Mathematics 429.31
Improving Student Understanding of Geometry Proofs
July 17-21, 2000

M, T, W, Th, F
Stevenson Hall 332, 8:30am - 12:00pm

 

Course Description:
Participants will read and view materials related to proof instruction. They will be given opportunities to investigate student understanding of geometry proofs by reading research in this area as well as by analyzing actual data from local high school classrooms (data may include questionnaires about proofs, proof-related quizzes, and videos of geometry classrooms). Participants will work collaboratively to develop proof-related instructional materials for their classes.

Instructors:
Dr. Tami Martin, STV 326D, 438-7864, tsmartin@math.ilstu.edu
Dr. Sharon Soucy McCrone, STV 328, 438-7089, smccrone@math.ilstu.edu

Graduate Assistants:
Cindy Pulley, STV 334, 438-5528, capope@ilstu.edu
Arsalan Wares, STV 312E, 438-7288, Awares@aol.com

Web Site:
http://www.math.ilstu.edu/~smccrone/TIP_2000/TIP2000.html

Required Textbooks and Materials:

National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM (available on-line at: http://standards.nctm.org).

PIP Course Packet #25 (pick up at PIP office in the Bone Student Center)

Course Objectives:

  • To explore students' understanding of geometry proofs by reading related research and examining samples of student work.
  • To investigate pedagogical methods for the teaching of proof with the goal of identifying important components of instruction that may improve student understanding.
  • To develop instructional materials that can be used to enhance the teaching and learning of geometry proof.

Course Requirements and Assessments:

  • Two written analyses of readings. (30%)
  • Completion of instructional materials project. The materials must reflect class discussions and the research on students' understanding of proof. (60%)
  • Class participation (10%)

Expectations:
Your active involvement -- individually, in small groups, and with the entire class -- will help you to meet the course objectives. For you to be involved, you must be present. Please let us kno of any conflicts as soon as possible. The due dates described in written requirements and stated in class are just that. Plan ahead to complete required tasks on time.

We invite and appreciate your comments and suggestions for the course. Please share with us in person or in writing your reactions and perceptions. We are eager to enhance the course for participants now and in the future.

Required Readings:
Dreyfus, T., & Hadas, N. (1987). Euclid may stay -- and even be taught. In M. M. Lindquist (Ed.) Learning and teaching geometry, K-12: 1987 Yearbook (pp. 47-58). Reston, VA: NCTM.

Dreyfus, T., & Hadas, N. (1996). Proof as answer to the question why. International Reviews on Mathematical Education, 28(1), 1-5.

Driscoll, M. (1982). Research within reach: Secondary school mathematics. Washington, DC: US Department of Education.

Hoyles, C. (1997). The curricular shaping of students' approaches to proof. For the Learning of Mathematics, 17, 7-16.

Knuth, E. J., & Elliott, R. L. (1998). Characterizing students' understanding of mathematical proof. Mathematics Teacher, 91 (8), 714-717.

NCTM (2000). Standard 7: Reasoning and proof. In Principles and standards for school mathematics (pp. 56-59, 122-127, 188-193, 262-267, 342-347). Reston, VA: Author.

Senk, S. L. (1985). How well do students write geometry proofs? Mathematics Teacher, Sept. 1985, 448-456.

Simon, M. A., & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior, 15 , 3-31.

Sowder, L. & Harel, G. (1998). Types of students' justifications. Mathematics Teacher, 91 (8), 670-675.

Further Readings:
Alibert, D, & Thomas, M. (1991). Research on mathematical proof. In D. Tall, Advanced mathematical thinking, (pp. 215-230). Dordrecht, Netherlands: Kluwer.

Battista, M. T., & Clements, D. H. (1995). Geometry and proof. Mathematics Teacher, 88(1), 48-54.

Chazan, D. (1993). High school geometry students' justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24(4), 359-387.

Hanna, G. (1995). Challenges to the importance of proof. For the Learning of Mathematics, 15(3), 42-49.

Hanna, G., & Jahnke, H. N. (1996). Proof and proving. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.) International handbook of mathematics education (pp. 877-908). Dordrecht, Netherlands: Kluwer.

Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24 (4), 389-399.

Leron, U. (1983). Structuring mathematical proofs. The American Mathematical Monthly, 90 (3), 174-185.

Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Eduction, 20, 41-51.

Mathematics Teacher:Proof focus issue, (91) 8, November 1998.

Movshovitz-Hadar, N. (1988). Stimulating presentation of theorems followed by responsive proofs. For the Learning of Mathematics, 8 (2), 12-19.

Senk, S. L. (1989). van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309-321.

Stiff, L. V., & Curcio, F. R. (1999). Developing mathematical reasoning in grades K-12: 1999 Yearbook. Reston, VA: National Council of Teachers of Mathematics.

Thompson, D. R. (1996). Learning and teaching indirect proof. Mathematics Teacher, 89 (6), 474-482.

Last updated July 7, 2000

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