Problem Solving MTH 303

Rohr Science 220 (619) 221-2604 crowMA@ptloma.edu



Syllabus for Problem Solving

Instructor:
Greg Crow, Ph.D. 		Text:
For All Practical Purposes:
Introduction to Contemporary Mathematics.
3rd. Edition.
COMAP, Inc.
New York: W. H. Freeman & Co. 		Table of Contents:

Course Description
Required Materials
Course Philosophy
Course Goals
Course Approach
Grading Policies
The Final Examination
References
Class meetings:
TR 1:35-2:50 p.m. (section 1) or
WF 10:45-12:00 p.m. (section 3)
Office hours:
Rohr Science 220


Last modified 9-August-1995






REQUIRED MATERIALS
  • Calculator: A scientific calculator is recommended.
  • Supplies: One 3.5" computer disk.


COURSE PHILOSOPHY
"Today's world is more mathematical than yesterday's, and tomorrow's world will be more mathematical than today's." "...mathematics...serves as a key to opportunity and careers."[ Everybody Counts, p.45, p.3]

"To participate rationally in a world where discussions about everything from finance to the environment, from personal health to politics, are increasingly informed by mathematics, one must understand mathematical methods and concepts, their assumptions and implications." [ 50 Hours, p.35]

In view of these statements and many other similar ones from national reports, this quantitative experience (MTH 303) has been included as part of the PLNC general education curriculum. Thus, all students will study "major concepts, methods, and applications of quantitative reasoning with emphases on active problem solving" [Catalog].



COURSE GOALS
The overall goal of the course is "to develop the ability to solve nonroutine problems through dynamic processes" [Catalog]. More specific goals to develop are:

  • To contribute to the student ability to solve nonroutine problems.
  • To expand the student methods of inquiry and exploration.
  • To contribute to the student ability to form conjectures and check implications.
  • To expand the student understanding of major concepts, methods and applications of quantitative reasoning.
  • To help the student understand the role of problems, problem solving and quantitative reasoning.
  • To help the student see the role of problem solving in modern society.
  • To involve the student directly in various problem solving activities.
  • To help the student understand the meaning of problem and problem solving.
The general method of the course is to involve students in "dynamic processes of inquiry and exploration, logical reasoning, making and testing conjectures, and investigating implications of conclusions" [Catalog]. Specifically, the focus is on the processes and tools of quantitative problem solving - learning what they are and developing ability to use them.



COURSE APPROACH
The ability to solve problems requires resourcefulness, flexibility, and efficiency in dealing with new obstacles. Research on teaching and learning problem solving suggests that certain factors are critical to successful problem solving, including resources, heuristics, control, and belief systems [ Schoenfeld, 1985].

  • Resources refers to whatever information problem solvers understand (or misunderstand) that might be brought to bear on a problem.
  • Heuristic refers to strategies and techniques problem solvers have (or lack) for making progress when working on nonroutine problems.
  • Control refers to the way problem solvers use (or fail to use) the information at their disposal.
  • Belief systems refers to the problem solver's "world view" of the problem domain, which determines the ways they use the knowledge in the first three categories.
The approach in MTH 303 develops and uses these factors to increase your problem solving ability. Classroom techniques used include:

  • the teacher as role model
  • whole-class problem solving with teacher as control
  • small-group problem solving with teacher as coach
In addition, you are assigned readings and problems that will help you identify and make progress in the four areas discussed above.



COURSE METHODS
Use of groups. There is almost a century of research showing that academic achievement, productivity, and self- esteem improve dramatically when students work together in groups. This method emphasizes teamwork, cooperation and support by others, rather than isolation and competition in learning.

Role of the classroom instructor. There will be less direct "lecturing" in class than usual, with many questions "answered" by another question to help you work through your own questions and difficulties. You are expected to learn problem solving through active involvement - reading, writing, and explaining to others what you are thinking and doing.

This may require some adjustment in the way you think about teaching and learning. Initially, you may wish for more direct information and answers, but your patience and effort will be rewarded with a deeper understanding and increasing independence in problem solving, as well as confidence in your ability to tackle new problems.



GRADING POLICIES
Grading Distribution
Three tests at 125 points each 375 points
Final Exam 200 points
Quizzes 100 points
Homework 110 points
Projects 90 points
Log book 75 points
Attendance/Participation 50 points
Total 1000 points

Grading scale. Grades are based on the number of points accumulated throughout the course.
Approximate minimal percentages required to obtain a given grade are:

Grading Scale in percentages
A B C D
+ (87.5, 90) (77.5, 80) (67.5, 70)
[92.5, 100] [82.5, 87.5] [72.5, 77.5] [62.5, 67.5]
- [90, 92.5)[80, 82.5) [70, 72.5) [60, 62.5)
Grade components. The grade components are tests, quizzes, written assignments, projects, the log book, attendance/involvement, and the final examination. Other factors that affect grades are
  • Late work. A written assignment or computer assignment is late if it is not received at the beginning of class on the due date. Late work need not be accepted. Work accepted late may be assessed a penalty. Make-up tests (or the exam) will be given only by arrangement with the instructor for reasons of documented emergency.
  • Questions on written assignments, tests, and exams: Written assignments and test/exam questions and problems must be formulated carefully in terms of words and symbols used in the course. Credit is determined by the degree to which answers and solutions respond to the specific question or problem stated. Maximize your credit by learning the language and symbols of the course.
  • Written Assignments. Assignments collected must be prepared in a style suitable for grading. The following guidelines are used to determine credit:
    • the organization must be easy to follow
    • the work must be legible
    • complete solutions must be written for problems (not just answers); answers must be clearly marked
    • use complete sentences to answer questions
  • Tests and Final Examination. Tests and the final exam will include problems and questions over material assigned in the text, readings and handouts, as well as material presented in class.


    THE FINAL EXAM IS A COMPREHENSIVE EXAMINATION.


REFERENCES
  • Baron, J. B. and Sternberg, R. J. Teaching Thinking Skills: Theory and practice. (1987). New York: W. H. Freeman.
  • Bransford, J. and Stein, B. (1984). The Ideal Problem Solver. New York: W. H. Freeman.
  • Brown, Stephen I., and Marion I. Walter. (1983). The Art of Problem Posing. Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Cheney, L. (Ed.) (19 ) 50 Hours (Cheney Report). HEW
  • Curcio, F.R. (Ed.). (1987). Teaching and Learning: A problem solving focus. Reston, VA: NCTM.
  • Duncker, K. (1945). On problem solving. Psychological Monographs 58, No. 5 Whole # 270.) Washington, DC: American Psychological Association.
  • Dunham, William. (1990). Journey Through Genius: The great theorems of mathematics. New York: John Wiley & Sons.
  • Eves, Howard. (1990). Foundations and Fundamental Concepts of Mathematics. 3rd ed. Boston: PWS-KENT.
  • Eves, Howard. (1983). Great Moments in Mathematics. (2 vols.). The Mathematical Association of America.
  • Gardner, Howard. (1985). The Mind's New Science. New York: Basic Books.
  • Hofmann, J. E. (1957). The History of Mathematics. New York: Philosophical Library.
  • Kilpatrick, Jeremy. (1987). "Problem Formulating: Where Do Good Problems Come From?" Cognitive Science and Mathematics Education, edited by Alan H. Schoenfeld, pp. 123-48. Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Kline, M. (1962). Mathematics: A Cultural Approach. Reading, MA: Addison-Wesley.
  • Kline, M. (1953). Mathematics in Western Culture. New York: Oxford University Press.
  • Krulik, S. (Ed.). (1980). Problem Solving in School Mathematics. 1980 Yearbook of the National Council of Teachers of Mathematics. Reston, VA: NCTM.
  • National Research Council. (1989).Everybody Counts: A Report to the Nation on the Future of Mathematics Education. Washington, DC: National Academy Press.
  • Newell, A., and Simon, H. (1972). Human Problem Solving. Englewood Cliffs, J: Prentice-Hall.
  • Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.
  • Paulos, John A. (1988). Innumeracy: Mathematical illiteracy and its consequences. New York: Hill and Wang.
  • Peterson, Ivars. (1988). The Mathematical Tourist. New York: Freeman.
  • Peterson, Ivars. (1990). Islands of Truth: A mathematical mystery cruise. New York: Freeman.
  • Polya, G. (1945). How To Solve It. Princeton: Princeton University Press.
  • Polya, G. (1954). Mathematics and Plausible Reasoning (2 vols.). Princeton: Princeton University Press.
  • Polya, G. (1962 [Vol. 1] and 1965 [Vol. 2]; combined paperback edition, 1981). Mathematical Discovery. New York: Wiley.
  • Polya, G., & Kilpatrick, J. (Eds.). (1974). The Stanford Mathematics Problem Book with Hints and Solutions. New York: Teachers College Press.
  • Rolf, Howard L. (1988). Mathematics. Dubuque, IA: Wm. C. Brown.
  • Schoenfeld, A. (1985). Mathematical Problem Solving. New York: Academic Press.
  • Schoenfeld, A. (Ed.). (1987). Cognitive Science and Mathematics Education. Hillsdale, NJ:Lawrence Erlbaum.
  • Steen, Lynn A. (Ed.) (1990). On the Shoulders of Giants: New Approaches to Numeracy. Washington, D.C.: National Academy Press.
  • Tannenbaum, P. & Arnold, R. (1992). Excursions in Modern Mathematics. Englewood Cliffs, NJ: Prentice-Hall.
  • Taylor A. (19950). Mathematics and Politics. Strategy, Voting, Power, and Proof. Springer-Verlag.
  • Wickelgren, W. (1974). How to Solve Problems. San Francisco: W. H. Freeman.