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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 ProblemSolving 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 problemsolving techniques. [EEO
1, 2, 3, 4, 5]
2. Demonstrate understanding of core concepts underlying standard and
nonstandard 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, higherorder thinking, and
statistical methods to modeling and solving realworld 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.
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