I. Number and Title of Course:

MED 683

Problem Solving and Problem Posing
 
 

II. Reasons for Addition to the Present Curriculum

The focus in teaching mathematics in a present day society is problem solving and problem posing. This course will provide teachers with the necessary background to teach with problem solving as the focus of learning mathematics. This is the first standard of the Standards for Curriculum and Evaluation of School Mathematics of the National Council of Teachers of Mathematics.
 
 

III. Major Objectives of the Course

Students will examine the techniques of problem solving and problem posing in mathematics. The course will initially encourage participants to reflect upon themselves as problem solvers and then use this experience to examine the role of teaching problem solving in the high school setting.
 
 

IV. Topical Outline:

A. What is problem solving?
 
 

B. Techniques of Problem Solving

1) Problem Solving Heuristics of George Polya

2) Rubic Model of John Mason, Leone Burton and Kaye Stacey.

3) What-if-not theory of Stephen Brown and Marion Walter
 
 
 
 

C. Research on learning and teaching problem solving

1) Psychological theory on Problem-Solving (i.e.. Werthemier, DeBono, Schoenfeld)

2) Can problem-solving be taught? What does the research say?
 
 

D. Problem Solving and Problem Posing in the curriculum

1) Algebra

2) Geometry

3) Trigonometry

4) Calculus

5) General Mathematics

6) With Technology

E. Organizing instruction to have Problem Solving be the focus of teaching mathematics

F. Techniques for evaluating Problem Solving.

1) Authentic Assessment Techniques

2) Special projects

V. Bibliography

A. Books and Articles

Alibert, D. "Towards new customs for the classroom." For the Learning of Mathematics. v8 n2 p31-35. June 1988

Brown, Stephen I. and Walter, Marion I. The Art of Problem Solving. Philadelphia, Pennsylvania: The Franklin Institute Press, 1983.

Brown, Stephen and Walter Marion Problem Posing - Reflections and Applications Lawrence Erlbaum Associates, Hillsdale, NJ 1993.

Crosswhite, F. Joe, ed. Organizing for Mathematics Instruction. Reston, Virginia: The National Council of Teachers of Mathematics, Inc., 1977.

Fortunato, Irene; And Others. "Metacognition and Problem Solving." Arithmetic Teacher v39. p38-40. December 1991.

Grouws, Douglas and Cooney, Thomas. Effective Mathematics Teaching. Lawence Erlbaum, Hillsdale, NJ 1988.

Hillman, A. P. and Alexanderson, G. L. Algebra Through Problem Solving. Boston, Massachusetts: Allyn and Bacon, Inc.,1966.

Kalomitsines, Spyros. "Some New Ways of Proceeding in Problem Solving". Pittsburgh University, Pa. Learning Research and Development Center. 1985.

Krulik, Stephen. Problem Solving in Mathematics. Reston, Virginia: The National Council of Teachers of Mathematics, Inc., 1980.

Krulik, Stephen and Rudnick, Jesse A. A Sourcebook for Teaching Problem Solving. Newton, Massachusetts: Allyn and Bacon, Inc., 1984.

Krulik, Stephen and Rudnick, Jesse A. Problem Solving: A Handbook for Teachers. Boston, Massachusetts: Allyn and Bacon, Inc., 1980.

Lakatos, Imre. Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge: Cambridge University Press, 1976.

Lampert, M. "When the problem is not a question and the solution not an answer: Mathematical knowing and teaching". American Educational Research Journal v27, p29-63. 1990.

Lester Jr., Frank K. and Garofalo, Joe, eds. Mathematical Problem Solving: Issues in Research. Philadelphia, Pennsylvania: The Franklin Institute Press, 1982.

Mason, John. et al Thinking Mathematically. London: Addison-Wesley Publishers Limited, 1991.

O’Daffer P. Problem Solving - Tips for Teachers NCTM Reston, VA 1988.

Pestel, Beverly C. "Teaching Problem Solving without Modeling through 'Thinking Aloud Pair Problem Solving'." Science-Education.v77. p83-94. January 1993.

Polya, George. How To Solve It. Garden City, New York: Doubleday Anchor Books, Doubleday & Company, Inc., 1957.

Polya, G. Introduction and Analogy in Mathematics. Princeton, New Jersey: Princeton University Press, 1954.

Polya, G. Mathematical Discovery: On understanding, learning, and teaching problem solving. Canada: John Wiley & Sons, Inc., 1981.

Polya, G. Patterns of Plausible Inference. London: Geoffrey Cumberlege, Oxford University Press, 1954.
 
 

Schoaff, Eileen Klimick. "A Study of a Use of Computers for a Problem Solving Approach to Learning School Mathematics." Ph.D. dissertation, SUNY-Buffalo 1988

Schoenfeld, Alan H. Problem Solving in the Mathematics Curriculum: A Report, Recommendations, and an Annotated Bibliography. The Mathematical Association of America Committee on the Teaching of Undergraduate Mathematics, 1983.

________________ Mathematical Problem Solving Academic Press London. 1985.

________________ "Teaching mathematical thinking and problem solving." in Towards the thinking curriculum : Current cognitive research. American Society for Curriculum Developers, Washington, DC p83-103. 1989.

_________________"Learning to Think Mathematically: Problem Solving, Metacognition and Sense Making in Mathematics" Handbook of Research on Mathematics Teaching and Learning. Grouws, D. ed. NCTM. Reston, VA 1992.

Sharron, Sidney, ed. Applications in School Mathematics. Reston, Virginia: The National Council of Teachers of Mathematics, Inc., 1977.

Silver, Edward A., ed. Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives. Hillsdale, New Jersey: Lawrence Erlbaum Associates Publishers, 1985.

Tuma, D. T. and Reif, F., eds. Problem Solving and Education: Issues in Teaching and Research. Hillsdale, New Jersey: The Halted Press Division of John Wiley & Sons, 1980.

Whimbey, Arthur and Lochhead, Jack. Problem Solving and Comprehension. Philadelphia, Pennsylvania: The Franklin Institute Press, 1982.

Wickelgren, Wayne A. How to Solve Problems. San Francisco: W. H. Freeman and Company, 1974.
 
 

B. Periodicals

Arithmetic Teacher

Computers in the Teaching of Mathematics and Science

For the Learning of Mathematics

Journal of Research in Mathematics Education

Mathematics Teaching

Mathematics Teacher
 
 

VI. Presentation and Evaluation

This class will be presented in a class discussion format. Student will present projects, write reaction papers to synthesize the readings and develop exemplary curriculum materials. The evaluation will be based upon the quality of this work.

VII. Prerequisites.

Admission into the Masters program.

VIII. Credits

3:0 semester hours

IX. Departmental approval.
 
 

X. Catalog Description

MED 683 Problem Solving and Problem Posing

This course will examine the techniques of problem solving and problem posing in mathematics. The course will initially encourage participants to reflect upon themselves as problem solvers and then use this experience to examine the role of teaching problem solving in the high school setting.

XI. Statement of Qualifications

A doctorate degree in mathematics education is the minimum formal education required.

Several members of the department who could teach this course are: Tom Giambrone (Ed. D, SUNY Buffalo 1983), Eileen Schoaff ( Ph.D. SUNY Buffalo 1988) Luella Johnson ( Ph.D SUNY Buffalo 1990), and Betty Krist (Ed. D SUNY Buffalo 1980).

XII. Support Services Required.

none.