Introduction to Mathematics for Elementary Teachers

MATH 127 – Introduction to Mathematics for Elementary Teachers Course Syllabus

Course Description: Elementary concepts of sets, numeration systems, number theory, and properties of the natural numbers, integers, rational, and real number systems with an emphasis on problem solving and critical thinking.
Credit Hours: 3
Course Prerequisites and Corequisites: See general course prerequisites

Course Outline: Approximate time spent
Techniques of problem solving and estimation skills 10%
• The following topics will be threaded throughout the course in order to develop the habits of mind necessary in mathematics:
o Introduce Polya’s Problem Solving Process: Understand the Problem, Devise a Plan, Carry Out Plan, Look Back
o Explore Basic Problem Solving Strategies
o Explore Patterns in Language, Figures, Numbers, Sequences and Geometry
o Develop Estimation Skills with Mental Arithmetic

• Sets and Logic: An Introduction 15%
o Classify and Sort Objects According to Attributes
o Introduce the Language of Logic Connectives : And, Or, Not, Implies
o Use Venn Diagrams as Problem-Solving Tools
o Introduce Set Terminology and Notation
o Explore Set Relations, Operations, and Properties
o Introduce Functions as Sets

• Whole Numbers and Numeration : Concepts and Algorithms 20%
o Define the Set of Whole Numbers
o Model Whole Number Operations using a Variety of Methods
o Verify Properties of Operations : Binary Operation; Closed, Commutative, Associative, Distributive - Multiplication over Addition, Identities, Multiplication by Zero; Division Algorithm
o Explore Place Value Systems using Base Five Arithmetic
o Develop and Apply Algorithms for Whole Number Operations
o Develop Definition and Properties for Whole Number Exponents

• Number Theory: An Introduction 10%
o Define and Explore Primes and Composites
o Explore Basic Divisibility Properties of Sums and Products
o Explore Applications of the Fundamental Theorem of Arithmetic
o Define the GCD and LCM and Use Algorithms for Finding Each
o Explore Applications of the GCD and LCM

• Integers: Concepts and Algorithms 20%
o Model Integer Operations Using A Variety Of Methods
o Investigate Extensions of Whole Number Operations and their Properties: Closed, Commutative, Associative, Distributive- Multiplication over Addition, Identities, Additive Inverse, Multiplication by Zero
o Define Absolute Value
o Revisit The Division Algorithm

• Real Numbers : Concepts and Algorithms 25%
o Investigate Practical Uses for Fractions
o Explore Connections between Fractions, Rational Numbers, Decimals, and Percents
o Investigate Rational and Irrational Number Representations
o Explore Concepts and Define/Demonstrate Properties of Rational Number Operations to Include: Additive Inverse, Addition Property of Equality, Multiplicative Identity, Multiplicative Inverse, Distributive Property of Multiplication over Addition, Multiplicative Property of Equality, Multiplicative Property of Zero
o Investigate Order And Operations in Decimal Form
o Investigate Irrational Number Order and Operations: Illustrate the Pythagorean Theorem
o Define and Demonstrate Properties of Real Numbers: Closure, Commutative, Associative, Distributive, Identity, Inverse, Density
o Develop Proportional Thinking to Include Ratio and Proportion, Properties of Proportions, Fundamental Law of Fractions

• Student Learning Outcomes (SLO): At the end of MTH 127, a student who has studied and learned the material should be able to:
1. Solve a variety of problems using multiple problem-solving techniques. [EEO 1, 2, 3, 4, 5]
2. Demonstrate understanding of core concepts underlying standard and non-standard algorithmic procedures for performing operations on subsets of real numbers. [EEO 1, 2,]
3. Communicate his/her knowledge effectively in multiple formats – verbally, concretely, and in writing. [EEO 2, 3, 6, 7]
4. Define, identify, and use the fundamental properties of real number operations. [EEO 1, 2, 4]
5. Provide logical justification of mathematical thinking. [EEO 1, 3, 5]
6. Use mathematical language and notation appropriately to communicate ideas. [EEO 3, 5, 7]
There are no specific program learning outcomes for this major addressed in this course. It is a general education core curriculum course and/or a service course.

Exemplary Educational Objectives (EEO):
1. To apply arithmetic, algebraic , geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations.
2. To represent and evaluate basic mathematical information verbally, numerically, graphically , and symbolically .
3. To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments.
4. To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results.
5. To interpret mathematical models such as formulas , graphs, tables and schematics, and draw inferences from them.
6. To recognize the limitations of mathematical and statistical models.
7. To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines.