Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

Hersh, R. ( 1993). "Proving is convincing and explaining". Educational Studies in Mathematics, 24, 389-399.

Horgan, J. ( 1993, October). "The death of proof". Scientific American, 74-82.

Jackiw, N. The Geometer's Sketchpad [Computer software]. Berkeley, CA: Key Curriculum Press.

Kline, M. ( 1973). Why Johnny can't add: The failure of the new math. New York: St. Martin's.

Kline, M. ( 1982). Mathematics: The loss of certainty. Oxford: Oxford University Press.

Kline, M. ( 1984). "The meaning of mathematics". In D. M. Campbell & J. C. Higgens (Eds.), Mathematics: People, problems, results (Vol. 2, pp. 11-18). Belmont, CA: Wadsworth.

Laborde, J.-M., & Bellemain, F. ( 1994). Cabri-geometry II [Computer software]. Dallas, TX: Texas Instruments.

Lakatos, I. ( 1976). Proofs and refutations. Cambridge: Cambridge University Press.

Lakatos, I. ( 1978). Mathematics, science and epistemology. Cambridge: Cambridge University Press.

Manin, Y. I. ( 1981). "A digression on proof". Two-Year College Mathematics Journal, 12( 2), 104-107.

Pollak, H. O. ( 1984). "The effects of technology on the mathematics curriculum". In A. I. Olivier (Ed.), The Australian experience: Impressions of ICME 5. Centrahil, South Africa: Association for Mathematics Education of South Africa.

Polya, G. ( 1954). Mathematics and plausible reasoning: Induction and analogy in mathematics (Vol. 1). Princeton, NJ: Princeton University Press.

Renz, P. ( 1981). "Mathematical proof: What it is and what it ought to be". Two-Year College Mathematics Journal, 12( 2), 83-103.

Schoenfeld, A. H. ( 1986). "On having and using geometric knowledge". In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 225-264). Mahwah: NJ: Lawrence Erlbaum Associates.

Schumann, H., & de Villiers, M. D. ( 1993). "Continuous variation of geometric figures: Interactive theorem finding and problems in proving". Pythagoras, 31, 9-20.

van A. G. Asch ( 1993). "To prove, why and how?" International Journal of Mathematical Education in Science and Technology, 24( 2), 301-313.

Volmink, J. D. ( 1990). "The nature and role of proof in mathematics education". Pythagoras, 23, 7-10.


APPENDIX

Worksheet 1
a. Construct a dynamic kite using the properties of kites explored and discussed in our previous lessons.
b. Check to ensure that you have a dynamic kite, i.e., does it always remain a kite no matter how you transform the figure? Compare your construction(s) with those of your neighbors--is it the same or different?
c. Next construct the midpoints of the sides and connect the midpoints of adjacent sides to form an inscribed quadrilateral.
d. What do you notice about the inscribed quadrilateral formed in this way?
e. State your conjecture.

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