** Catalog Description**This is designed specifically for students who seek elementary and middle school teacher certification. Topics include set theory, functions, numerations systems, number theory, emphasis on problem solving and critical thinking.

Course Learning Outcomes

The student will:

• Use models and manipulatives to demonstrate the four basic operations of the rational numbers.

• Demonstrate an understanding of place value through multiple representations including the use of grouping manipulatives, place value manipulatives and abstract representations such as with exponents and different number bases.

• Demonstrate an understanding of the attributes of numeration systems.

• Analyze mathematical situations and solve problems using mathematical heuristics.

Contact Hour Information

Credit Hours: 3

Lecture Hours: 3

Lab Hours: 0

External Hours: 0

Total Contact Hours: 48

Prerequistes

MATH 1314 OR placement by testing;

ENGL 0305 or ENGL 0365 OR higher level course (ENGL 1301), OR placement by testing

Corequisite

ENGL 0307

**Required Materials**

**Textbook:**

Long, DeTemple, Millman; *Mathematical Reasoning for Elementary Teachers, 6th ed.* with MyMathLab Access; Pearson, ISBN Numbers:

Textbook Plus MyMathLab Portal Access: 9781256388791

Textbook Only: 9780321693129

MyMathLab Portal Access: 9780558357603

**Calculator:**

Graphing Calculator required. TI 83, TI 84 or TI 86 series calculators recommended.

Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models.

Neither cell phones nor PDA’s can be used as calculators. Calculators may be cleared before tests.

Textbook Sections

**Chapter 1. Thinking Critically**

1.1 An Introduction to Problem Solving

1.2 Pólya's Problem Solving Principles

1.6 Reasoning Mathematically

**Chapter 2. Sets and Whole Numbers**

2.1 Sets and Operations on Sets

2.2 Sets, Counting and the Whole Numbers

2.3 Addition and Subtraction of Whole Numbers

2.4 Multiplication and Division of Whole Numbers

**Chapter 3. Numeration and Computation**

3.1 Numeration Systems Past and Present

3.2 Nondecimal Positional Systems

3.3 Algorithms for Adding and Subtracting Whole Numbers

3.4 Algorithms for Multiplication and Division of Whole Numbers

3.5 Mental Arithmetic and Estimation

**Chapter 4. Number Theory**

4.1 Divisibility of Natural Numbers

4.2 Tests for Divisibility

4.3 Greatest Common Divisors and Least Common Multiples

**Chapter 5. Integers**

5.1 Representations of Integers

5.2 Addition and Subtraction of Integers

5.3 Multiplication and Division of Integers

**Chapter 6. Fractions and Rational Numbers**

6.1 The Basic Concepts of Fractions and Rational Numbers

6.2 Addition and Subtraction of Fractions

6.3 Multiplication and Division of Fractions

6.4 The Rational Number System

**Chapter 7. Decimals, Real Numbers and Proportional Reasoning**

7.1 Decimals and Real Numbers

7.2 Computations with Decimals

7.3 Proportional Reasoning

7.4 Percent

**Chapter 8. Algebraic Reasoning and Representation**

8.1 Algebraic Expressions, Functions and Equations

8.2 Graphing Points, Lines and Elementary Functions