McGraw-Hill Ryerson, Principles of Mathematics 9 by Darling, Erdman, Ferneyhough, MCCudden, Meisel & Speijer. McGraw-Hill Ryerson, 1999
[22] OME. (2006). Targeted Implementation and Planning Supports for Revised Mathematics Continuum and Connections: Patterning to Algebraic Modelling (TIPS4RMCC) Grades 7 & 8. A Ministry of Education, Ontario resource. [Online]. Available: http://www.edu.gov.on.ca/eng/studentsuccess/lms/files/tips4rm/TIPS4 RMccpatterns.pdf
[23] R. Leikin, and A. Levav-Waynberg, “Solution spaces of multiplesolution connecting tasks as a mirror of the development of mathematics teachers’ knowledge.” Canadian Journal of Science, Mathematics and Technology Education, vol. 8, pp.233-251, 2008.
[24] M. L. Blanton, and J. J. Kaput, “Characterizing a classroom practice that promotes algebraic reasoning,” vol. 35, pp. 412-446, Nov. 2005.
[25] J. W. Stigler, P. A. Gonzales, T. Kawanka, S. Knoll, & A. Serrano, “The TIMSS videotape classroom study: Methods and findings from an exploratory research project on eighth-grade mathematics instruction in Germany, Japan, and the United States,” Washington, DC: U.S. Department of Education, National Center for Education Statistics., 1999
[26] M. Cordy, (2012). Mild, Medium and Spicy: The mathematics of Chopsticks. [Online]. Available: http://publish.ed.uwo.ca/george.gadanidis/Michellel/index.html
[27] M. Small, Big Ideas from Dr. Small: Creating a comfort zone with teaching mathematics, Grades 4-8. Toronto: Nelson, 2009.
[28] Ontario Ministry of Education. A guide to effective instruction in mathematics: Kindergarten to Grade 6, volume 2. Toronto: Ontario Ministry of Education, 2009..
[29] NCTM (2011). Supreme Court welcome. [Online]. Available: http://illuminations.nctm.org/LessonsDetail.aspx?ID=L630.
[30] M. L. Blanton, and J. J. Kaput, Developing Elementary teachers’ “Algebra eyes and ears.” Teaching Children Mathematics. Reston: NCTM, 2003.
[31] A. Kajander, Big ideas for small mathematicians: Kids discovering the beauty of math with 22 ready-to-go activities. Tucson, AZ: Zephyr, 2003.

Citation :

Immaculate K. Namukasa, Elena Polotskaia, "Teaching through Mathematics Problems: Redesigned for a Focus on Mathematics," International Journal of Mathematics Trends and Technology (IJMTT), vol. 1, no. 1, pp. 50-56, 2011. Crossref, https://doi.org/10.14445/22315373/IJMTT-V1I1P6

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