APPENDIX C

Description of Some Foundations Courses

  1. At Bloomsburg State University in Pennsylvania a foundations course presupposes only arithmetic and emphasizes the use of elementary mathematics in decision making and problem solving. Game theory is used to motivate the study of problem solving strategies. Hand calculators are standard tools. Materials written for the course have appeared as Mathematics in Daily Life by J. Growney published by McGraw Hill. Exercises in the book take on a variety of forms from those that require a brief application of a specific concept or method to those which require discussion or multistep application and evaluation of several ideas or procedures.

  2. At Northern Illinois University a foundations course presupposes two years of high school mathematics including one year of algebra. The course aims to develop in the student a competency in problem solving and analysis which is helpful in personal decision- making; in evaluating concerns in the community, state, and nation; in setting and achieving goals; and in continued learning. A hand calculator is used throughout the course. The mathematical content is one-third probability and statistics and two-thirds logical statements and arguments, geometry in problem solving, estimation and approximation (inequalities, functions, average rates of change), and general problem solving (including personal business applications). Problem sets consist of routine and nonroutine exercises. Materials written for the course have been published by Kendall/Hunt as Mathematical Thinking in a Quantitative World by L.R. Sons and P.J. Nicholls.

  3. At the University of Tennessee the foundations course "Algebraic Reasoning: Motivated by Actual Problems in Personal Finance" presupposes two years of high school algebra and one year of high school geometry. The course assumes use of a hand calculator and places its emphasis "on the importance and applicability of mathematics in real life." Problems used to motivate algebraic concepts are relevant to most college students' experience. Topics covered include borrowing money to complete college, saving a lump sum for college education, consolidation of debts, periodic payments, amortization schedules and more! The course uses material developed locally by J. Harvey Carruth.

  4. At the \ulUniversity of Chicago a trio of faculty have produced a series of ten-week (quarter) courses composed of short mini-courses each devoted to a single theme. Funded by the Sloan Foundation, the course development has involved the production of units such as statistical analysis of literary style, quantitative arguments and scientific method, the organization of the brain, dynamical systems, and risk assessment and epidemiology. Computer software was developed by the faculty for use in the course as were other resource materials. J. Cowan, S. Kurtz (Computer Science), and R. Thisted (Statistics) have worked on the courses.

  5. The Sloan Foundation also funded the development of a quantitative methods course at SUNY Stony Brook taught by D. Ferguson- the Department of Technology and Society. The course builds mathematical models and uses these models to get approximate answers to questions which arise out of human need. Some examples of models are stock market simulation, drug testing, life insurance, and quality control in production. Computers are used in the course, and mathematical tools include probability and linear programming. Quantitative methods are portrayed as a "way of knowing" the world and mathematical techniques are developed in the context of real problems. The course uses three textbooks and notes, examples, and laboratory activities developed locally. The textbooks are Probability Examples by J. Truxal and N. Copp's {Vaccines: An Introduction to Risk both of which are in the New Liberal Arts Monograph Series, and How to Model It: Problem Solving for the Computer Age by A. Starfield, K. Smith, and A. Bleloch which is published by McGraw Hill.

  6. Trinity College (Connecticut) developed a course "Essential Applications of Mathematics" aimed at enabling students to "be conversant and comfortable with the reasoning underlying such issues as environmental protection, the nuclear arms race, the spread of AIDS, and the budget deficit." The course focuses on five areas: numerical relations; proportions and percents; data analysis, probability and statistics; mathematical reasoning; and applications of algebra, geometry, and functions. Microcomputers are used. Laboratories are a part of the course. Materials have been developed locally. T.Craine and L. Deephouse have been involved in the course development which was linked to the adoption of a college mathematical proficiency requirement.

  7. At Dartmouth College L. Snell and R. Prosser have developed with the participation of faculty at Grinnell, Middlebury, and Spelman College a course called CHANCE. The course develops concepts of probability and statistics only to the extent needed to understand the applications. An important part of the text material for the course is the journal Chance started by Springer-Verlag in 1988. Computer simulations and software packages are used. Units for study include maintaining quality of manufactured goods in the face of variation, and scoring streaks and records in sports. The New York Times is also a resource for the course, and writing is a means used in teaching the course.

  8. Another course developed with the help of the Sloan Foundation is "Case Studies in Quantitative Reasoning: An Interdisciplinary Course" at Mount Holyoke College. H. Pollatsek and R. Schwartz have divided the course into the three units: I. Narrative and Numbers: Salem VillageWitchcraft;

    II. Measurement and Prediction: SAT Scores and GPA;

    III. Rates of Change: Modeling Population and Resources.

    A three-hour weekly computer laboratory is an integral part of the course's structure. The emphasis is on reasoning and ways to construct and evaluate arguments. Besides study of probability and statistics, the course involves simple algebra, graph reading, linear and exponential models, rates of change,and simulation. Students are required to write three substantial papers in the course and do six laboratory reports besides homework exercises. Resource materials consist of a readings list rather than a specific textbook.

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