SEMINAR IN
PROFESSIONALIZED SUBJECT MATTER IN MATHEMATICS
MA 650
1.
Catalog Description
This
seminar is designed to provide an advanced integration and extension of
concepts of professionalized subject matter in such areas as algebra, geometry,
and pre-calculus. The seminar will
include investigation of the potential impact of advanced mathematical concepts
not only in senior high schools but also in junior high schools and junior
colleges.
Prerequisite: Math 620
and/or Math 622 or equivalent.
2.
Goals of the Course
1. To improve familiarity with
current and past literature in various fields of professionalized subject
matter in mathematics.
2. To enhance the insight of mathematics teachers in branches of mathematics taught by such teachers.
3. To contribute to the improved ability of mathematics teachers to provide lucid and motivational approaches to the learning of secondary school mathematics.
4. To help students develop a reservoir of P.S.M. for subsequent use in creation of theses (Masters or Doctoral), articles, and textbooks.
Instructional
Procedures
1. Lectures and discussion
2. Utilization of outside sources (library and technology).
3. Student presentations of results of independent research.
Course Content
1. The history of
professionalized subject matter in mathematics.
2. Advanced structures and consequent alternative approaches for various areas of secondary school mathematics. (e.g., geometry, trigonometry, and algebra)
3. Utilization of professionalized subject matter in mathematics in secondary school special education.
a. Gifted students
b. Reluctant learners
4. Potential role in junior
high school mathematics of number theory, intuitive approach to differential
calculus and maxima and minima aspects of areas and volumes.
5. Utilization in secondary school mathematics of the modern alliance of algebra and geometry.
6. Mathematical modeling as a basis for enrichment of studies of applications of secondary school mathematics.
7. Utilization in secondary school mathematics classes of research in educational psychology.
8. Investigation of the potential use of discoveries resulting from Master’s or Doctoral research in secondary school mathematics.
9. Utilization in secondary school mathematics of historical topics, such as the history of theory of equations.
Evaluation
Measures
1. Participation in classwork
2. Preparation of reports an assignments
3. Written examinations
Bibliography
1. Cooke, Roger, The History of Mathematics, John Wiley &
Sons,
2. Gay, David, Geometry by
Discovery, John Wiley & Sons,
3. Kalman, Dan, Elementary
Mathematical Models: Order Aplenty and a Glimpse of Chaos,
Mathematical Association of
4. Kostelich, Eric and
Armbruster, Dieter, Introductory Differential Equations: From Linearity
to Chaos, Addison-Wesley,
5. Sullivan,
6. Zimmermann, Walter and Cunningham, Steve, Visualization in Teaching and Learning Mathematics.
7. Zill, Dennis and Cullen,
Additional
Teaching Aids
· Periodicals
1. The Mathematics Teacher
2. School Science and Mathematics
3. The American Mathematical Monthly
·
Mathematical Association of
Resources For Calculus Collection,
Vol. 1: Learning by Discovery: A Lab Manual for
Calculus
Vol. 2: Calculus
Problems for a New Century
Vol. 3: Applications
of Calculus
Vol. 4: Problems for Student
Investigation
Vol. 5:
·
National Council of Teachers
of Mathematics,
Calculators for Classrooms: Videotape and Guidebook, 1992
Calculators in Mathematics Education, 1992
Historical Topics for the Mathematics Classroom, 1989
Mathematics for the Middle Grades, 1982
Teaching and Learning Mathematics in the 1990’s, 1990