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PED 3187
EDU 5357
EDU 7163

 PED 3187: Teaching Mathematics at the Intermediate Division

Course objectives and content:
The goal of this course is to help teachers develop the confidence, knowledge, and resources to facilitate mathematical understanding of learners in grades 7-10. To accomplish this, we will engage teacher candidates in an exploration of mathematics-for-teaching and ways of teaching mathematics. Mathematics-for-teaching is a demanding aspect of mathematical work that requires not only an understanding of mathematical concepts, and the mathematics curriculum, but also an understanding of how learners come to know mathematics in multiple ways. This also requires that educators understand how mathematical concepts are related. Further, this course focuses on ways to promote mathematical inquiry and mathematical argumentation. In this seminar we will engage teacher candidates with the mathematics curriculum for grades 7-10 in Ontario, current research articles on mathematics teaching/learning, along with a large array of resources for mathematics teaching/learning.

In particular, we explore mathematics curriculum, assessment and instruction and connect these practices with an understanding of how students learn mathematics. Further, we explore particular mathematics content with a view to developing an understanding of mathematics-for-teaching.

Resources:
  • Algebra to Go. (2000). Nelson Thomson Learning.
  • Battista, M.T. (1999). The mathematical miseducation of America’s youth. Phi Delta Kappan. http://www.pdkintl.org/kappan/kbat9902.htm
  • Black, P. & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80 (2): 139-148. http://www.pdkintl.org/kappan/kbla9810.htm
  • Boaler, J., & Humphreys, C. (2005). Connecting mathematical ideas. Portsmouth, NH: Heinemann.
  • Boaler, J. (2002). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education, 33(4), 239-258.
  • Davis, B., & Simmt. E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal of Research in Mathematics Education 34(2): 137-167. http://www.ualberta.ca/~bdavis/DavisSimmtJRME.pdf
  • Davis, B., & Simmt. E. (2006). Mathematics-for-teaching: An on-going investigation into the mathematics that teachers (need to) know. Educational Studies in Mathematics 61(3), 291-319.
  • Devlin, K. (2005). The math instinct: Why you’re a mathematical genius (along with lobsters, birds, cats, and dogs). New York: Thunder’s Mouth Press
  • Heid, M.K., Blume, G.W., Hollebrands, K., Piez, C. (2002). Computer algebra systems in mathematics instruction: Implications from research. Mathematics Teacher, 95(8). 586 – 591
  • Lakoff, G., & Nunez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
  • Lannin, J. (2003). Developing algebraic reasoning through generalization. Mathematics Teaching in the Middle School, 8(7). 342 – 348.
  • Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. Addison Wesley.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston VA: National Council of Teachers of Mathematics. http://standards.nctm.org/ - entire document on-line. Other materials also available such as e-examples (interactive problems and examples)
    Executive summary of NCTM Principles and Standards for School Mathematics http://www.nctm.org/standards/12752_exec_pssm.pdf
  • Ontario Ministry of Education and Training. (2005). The Ontario Curriculum Grades 1-8 Mathematics (Revised). Toronto: Queen’s Printer.
    Ontario Ministry of Education and Training. (2005). The Ontario Curriculum Grades 9-10 Mathematics (Revised). Toronto: Queen’s Printer.
    Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4-13.
  • Silver, E., A. & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3). 129- 135.
  • Simmt, E. (July 2006). Complexity and mathematics education: Discussion paper. Paper presented at the 30th Conference of the International Group for the Psychology of Mathematics Education, PME-30, Prague.

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