Mathematics and Science Teacher Education
May 16 - 20, 2009
This is the web site page is for use in workshop, in Sana'a Yemen, for the Mastery Project, Mathematics and Science Teacher Education in Yemen.
The material is taken from the EMAT 6600 Problem Solving in Mathematics course that is taught at the University of Georgia, as organized and led by Jim Wilson. Other instructors at the University of Georgia and elsewhere use some of the material in similar courses but no links to other courses is provided here. The material for the workshop draws heavily from EMAT 6600. Click here to go to the EMAT 6600 web site if that is desired.
EMAT 6600 Problem Solving in Mathematics is taught in the Department of Science and Mathematics Education. At other universities a similar course is often taught in a Department of Mathematics.
Special Web instruction: Use the browser back key to return to this workshop page. Links provided in the problem sets will return you to the EMAT 6600 page rather than the workshop page. I have placed a link on the EMAT 6600 page to return here if you inadvertantly go that route.
Last modified on April 13, 2009
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-- To explore what a course on mathematics problem solving for secondary school teachers might be.
-- To explore the objectives and assessment of a mathematics problems solving course.
-- Doing mathematics requires doing problem solving.
-- Using technology when appropriate
-- Other descriptions of Problem Solving -- inquiry, exploration, reasoning, proving
• Polya, G. (1945) How to Solve It: A New Aspect of Mathematical Method. Princeton, NJ: Princeton University Press. Second edition 1956.
• Polya, G. (1965) Mathematical Discovery, Vol I & II. New York: Wiley.
Chapters 1-4 of Volume 1 contain extensive problem sets that Polya developed for The Stanford-Sylvania Mathematics Institutes for Teachers.
• Polya, G. (1954) Mathematics and Plausible Reasoning. Vol.1 Induction and Analogy in Mathematics; Vol. II Patterns of Plausible Inference. Princeton, NJ: Princeton University Press.
•Polya, G., & Kilpatrick, J. (1974) The Stanford Mathematics Problem Book. New York: Teachers College Press.
•Brown, S. I., & Walter, M. I. (1990) The Art of Problem Posing. 2nd edition. Hillsdale, NJ: Erlbaum.
• Courant, R., & Robbins, H. (1941) What is Mathematics? An Elementary Approach to Ideas and Methods. New York: Oxford University Press. (Revised Edition prepared by Ian Stewart, 1996)
•Taylor, H. & Taylor, L. (1993) George Polya: Master of Discovery. Palo Alto, CA: Dale Seymour Publications.
•Steinhaus, H. (1950) Mathematical Snapshops. New York: Oxford University Press.
Polya, G. (1964) Let us Teach Guessing. Film/Video. Washington, DC: Mathematical Association of America
Math Forum (alias Geometry Forum). Formerly at Swarthmore. Now at Drexel University. (HIGHLY RECOMMENDED)
Mathematical Association of America
Mathematical Sciences Education Board
National Council of Teachers of Mathematics
A Visual Dictionary of Special Plane Curves
MacTutor History of Mathematics Site -- St. Andrew's University
6600 Syllabus - General
information about the objectives and operation of the course.
Synthesis of Research on Problem Solving. This paper was published as Chapter 4 in
Wilson, P. S. (Ed.) (1993). Research Ideas for the Classroom: High School Mathematics. New York: MacMillan.
The book was part of the National Council of Teacher of Mathematics Research Interpretation Project, directed by Sigrid Wagner.
The bibliographic reference for the published version is
Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem solving. In P. S. Wilson (Ed.), Research Ideas for the Classroom: High School Mathematics (pp. 57-78). New York: MacMillan.
Squares. X What is the ratio of areas of the two squares? This is a discussion of some exploration and extensions of this problem.
with Heron's Formula. X This is a paper on the development and demonstration of
Heron's formula for the area of a triangle given the lengths of its three
sides. Problems and explorations are included for using Heron's formula.
Investigation with Parametric Equations. This paper examines the movement
of triangles when one vertex is moved along the x-asis and another is moved
along the y-axis. We trace trace the movement of the third vertex.
Project InterMath has a web site with many investigations deemed appropriate for Middle School mathematics teachers. I believe secondary mathematics teachers may find some challenges here as well. Please access the site: Project INTERMATH
Bouncing Barney X *new*
Ceva's Theorem X *new*
Color a Circle
Coloring CirclesConstruct Equilateral Triangle with vertices on three given parallel lines X
Inscribed Equilateral Triangle in a Square – Construction X
Inscribed Equilateral Triangle in a Square – Problem X
Inscribed Triangle in a given triangle X
Ratio on a line segment -- Something Golden
Solve by iteration.
Solve by iteration
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