Course Description:
Participants will explore several geometry problems over the week, make conjectures based on explorations, and justify conjectures. This model of geometric reasoning will be discussed as it relates to investigations done in class, and research on student understanding.  Participants will be given opportunities to investigate student understanding of geometric reasoning by looking at student work and viewing videos from geometry classrooms.  Participants will work collaboratively to develop instructional materials for their classes related to enhancing geometric  reasoning ability.

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
Heidi Staebler, STV 334, 438-5528, hastaeb@ilstu.edu
J. Daya Dindyal STV 312D, 438-7684, jdindya@ilstu.edu

Web Site:
http://www.cas.ilstu.edu/proofproject/webpage/index/relatedworkshops/TIP2001.html

Required 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).

Dreyfus, T. & Hadas, N. (1987). Euclid may stay - and even be taught. In M.M. Lindquist & A.P. Shulte (Eds.), Learning and teaching geometry, K-12 (pp. 47-58). Reston, VA: The National Council of Teachers of Mathematics.

PIP Course Packet (distributed in class)

Course Objectives:
1.  To explore geometry problems through investigating, conjecturing, and justifying.
2.  To explore students' understanding of geometric reasoning by reading related research, examining samples of student work, and viewing videos.
3.  To investigate pedagogical methods for the teaching of reasoning and proof with the goal of identifying important components of instruction that may improve student understanding.
4.  To identify or develop instructional materials that may be used to enhance the teaching and learning of geometric reasoning.

Course Requirements and Assessment:
1.  Completion of instructional materials project. The materials must reflect class discussions and the research on students' understanding of proof. (70%)
2.  Participation in discussions and sharing of ideas. (30%)

Expectations:
Your active involvement - individually, is small groups, and with the entire class - is an important way for you to help meet the course objectives. For you to be involved, you must be present. Pleases let us know of any conflicts as soon as possible.

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:
De Villiers, M.D. (1999). Introduction to Rethinking proof (pp. 1-20). Emeryville, CA: Key Curriculum Press.

Dreyfus, T. & Hadas, N. (1987). Euclid may stay - and even be taught. In M.M. Lindquist & A.P. Shulte (Eds.), Learning and teaching geometry, K-12 (pp. 47-58). Reston, VA: The National Council of Teachers of Mathematics, Inc.

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

Driscoll, M. (1983). Research within reach: Secondary school mathematics. Washington, DC: National Institute of Education.

Holyes, C. (1997). The curricular shaping of students' approaches to proof. For the Learning of Mathematics, 17 (1), 7-16.

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

Thompson, D.R., & Senk, S.L. (1993). Assessing reasoning and proof in high school. In N.L. Webb (Ed.), Assessment in the mathematics classroom: 1993 yearbook, (pp. 167-176). Reston, VA: National Council of Teachers of Mathematics.

Further Readings:
Knuth, E.J. & Elliott, R.L. (1998). Characterizing students' understandings of mathematical proof. MathematicTeacher, 91 (8), 714-717.

Lipp, A. (2000). The angles of a star. Mathematics Teacher, 93 (6), 512-516.

Movshovitz-Hadar, N. (1988). Stimulating presentation of theorems followed by responsive proofs. For the Learning of Mathematics, 8 (2), 12-19, 30.

Senk, S.L. (1985). How well do students write geometry proofs? Mathematics Teacher, 78 (6), 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.