Mathematics Education
EMAT 8990 Research Seminar
Instruction J. Wilson
Purpose:
This is a seminar. The topic is the research on the teaching and learning of geometry ideas. As an EMAT 8990 seminar the specific investigations, discussions, and topics for the seminar will be determined by the group.
For a start we have specified the following potential concerns/topics/preferences:
-- Secondary level or middle school level
-- How does emphasis on measuring inhibit reasoning and proof?
-- Particular issues of learning indirect proof.
-- Role of axiomatics; rigor vs rigor mortis
-- Geometry in a GPS curriculum . . .
-- Role of technology
--Impact of technology on learning
-- geometric concepts
-- proof-- Problem solving in geometry
-- How to teach geometry in a GPS (Georgia Performance Standards) environment.
-- Teaching solid (i.e. 3-D) geometry
-- Comparison of Geometry learning in different countries
| Participants, Spring 2009 |
|---|
Philip Bergonio <phildm@uga.edu>
Tonya Brooks <tiaga1998@gmail.com>
Richard Francisco <rtfran@uga.edu>
Brian Gleason <gleason@uga.edu>
Eric Gold <egold@uga.edu>
Doug Griffin <doug1115@uga.edu>
Allyson Hallman <ahallman@uga.edu>
Hulya Kilic <hkilic@uga.edu>
Ana Kuzle <ana.kuzle@gmail.com>
Margaret Morgan <mlmorgan@uga.edu>
Jackie Ruff <jhruff@uga.edu>
Susan Sexton <susans99@gmail.com>
Kyle Schultz <kschultz@UGA.EDU>
Ken Montgomery <kenm@sports.uga.edu
Schedule: We will meet on Wednesday, 2:30 to 4:30, Room 112 Aderhold, beginning January 14.
References:
Harel, G., & Sowder, L. (2007) Toward Comprehensive Perspectives on the Learning and Teaching of Proof. In F. K. Lester, Jr., (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Publishing.
Battista, M. T. (2007) The development of Geometric and Spatial Thinking. In F. K. Lester, Jr., (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Publishing.
Clelments, D. H., & Battista, M. T. (1992) Geometry and Spatial Reasoning. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning. New York: MacMillan.
Silver, E. A., & Herbst, P. G. (2007) Theory in Mathematics Education Scholarship. In F. K. Lester, Jr., (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Publishing.
Fawcett, H.F. (1938) The Nature of Proof. NCTM, 13th Yearbook, (Reprint 1995).
Schoenfeld, A. H. (1992) Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. In D. A. Grouws, (Ed.), Handbook of Research on Mathematics Teaching and Learning. New York: MacMillan.
Burger, W. F., & Culpepper, B. (1993) Restructuring Geometry. Chapter 8 in P. S. Wilson (Ed.), Research Ideas for the Classroom: High School Mathematics. New York: MacMillan.
Fuys, D. J., & Liebov, A. K. (1993) Geometry and Spatial Sense. Chapter 9 in R. J. Jensen (Ed.), Research Ideas in the Classroom: Early Childhood Mathematics. New York: MacMillan.
Geddes, D., & Fortunato, I. (1993) Geometry: Research and Classroom Activities. Chapter 11 in D. T. Owens (Ed.), Research Ideas for the Classroom: Middle Grades Mathematics. New York: MacMillan.
Lakatos, I. (1976) Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge: Cambridge University Press.
Gerdes, P. (1999) Geometry from Africa: Mathematical and Educational Explorations. Washington, DC: MAA.
Van Hiele Theory of Geometry Learning
Mason, M. ( ) The Van Hiele Levels of Geometric Understanding. (PDF)
Usiskin, Z., (1982) Van Hiele Levels and Achievement in Secondary School Geometry. http://ucsmp.uchicago.edu/van_Hiele.html (PDF)
Senk, S. L. (1983) Proof-Writing Achievement and van Hiele Levels Among Secondary School Geometry Students. Ph.D. dissertation, The University of Chicago, 1983.
Senk, S. L. (1985) How Well Do Students Write Geometry Proofs? Mathematics Teacher, 78 (6): 448-456 (September 1985).
Senk, S. L. (1989) Van Hiele Levels and Achievement in Writing Geometry Proofs. Journal for Research in Mathematics Education, Vol. 20 (3): 309-321.
Senk, S. L., & Usiskin, Z. (1983) Geometry Proof-Writing: A New View of Differences in Mathematical Ability. American Journal of Education, 91 (2): 187-201.
Piaget, J., & Inhelder, B. (1967). The Child's Conception of Space. New York: W.W. Norton.
Piaget, J., Inhelder, B, & Szeminska, A. (1960) The Child's Conception of Geometry. London: Routledge.
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