7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Intermediate algebra and one year of high school geometry or Math. D and B with grades of "C" or better, or placement by matriculation assessment process

7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)

7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)

9b. Catalog Description:

Exploration of mathematical patterns and relations, formulation of conjectures based on them, proving (or disproving) the conjectures. Includes different problem solving techniques, number theory, operations with sets, sequences and series, and geometry. Intended for future elementary school teachers.

10. Student Performance Outcomes: (Outcomes for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Outcomes must be related to items listed in Section 11.)

For each topic, the students will:
1. develop a strategy for approaching problems with which they are unfamiliar;
2. construct clear and logical solutions or proofs for each problem;
3. evaluate solutions for flaws and/or mistakes and correct these flaws or mistakes.

I. A. Examine and organize information in unfamiliar problems as an initial approach to solving;
B. construct tables, graphs, and diagrams and utilize as a problem solving technique;

II. A. propose, test, debate, and construct a clear, logical, and sound solution to these problems in groups;
B. solve other problems using the Euclidean Algorithm;

III.A. categorize information in a problem into clear sets, subsets, and complementary sets;
B. calculate the number of elements in intersections and unions of sets using Venn Diagrams;

IV. A. propose, test, debate, and construct a solution to the Buffon Needle (Noodle) Problem based on experimental data;
B. solve problems using counting techniques, such as combinations and permutations;
C. select the best solution to a problem using probability and expected values;

V. A. propose, test, debate, and construct a solution to the Highway Inspector Problem;
B. design networks with given numbers of vertices and test them for transferability;
C. propose, test, debate, and construct solutions to open-ended problems involving geometry;

VI. A. propose, test, debate, and construct a solution to the Handshake Problem;
B. 1. predict the entries in a sequence by following the pattern in a sequence;
2. construct a series that correctly represents information in a problem.

11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

Concepts of Mathematics is a course designed to encourage critical thinking skills in students as they explore various investigation topics and open-ended questions. Students will observe patterns, analyze data, make conjectures about these observations and test their conjectures. Their process and results will be formally communicated in writing and in oral presentations. This course is also designed to show students the beauty of Mathematics, along with providing them with an opportunity to discover the joy and power of mathematical thinking.

I. Problem Solving Techniques
A. Common approaches to problem solving -
look for a pattern, guess and check, convert to algebra
B. Organization of information -
making tables, draw a diagram, use a graph

II. Number Theory
A. The Potato Balancing Problem, jug problems, stamp problems
B. The Euclidean Algorithm

III. Set Theory
A. Sets, subsets, and complements
B. Venn Diagrams

IV. Probability
A. The Buffon needle (noodle) problem
B. Theoretical probability and various counting and combinatoric techniques
C. Expected value and fair game problems

V. Geometry and Networks
A. The Highway Inspector Problem
B. Networks
C. Geometry - tessellation, polygons, polyhedra

VI. Sequences and Series
A. The Handshake, pizza cutting, sidewalk dividing problems
B. Properties of Sequences and Series -
Finding sum formulas for various consecutive counting number sequences

12. Typical Assignments: (List types of assignments, including library assignments.)

a. Reading Assignments: (Submit at least 2 examples)

1. Find an internet discussion of Venn Diagrams and come to class prepared to discuss the logic of the Venn Diagram.

2. Read the homework handouts to determine the questions being asked and the work that will need to be done to accomplish the solution.

3. Read a solution to a problem prepared by another group and analyze that solution for correct logic or implied flaws.

4. Read article "Teaching Mathematics Requires special skills" by Debbie Ball (or similar article on same topic). Write journal entry and discuss in class.

b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Working in groups, develop a possible solution for the "Highway Inspector" network problem. Test the conjecture for accuracy and write up a clear, logical proof for the solution.

2. Within a group that has discovered a flaw with another group's solution to a problem, write a paper indicating how the solution was in error and a proposal on how to fix that error.

c. Other (Terms projects, research papers, portfolios, etc.)

1. Geometry Group Project- Polyhedra building/investigation
dualism, stellating, truncating, and compounds

2. Collection and organization of experimental data for Buffon Needle (Noodle) problem.

3. Researching historical math approaches to various problems given in class, with use of a library or internet.

4. Research mathematicians past or present and give presentation in class, with use of library or internet.

SECTION D

SECTION E

SECTION F

SECTION G