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Graph Theory: A Topic for Helping Secondary Teachers
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prominent in the secondary curriculum, but teachers’ understandings of how to teach graph theory seem more open to innovative ideas. Perhaps this is because they did not learn the concepts in traditional ways. As the quote above suggests, many have not learned about graph theory at all and perceive that they do not understand it very well themselves. Perhaps their understandings of graph theory concepts are not as formal and traditional as their views about functions. It might also be the case that teachers are more willing to “experiment” with content they perceive to be not a major part of the curriculum, but regardless of why they seem to be more open to innovative teaching ideas in the context of this topic, they seem to be. The statement above (and others like it) leads us to wonder about graph theory being a good context for helping teachers to develop orientations that support innovative teaching.
References
Coxford, A.F, Fey, J.T., Hirsch, C.R., Schoen, H.L, Burril, G., (2003) Contemporary
Mathematics in Context: Course 2 Part B (Teacher’s Edition). Columbus, Ohio:McGraw-Hill.
Demana, F, Schoen, H. L., & Waits, B. L. (1993). Graphing in the K-12 curriculum: The impact
of the graphing calculator. In T. A. Romberg, E. Fennema, & T. P. Carpenter (eds.), Integrating research on the graphical representation of function (pp. 11-40). Hillsdale, NJ: Lawrence Earlbaum Associates.
Graubart, C.B., (1997) Mathematical Modeling: Using Graphs and Matrices.(Win
version)[Software & Teacher’s Manual]. EE.UU: Learning in Motion, Inc.
Jackiw, Nicholas, (1997) The Geometer’s Sketchpad. (Win version 3.08N): Key Curriculum
Press
Kenney, Margaret J. (1991) Discrete Mathematics across the curriculum K-12. Yearbook of the
National Council of Teachers of Mathematics.Reston, VA: NCTM. Kenney, M.J. & Bezuzka, S. (1993) Implementing the Discrete Mathematics Standards: Focusing on Recursion. Mathematics Teacher, 86, 676-680
King, P. M., & Kitchener, K. S. (1994). Developing reflective judgment. San Francisco, CA:
Jossey-Bass.
National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for
School Mathematics. Reston, VA: NCTM
National Council of Teachers of Mathematics (2000). Principles and Standards for School
Mathematics. Reston, VA: NCTM.
Rosenstein, J.G, Franzblau, D. R Roberts, F.S.,(1997) Discrete Mathematics in Schools.
American Mathematical Society: NCTM
Wilson, M. R., & Lloyd, G. M. (2000). The challenge to share mathematical authority with
students: High school teachers’ experiences reforming classroom roles and activities through curriculum implementation. Journal of Curriculum and Supervision, 15, 146-169.
Wilson, M. R.
& Krapfl, K. M. (1994). The impact of graphic calculators on students’
understanding of function. Journal of Computers in Mathematics and Science Teaching
13,
252-264.
Wilson, M., Spielman, L. (2003). Teachers' conceptions of graph theory and functions:
Implications for teaching. In
N. Pateman, Dougherty, B., & Zilliox, J. (Eds.),
Proceedings of the 2003 Joint Meeting of PME and PMENA (vol. 1, p. 335). Honolulu, Hawaii: CRDG, College of Education, University of Hawaii
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| | Authors: Wilson, Skip. and Rivera-Marrero, Olgamary. |
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prominent in the secondary curriculum, but teachers’ understandings of how to teach graph
theory seem more open to innovative ideas. Perhaps this is because they did not learn the
concepts in traditional ways. As the quote above suggests, many have not learned about graph
theory at all and perceive that they do not understand it very well themselves. Perhaps their
understandings of graph theory concepts are not as formal and traditional as their views about
functions. It might also be the case that teachers are more willing to “experiment” with content
they perceive to be not a major part of the curriculum, but regardless of why they seem to be
more open to innovative teaching ideas in the context of this topic, they seem to be. The
statement above (and others like it) leads us to wonder about graph theory being a good context
for helping teachers to develop orientations that support innovative teaching.
References
Coxford, A.F, Fey, J.T., Hirsch, C.R., Schoen, H.L, Burril, G., (2003) Contemporary
Mathematics in Context: Course 2 Part B (Teacher’s Edition). Columbus, Ohio:McGraw-
Hill.
Demana, F, Schoen, H. L., & Waits, B. L. (1993). Graphing in the K-12 curriculum: The impact
of the graphing calculator. In T. A. Romberg, E. Fennema, & T. P. Carpenter (eds.),
Integrating research on the graphical representation of function (pp. 11-40). Hillsdale, NJ:
Lawrence Earlbaum Associates.
Graubart, C.B., (1997) Mathematical Modeling: Using Graphs and Matrices.(Win
version)[Software & Teacher’s Manual]. EE.UU: Learning in Motion, Inc.
Jackiw, Nicholas, (1997) The Geometer’s Sketchpad. (Win version 3.08N): Key Curriculum
Press
Kenney, Margaret J. (1991) Discrete Mathematics across the curriculum K-12. Yearbook of the
National Council of Teachers of Mathematics.Reston, VA: NCTM. Kenney, M.J. &
Bezuzka, S. (1993) Implementing the Discrete Mathematics Standards: Focusing on
Recursion. Mathematics Teacher, 86, 676-680
King, P. M., & Kitchener, K. S. (1994). Developing reflective judgment. San Francisco, CA:
Jossey-Bass.
National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for
School Mathematics. Reston, VA: NCTM
National Council of Teachers of Mathematics (2000). Principles and Standards for School
Mathematics. Reston, VA: NCTM.
Rosenstein, J.G, Franzblau, D. R Roberts, F.S.,(1997) Discrete Mathematics in Schools.
American Mathematical Society: NCTM
Wilson, M. R., & Lloyd, G. M. (2000). The challenge to share mathematical authority with
students: High school teachers’ experiences reforming classroom roles and activities through
curriculum implementation. Journal of Curriculum and Supervision, 15, 146-169.
Wilson, M. R.
& Krapfl, K. M. (1994). The impact of graphic calculators on students’
understanding of function. Journal of Computers in Mathematics and Science Teaching
13,
252-264.
Wilson, M., Spielman, L. (2003). Teachers' conceptions of graph theory and functions:
Implications for teaching. In
N. Pateman, Dougherty, B., & Zilliox, J. (Eds.),
Proceedings of the 2003 Joint Meeting of PME and PMENA (vol. 1, p. 335).
Honolulu, Hawaii: CRDG, College of Education, University of Hawaii
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