SAMPLE GENERAL EDUCATION COURSE CERTIFICATION PROPOSAL
Proposal to certify Math 117 as a general education course in math and statistics.
1. Course Title and Catalog Description
Math 117 Mathematical Modeling and Problem Solving (3 credits).
Investigating and developing problem solving strategies, mathematical reasoning skills, and mathematical models of real world situations; content selected from topics in finance, art, the natural and social sciences, and everyday life. Every semester. Prerequisite: Three years of college preparatory mathematics and placement level 20, or Math 106 with a minimum grade of C.
2. Syllabus Information (NB: the model syllabus should appear in the customary format for syllabi).
Course objectives (expansion of course description)
- To develop the ability of students not majoring in mathematics-related disciplines to: (1) think logically and creatively about quantitative problems, (2) use mathematical reasoning, and (3) be able to interpret, develop, and use some basic mathematical models of real world phenomena;
- To focus on mathematical applications relevant to students as informed consumers, decision makers, and educated citizens;
- To demonstrate the use of mathematics as a powerful language in many disciplines and its significant role in human development;
- To use mathematical tools developed in precollege-level mathematics courses to solve problems and develop models, including basic arithmetic and algebraic manipulations and familiarity with polynomial, exponential, and logarithmic functions;
- To develop students' understanding of proportionality and rates of change;
- To explore a few new mathematical topics, including logistic models, matrices, and Markov chains.
- <specify textbook/s to be used>.
Assignments and evaluation
- Grading scale: A = 100-90%, B = 89-80%, C = 79-70%, D = 69-60%.
- Group problems: (weight: 20%)
Group problems are assigned about once every two weeks. You and your group are expected to work on these problems together, and to turn in one final version of your work, signed by all group members.
- Skills Test: (weight: 10%)
You must achieve mastery (90%) on a test of basic arithmetic and algebra. This skills test is to be taken in the Math Lab by the date specified and must be repeated until mastery is reached.
- Three Major Tests: (weight: 45%)
There will be a major test about every four weeks.
- Comprehensive Final Examination: (weight: 25%)
- Writing assignments: All tests will include problems in which students must describe, explain, or justify work using full sentences. For example students may be asked to describe situations in which certain financial formulas apply, explain why certain probability rules make sense, or justify their use of a particular function to model a problem. Such problems will constitute at least 15% of the grade on these tests, or at least 10% of the overall course grade. In addition, group problems will be similar to lab reports, so that written explanations will constitute at least half of the group grade, or another 10% of the overall course grade. Finally, the development of mathematical models includes the development of equations, which are full symbolic sentences. So the written components of this course will count for at least 20% of the course grade.
Topical outline of course (to be developed further by indicating approximate amount of time devoted to each topic)
- Mathematical reasoning (inductive and deductive reasoning, investigating patterns, problem solving strategies)
- Ratios, proportions, and percents (applications involving proportional reasoning)
- Combinatorics (fundamental Principle of Counting, factorials, permutations, combinations, with applications)
- Probability (basic rules of probability, conditional probability, independence, Bayes' Theorem, and applications related to medicine, gambling, genetics, etc.)
- Finance (compound interest, annuities, amortized loans)
- Exponential, logarithmic, and logistic models of growth, decay, seismic activity, etc.
- Matrices and Markov chains
3. Discussion of how the course meets the specific guidelines and requirements for math and statistics courses (MA and ST)
- Develop a variety of quantitative problem solving strategies requiring logical thinking and persistence, including the ability to pose questions, identify and analyze critical information, and test hypotheses or conclusions. This problem solving course addresses this guideline directly. In particular, students will be expected to solve nonstandard problems and to determine if their solutions make sense.
- Emphasize basic quantitative concepts, such as number sense, data collection and analysis, the use and interpretation of abstract symbols, variable relationships and rates of change, distributions, graphs, and the properties of geometric shapes. This algebra-based course emphasizes "common sense" with regard to numbers,variables, and shapes, necessary requirements for successful problem solving and model building.
- Develop some mathematical or statistical models of phenomena from the world around us. Mathematical model building is the second focus of this course.Students will analyze situations using a range of models from linear to exponential and perhaps logistic.
- Cultivate the use of mathematical reasoning skills. This is another explicit emphasis of this course. Students' reasoning skills will be cultivated through problem solving and model building.
- Develop a sense of the nature of proof and its critical role in mathematical thinking, and explore the strengths and limitations of mathematics and statistics in addressing many human problems. Students will be expected to make logical mathematical arguments to defend their solutions to problems. They will also be made aware that many problems cannot be solved via mathematical techniques.
- Foster appreciation for historical, logical, or intuitive aspects of the development of mathematical or statistical concepts. The course will include historical notes to emphasize the context in which mathematical ideas have developed.
- Communicate using appropriate mathematical and statistical vocabulary and notation. Students will be expected to describe solutions to problems and to justify their answers.
- Include appropriate computational and procedural skills. Students will be performing computations, solving equations, and so on.
- Use appropriate technology to aid in the understanding of mathematical principles and in the solution of realistic mathematical problems. Calculators will be required in this course. We may also use spreadsheets and other software.
- Include at least Mathematics Placement Level 20 or equivalent as a prerequisite. Level 20 is a prerequisite for this course because students will be expected to be familiar with high school mathematics through Algebra II, including exponential and logarithmic functions.
- Include a writing component which counts for at least 1/5 of the grade. Writing in this category is defined to mean the use of English sentences and symbolic representations, such as formulas or equations, for the purpose of demonstrating students' understanding of the concepts articulated in the above guidelines for this category. At least 1/5 of the course grade will be based on projects or test problems in which students must explain answers, justify their reasoning, or describe situations or models using appropriate mathematical vocabulary. We expect these writing assignments to increase their ability to think carefully through problems and to increase their understanding of mathematical modeling.