ROCHESTER COMMUNITY & TECHNICAL COLLEGE
COMMON COURSE OUTLINE: Math 1112 – Mathematical Reasoning

A. CATALOG DESCRIPTION

1. Math 1112

2. Mathematical Reasoning

3. 3 credits

4. 3 hours per week

5. Offered Spring

6. Prerequisites:

a. Successful completion of Math 1111 (C or higher)

b. Reading level

c. Writing level 2

MNTC: Critical Thinking (CT), Mathematics/Logical Reasoning (MA)
This course is designed for Elementary Education majors or anyone desiring to continue his/her study of liberal arts mathematics topics. The purpose of the course is to further develop students’ mathematical reasoning and effective thinking skills. This course continues from Math 1111 and topics may vary, depending on the instructor and/or the text. Possible topics: Numeration Systems, Geometry, Logic, Trigonometry, Finance Mathematics, Probability, Statistics, Voting Methods, Apportionment, Graph Theory, Sets, Discrete Mathematics, Problem Solving, Number Theory, and Game Theory.

Grading is A-F.

Note that while Math 1111 and 1112 are in a sequence, Math 1113 is not a part of that sequence.

B. EFFECTIVE DATE

Effective November, 2000 and will be reviewed concurrent with a change of textbook and/or instructors.

C. RECOMMENDED ENTRY SKILLS/KNOWLEDGE:

1. Solve linear equations

2. Add, subtract, and multiply polynomials.

3. Apply the laws of exponents.

4. Operations with rational expressions

5. Convert between standard and scientific notation

6. Apply the Pythagorean Theorem

7. Basic geometry skills – perimeter, area of basic polygons.

D. MAJOR CONTENT AREAS TO BE SELECTED FROM:

1. Numeration systems

2. Geometry

3. Logic

4. Trigonometry

5. Finance Mathematics

6. Probability

7. Statistics

8. Voting Methods

9. Apportionment

10. Graph Theory

11. Sets

12. Discrete Mathematics

13. Problem Solving

14. Number Theory

15. Game Theory

16. Quantitative Analysis

E. LEARNING OUTCOMES:

MNTC (Math) Students will be able to

a. illustrate historical and contemporary applications of mathematical/logical systems

b. clearly express mathematical/logical ideas in writing

c. explain what constitutes a valid mathematical/logical argument (proof)

d. apply higher-order problem-solving and/or modeling strategies

MNTC (CT) Students will be able to

a. gather factual information and apply it to a given problem in a manner that is relevant, clear, comprehensive, and conscious of possible bias in the information selected.

b. imagine and seek out a variety of possible goals, assumptions, interpretations, or perspectives, which can give alternative meanings or solutions to given situations or problems.

c. analyze the logical connections among the facts, goals, and implicit assumptions relevant to a problem or claim; generate and evaluate implications that follow from them.

d. recognize and articulate the value assumptions which underlie and affect decisions, interpretations, analyses, and evaluations made by ourselves and others.

3. (Other – these will vary depending on the topics selected.) Students will be able to

a. illustrate historical and contemporary applications of numeration systems.

b. understand the difference between Euclidean and non-Euclidean geometries

and apply the principles of both.

c. apply the basic principles of trigonometry to real world problems.

d. apply the formulas of finance to real world problems.

e. calculate probabilities and analyze games of chance.

f. interpret data and its presentation.

g. apply common strategies for problem solving.

h. use set theory notation and apply the operations of sets.

i. use some of the voting methods such as majority rule, the plurality method, binary voting, Condorcet winner, and the Forda method.

j. apply the basic principles of graph theory.

k. apply and analyze game strategies.

F. METHODS FOR EVALUATION OF STUDENT LEARNING:

1. Tests and/or

2. Quizzes and/or

3. Homework and/or

4. Cooperative group work and/or

5. Writing assignments and/or

6. Portfolios

G. SPECIAL INFORMATION (A scientific calculator is required. ):