Research implications for teaching and learning strategies in undergraduate mathematics

Medhat Hishmat Rahim 1 *
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1 Lakehead University, Thunder Bay, Ontario, Canada
* Corresponding Author
EUROPEAN J SCI MATH ED, Volume 2, Issue 2A, pp. 122-130. https://doi.org/10.30935/scimath/9634
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ABSTRACT

In preparing an address that fits well within the themes of the Frontiers in Mathematics and Science Education Research Conference 2014, I have chosen geometry. Evidently, geometric applications in Calculus, Algebra and other fields are essential for these disciplines’ development. In addition, the widespread use of geometry by pre-service and in-service teachers in elementary, middle, and secondary schools and universities makes it an indispensable discipline for a large population in education. In what follows I will try to highlight and present the main trends in recent research activities in teaching and learning undergraduate geometry that were carried out throughout the second half of the twentieth century up to the present. In particular, research on studying children and young adults’ processes of how they construct geometric and spatial ideas of objects will be discussed. Additionally, research in mathematics on proofs and proving with selected examples of proving the Pythagorean Theorem visually and through geometric construction including my own proof will be introduced.

CITATION

Rahim, M. H. (2014). Research implications for teaching and learning strategies in undergraduate mathematics. European Journal of Science and Mathematics Education, 2(2A), 122-130. https://doi.org/10.30935/scimath/9634

REFERENCES

  • Bogomolny, A. (2012). A collection of 101 proofs for the Pythagorean Theorem compiled in the Internet Link: http://www.cut-the-knot.com/pythagoras/
  • Commission on Standards for school Mathematics (1989). Curriculum and Evaluation Standards Report. The internet link: http://www.mathcurriculumcenter.org/PDFS/CCM/summaries/standards_summary.pdf
  • Crawley, Mary L. (1987). The van Hiele Model of the Development of Geometric Thought. In Learning and Teaching Geometry, K-12, 1987 Yearbook of the National Council of Teachers of Mathematics, edited by Mary M. Lindquist, pp. 1-16. Reston, Va.: NCTM.
  • Eves, H. (1972). A Survey of Geometry. Boston: Allen & Bacon.
  • Freudenthal, Hans. (1973). Mathematics as an Educational Task. Dordrecht, Netherland: D. Reidel.
  • Loomis, E. S. (1968). The Pythagorean Proposition. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Rosten, VA.: NCTM.
  • O’Daffer, P., & Clemens, S. (1992). Geometry: An Investigative Approach. Addison-Wesley Publishing Co.
  • Piaget, J. (1962). Comments on Vygotsky’s critical remarks concerning The Language and Thought of the Child, and Judgment and Reasoning in the Child. The MIT Press, Massachusetts Institute of Technology (MIT).
  • Piaget, J., Bärbel Inhelder, and Alina Szeminska (1960). The Child's Conception of Geometry. New York: Basic Books, Inc., 1960.
  • Rahim, M. (2003). A new proof of the Pythgorean using a compass and unmarked straight edge. International Journal of Mathematical Education in Science and Technology, Vol. (34), No. 1, January-February, 144-150.
  • Rahim, M, Sawada, D., & Strasser, J. (1996). The Boy with the ruler. The Mathematics Teaching (MT),Vol. 154, March 1996, pp. 23-29.
  • Rahim, M., & Sawada, D. (1990). The Duality of qualitative and quantitative knowing in school geometry. International Journal of Mathematical Education in Science and Technology, Vol. (21), No. 2, 303-308.
  • Shaughnessy, J.M., & Burger, W.F. (1985). Spadework prior to deduction in geometry. Mathematics Teacher, 78, 419-428.
  • van Hiele, Pierre M. "A Child's Thought and Geometry.” In English Translation of Selected Writings of Dina van Hiele-Gildof and Pierre M. van Hiele, edited by Dorothy Geddes, David Fuys, and Rosamond Tischler as part of the research project "An Investigation of the van Hiele Model of Thinking in Geometry among Adolescents," Research in Science Education (RISE) Program of the National Science Foundation, Grant No. SED 7920640. Washington, D.C.: NSF, 1984a. (Original work published in 1959.)
  • van Hiele, Pierre M. "English Summary by Pierre Marie van Hicle of the Problem of Insight in Connection with School Children's Insight into the Subject Matter of Geometry." In English Translation of Selected Writings of Dina van Hide-Geldof and Pierre M. van Hiele, edited by Dorothy Geddes, David Fuys, and Rosamond Tischler as part of the research project "An Investigation of the van Hicle Model of Thinking in Geometry among Adolescents," Research in Science Education (RISE) Program of the National Science Foundation, Grant No. SED 7920640. Washington, D.C.: NSF, 1984b. (Original work published in 1957.)
  • van Hiele-Geldof, Dina. "Dissertation of Dina van Hiele-Gcldof Entitled: The Didactic of Geometry in the Lowest Class of Secondary School." In English Translation of Selected Writings of Dina van Hiele-Geldof and Pierre M. van Hiele, edited by Dorothy Geddes, David Fuys, and Rosamond Tischler as part of the research project “An Investigation of the van Hiele Model of Thinking in Geometry among Adolescents," Research in Science Education (RISE) Program of the National Science Foundation, Grant No. SED 7920640. Washington, D.C.: NSF, 1984a. (Original work published in 1957.)
  • van Hiele-Geldof, Dina. "Last Article Written by Dina van Hiele-Geldof entitled: Didactics of Geometry as Learning Process for Adults." In English Translation of Selected Writings of Dina van Hiele-Geldof and Pierre M. van Hiele, edited by Dorothy Geddes, David Fuys, and Rosamond Tischler as part of the research project "An Investigation of the van Hiele Model of Thinking in Geometry among Adolescents," Research in Science Education (RISE) Program of the National Science Foundation, Grant No. SED 7920640. Washington, D.C.: NSF, 1984b. (Original work published in 1958.)
  • Wirszup, Izaak. (1976). Breakthroughs in the Psychology of Learning and Teaching Geometry. In Space and Geometry: Papers from a Research Workshop, edited by J. Martin. Columbus, Ohio: ERIC/SMEAC.
  • Zimba, J. (2009). On the Possibility of Trigonometric Proofs of the Pythagorean Theorem Forum Geometricorum, Volume 9, 275-278