PROBLEM SOLVING IN MATHEMATICS MATH 205

1. Catalog Description

This course seeks to prepare education majors to pass the national test required for teacher certification. It provides a thorough review of problem solving skills through Pre-Calculus for others. This course is a General Studies course and may not be counted toward the Math Major or minor.

Pre-requisite: MATH 112 Intermediate Algebra or equivalent

(3 credits)

2. Goals of the Course

a. Students will acquire good number sense (understanding of how numbers behave) and use numbers appropriately to meet various needs.

b. Students will recognize mathematical relationships and use them appropriately.

c. Students will learn alternative approaches to solving problems in Math.

d. Students will understand deductive reasoning and how to use it appropriately.

e. Students will learn to organize and summarize statistical data and learn fundamental probability concepts.

f. Students will be able to read and comprehend mathematical materials and texts.

g. Students will learn to interpret graphs, charts, diagrams, and frequency distributions.

h. Students will be able to express mathematical concepts and solutions in writing. Students will learn to write age appropriate word problems for elementary math concepts.

3. Instructional Procedures

4.

a. Lecture/Discussion/Group exploration.

b. Daily reading of the textbook and homework assignments with in-class discussion of solutions.

c. Student presentations and discussions of solutions to specific math problems at the blackboard.

d. Videos/software in computer lab (optional).

4. Course Content

I. Tools for Problem Solving

II. a. Exploration with patterns

b. Using the problem solving process

c. Logic: Flow chart

d. Reading a computer program (optional)

e. Use of the calculator in an elementary classroom

f.

III. The Integers

IV. a. The Integers on the number line

b. Prime and Composite numbers

c. Greatest common divisor

d. Least common multiple

V. Rational numbers

a. The set of rationals on the line

b. Addition, subtraction, multiplication, and division of rational numbers

c. Solving equations and inequalities

d. Ratio and proportions

VI. Decimals

a. Decimals on the number line

b. Decimal operations: Addition, subtraction, multiplication and division

c. Relations between rational numbers and decimals

d. Percents and computing interest

e. Real Numbers

f. Radicals and rational exponents

g. Approximating square roots

VII. Concepts of Measurements

a. Units of lengths

b. Areas of polygons and circles

c. Surface areas of three-dimensional figures

d. Volumes

e. Mass and temperature

VIII. Probability and statistics

a. Measures of central tendency

b. Measures of Variability

c. Frequency Distributions

d. Basic Probability

e. Discrete probability distributions

f. The continuous standard normal distribution

g.

IX. Graphs

X. a. Creating and interpreting circle graphs

XI. b. Creating bar graphs, line graphs, scatter graphs, and charts.

XII. c. Interpreting data sets, graphs, diagrams

XIII. d. Using the graphics calculator

XIV. Geometry

a. Basic notions: lines, angles, and triangles

b. Parallel lines and their properties

c. Congruence properties

d. Similar triangles and figures

5. Evaluation Measures

a. Students will be graded on their ability to communicate mathematically in written and oral presentation.

b. Quizzes on assigned reading and homework.

c. Short reaction papers to films, concepts, or journal articles.

d. Group problems or presentations.

e. In-class examinations and a comprehensive final exam.

6. Bibliography

A. Required text

B.

C. Bennett and Nelson, Mathematics for Elementary Teachers: A Conceptual Approach, 4^th ed., WCB McGraw Hill Publishers, 1998.

D.

E. Billstein, Libeskind, and Lott, A Problem Solving Approach to Mathematics for Elementary School Teachers, 6^th ed., Addison Wesley Longman, Inc., 1997.

Long, Calvin, and Duane DeTemple, Mathematical Reasoning for Elementary Teachers, Addision Wesley, 1996.

B. Additional Required Readings

Bassarear, Tom, Mathematics for Elementary School Teachers, Houghton Mifflin Co., 1997.

Brown and Chase, General Statistics, 2^nd ed., John Wiley and Sons, Inc., 1992.

Growney, Joanne S., Mathematics in Daily Life—Making Decisions and Solving Problems, McGraw Hill Co., 1986.

National Council of Teachers of Mathematics (NCTM), Historical Topics for the Classroom, 31^st Yearbook, 1967.

Sonnabend, Thomas, Mathematics for Elementary Teachers, Saunders College Publishing, 1993.

C. Supporting Bibliography

National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics, 1989.

Sgroi/Sgroi, Mathematics for Elementary School Teachers, PWS-Kent Publishing Co., 1993.

D. Relevant Periodical Sources

National Council of Teachers of Mathematics (NCTM), Teaching Children Mathematics (formerly Arithmetic Teacher).

NCTM, Mathematics in the Middle School.

E. Software

Aufmann, Baker, Lockwood, Elementary Algebra with Basic Mathematics, The Computer Tutor, Houghton Mifflin College Software, Boston, Mass., 1989.

Kemeny, Kurtz, Algebra, Tru Basic Inc., Hanover, New Hampshire, 1988.

Wise, Beginning Algebra & Problem Solving, Harcourt Brace Janovich, 1989.

Algebra 1 Ideal Software (Complete) - APL. 11.

Roberts, Janice, Algebra without Anxiety, Gadsden, Ala., 35902: 1984 - APL. 11.

M159 Factoring Algebraic Expressions - APL. 11.