STATE UNIVERSITY COLLEGE AT BUFFALO
Department of Mathematics
Request for Course
I. Number and Title of Course:
MED 605 Teaching of Algebraic Concepts.II. Reasons for Addition to the Present CurriculumFundamental to the high school curriculum are the concepts of Algebra This course was developed to give our graduate students the background of learning theory, pedagogy, mathematical models and new developments specific to the teaching of algebraic concepts in the high school curriculum. No such course exists at present.III. Major Objectives of the CourseA. To familiarize students with the curriculum materials available for teaching algebraic concepts.IV. Topical Outline:B. To have students learn how to organize algebraic presentations using the unifying themes of: history, structure, intuition, function, and applied mathematics.
C. To have students understand the main problems that confront children in the learning of algebraic concepts.
D. To have students teach algebra in a problem-solving mode.
E. To have students develop a variety of techniques to teach a given concept.
F. To have students understand the role of algebra in a technological age.
A. What to teach in an algebra course?V. Bibliography1) Graphing and the role of the computer.
2) The concept of variable - its role and development.
3) Factoring, rational expressions, and the search for roots.
4) Theory of equations.
5) The real plane.
6) Trigonometry - two looks
7) Sequences and series.
8) Precision versus rigor.
B. Organizing an algebra course.
1) Teaching algebra using history as a unifying theme.
2) Teaching algebra from an applied approach.
3) Teaching algebra from a structural point of view.
4) Teaching algebra from an intuitionist approach.
C. Problem - solving in algebra.
1) Standard book problems - Do they teach problem solving?
2) Problem solving heuristics.
3) Using the computer to create problem solving situations.
4) Modeling in algebra.
5) Creating problems in an algebra curriculum.
D. Psychological issues in the teaching of algebra.
1) The role of understanding in the learning of algebra.
2) The concepts of structure, readiness, and rigor ( Jerome Bruner ).
3) The concept of variable ( Piaget, Hercovits, Kilpatrick, )
4) Current research in the teaching and learning of algebra.
E. Concept that students find difficult and overcoming the difficulty.
1) Diagnosing errors.
2) Common mistakes and the reasons behind them.
3) Word problems.
4) Gender differences
5) Overcoming math anxiety.
A. Books and ArticlesVI. Presentation and EvaluationBeberman, Max. An Emerging Program of Secondary School Mathematics. Cambridge, Mass.: Harvard University Press, 1958.
Beberman, Max. "The Old Mathematics in the New Curriculum." Educational Leadership v19 p373-375. March 1962.
Begle, E. G. "The Reform of Mathematics Education in the United States of America." In Mathematical Education of the Americas, edited by Howard Fehr. New York: Bureau of Publications, Teachers College, Columbia University, 1963.
Begle, E. G. "SMSG: The First Decade." Mathematics Teacher v61 p239-245. December 1968.
Begle, E. G. "Curriculum Research in Mathematics." In Research and Development Toward the Improvement of Education. Madison, Wisconsin: Dembar Educational Research Services, 1969.
College Entrance Examination Board. "Report of the Commission on Examinations in Mathematics." Mathematics Teacher v28 p154-166 March 1935.
Commission on Post-War Plans of the NCTM. "First Report of the Commission on Post-War Plans." Mathematics Teacher v37 p225-232 May 1944
Committee on the Foundation of Mathematics in General Education of the Commission on the Secondary School Curriculum of the Progressive Education Association. Mathematics in General Education. New York: D. Appleton-Century Co., 1940.
Cooney, Thomas; Davis, Edward J.; and Henderson, K. B. Dynamics of Teaching Secondary School Mathematics. Boston: Houghton Mifflin Co., 1975.
Davis, Robert B. "The 'Madison Project' of Syracuse University." Mathematics Teacher v53 p571-575. December 1960.
Davis, Robert B. Discovery in Mathematics: A Text for Teachers. Reading, Massachusetts: Addison-Wesley Publishing Co., 1964.
Dick , Thomas P. "Symbolic Graphical Calculators : Teaching Tools for Mathematics." School Science and Mathematics v92 p1-5 January 1992
Dugdale, Sharon et. el "Visualizing Polynomial Functions: New insights from an Old Method in a New Medium." Journal of Computers in Mathematics and Science teaching. v11 p123-41 1992.
Erickson, Dianne K. "Dancing Functions from a Graphing Calculator" Computing Teacher. v19 p24-26. May 1992
Giambrone, Tom M. " I have.. Who has..."." Mathematics Teacher v73: p504:506 October 1980.
_________________ "Challenges for the Gifted: Algebra" Mathematics Teacher April 1983
Hale, William T., in cooperation with Miss Eleanor McCoy. "UICSM's Decade of Experimentation." Mathematics Teacher v54 p613-619 December 1961
Harkin, Joseph B. and Rising, Gerald R. "Some Psychological and Pedagogical Aspects of Mathematical Symbolism." Educational Studies in Mathematics 5 255-260 1974
Hendrix, Gertrude. "Prerequisite to Meaning." Paper read at the Meeting of the National Council of Teachers of Mathematics, St. Louis, MO. 3 July 1950.
Hillel, Joel et. el. "Basic Functions Through the lens of Computer Algebra Systems" Journal of Mathematical Behavior v11, p119-58 June 1992
Kysh, Judith "Implementing the Curriculum and Evaluation Standards: First Year Algebra" Mathematics Teacher v 84 p715-22 December 1991
Mercer, Joseph " What is left to Teach If Students Can Use Calculators?" Mathematics Teacher 85 :415-417 September 1992
Meyerson, Lawrence Nils and McGinty, Robert Leroy. "Learning Without Understanding." Mathematics Teaching no. 84 p48-49 September 1978.
Moise, Edwin E. "The SMSG Geometry Program." Mathematics Teacher 73 p437-444. October 1980:
National Council of Teachers of Mathematics. The Revolution in School Mathematics. A Report of regional orientation conferences in mathematics. Washington, D. C.: NCTM, 1961.
Parish, Charles, " Inequalities, Absolute Value, and Logical Connectives" Mathematics Teacher v85 p756-57 December 1992.
1988 NCTM Yearbook: Teaching of Algebra. Reston, VA: 1988.
Sandefur, James T. "Drugs and Pollution in the Algebra Class " Mathematics Teacher v85 p135-45 February 1992
Sutherland, Rosamund "Some Unanswered Research Questions on the Teaching and Learning of Algebra." For the Learning of Mathematics v11 p40 46 November 1991.
The School Mathematics Project. New York: Cambridge University Press, 1970.
School Mathematics Study Group. Mathematics for High School: First Course in Algebra, Pts. 1 & 2. New Haven: Yale University Press, 1961.
University of Illinois Committee on School Mathematics. High School Mathematics: Unit I The Arithmetic of Real Numbers. Rev. ed., edited by Herbert E. Vaughan and directed by Max Beberman. Urbana: University of Illinois Press, 1960.
Usiskin, Zalman, director. Algebra Through Applications with Probability and Statistics, Part I & II. The National Council of Teachers of Mathematics: Reston, Virginia, 1979.
_______________ University of Chicago School Mathematics Project. Addison Wesley. Chicago, 1990.
Van Engen, Henry. "The Formation of Concepts." In The Learning of Mathematics: Its Theory and Practice, twenty-first Yearbook. Washington, D. C.: National Council of Teachers of Mathematics, p.69-98. 1953.
Waits, Bert ; Demana, Franklin "A Case against Computer Symbolic Manipulation in School Mathematics Today." Mathematics Teacher V85 p. 180-83 March 1992
Walter, Marion and Brown, Stephen I. "Musing Ingredients in Teacher Training: One Remedy." Mathematical Education p399-404 April 1971 :.
Walter, Marion and Brown, Stephen I. "Problem Posing Solving: An Illustration of Their Interdependence." Mathematics Teacher 70 p4-13 January 1977.
Wheeler, David. "Mathematization as a Pedagogical Tool." Department of Mathematics, Concordia University, Montreal, Canada.1976
Wheeler, David. "Teaching for Discovery." Department of Mathematics, Concordia University, Montreal, Canada1976.
Wheeler, David. "Humanizing Mathematical Education." Mathematics Teaching no. 71 June 1975.
Wheeler, David. "After the New Mathematics." Mathematics Teaching no. 75 June 1979
B. Periodicals.
Arithmetic Teacher
For The Learning of Mathematics
Mathematics Teacher
Mathematics Teaching
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 and traditional tests.VII. Prerequisites.Admission into the Masters program.VIII. Credits3: 0 semester hoursIX. Departmental approval.This course was examined with the recommended procedures and was approved by the graduate faculty of the Mathematics Department on May 13, 1993.X. Catalog Description_________________________ Department Chair
MED 605 Teaching of Algebraic ConceptsXI. Statement of QualificationsThis course will examine the structuralist, intuitive, historical and applied approaches to the teaching the concepts of algebra. This course will provide a background of: learning theory, pedagogy, mathematical models and new developments specific to the teaching of algebraic concepts in the high school curriculum.
A doctorate degree in mathematics education is the minimum formal education required.XII. Support Services Required.Several members of the department who could teach this course are: Tom Giambrone(EdD, SUNY Buffalo 1983), Eileen Schoaff ( Ph.D. SUNY Buffalo 1988) Luella Johnson (PhD SUNY Buffalo 1990), and Betty Krist (Ed D SUNY Buffalo 1980).
none.