MATH 180 - Number Theory for K-8 Teachers

5 Credits

This course guides students in examining the ideas and reasoning underlying the real number system and its associated operations. Students will also study the reasoning behind common and unfamiliar computation algorithms; physical, visual, and symbolic representations of numbers; percentages and proportions; problem solving; and will practice communicating mathematical ideas. Recommended for prospective or practicing K-8 teachers.

Pre-requisite(s) MATH 091 min 2.0
Placement Eligibility Math 107, 111, 146, 180, 098
Fees

Quarters Typically Offered

Winter Day

Designed to Serve Elementary education majors (especially those completing the Elementary Education DTA), along with interested parents and paraeducators.
Active Date 2014-02-03

Grading Basis Decimal Grade
Class Limit 32
Contact Hours: Lecture 55 Lab 0 Field Studies 0 Clinical 0 Independent Studies 0
Total Contact Hours 55
Degree Distributions:
AA

Quantitative Skills
Science

ProfTech Related Instruction

Computation

Course Outline

(Throughout the course) Problem solving
(Throughout the course) Error patterns and reasoning of students learning about numbers and operations
State and national standards for mathematics education
Concept of a number
Process and features of numeration
Structure of numbers (order, divisibility, common multiples/factors)
Meaning of basic whole number operations (add, subtract, multiply, divide; exponentiation)
Alternative algorithms for whole number computation
Concept of and arithmetic with decimals
Concept of and arithmetic with fractions
Concept of and arithmetic with ratios (rates), percentages, and proportions
Concept of and arithmetic with integers
Concept of and arithmetic with rational and real numbers
(Optional) The use and effects of current technology on teaching and learning mathematics

Student Learning Outcomes
Summarize mathematics standards relevant to K-8 students from a variety of sources, such as national (e.g., NCTM) or state standards.

Apply knowledge about features of our number system to analyze (1) other number systems and (2) common error patterns that arise when children are learning our number system.

Describe the concept of a whole number as well as relationships between them (order, divisibility, factorization, and common factors/multiples).
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Describe the purpose of basic operations on whole numbers and the concepts underlying these basic operations.

Represent decimals, fractions, integers, ratios (rates), percentages, and proportions in multiple ways.

Compare and contrast decimals, fractions, and integers with whole numbers and each other.

Compare and contrast ratios (rates), percentages, and proportions.

Compare and contrast the standard algorithms for computing with decimals, fractions, and integers with those for whole numbers.

Analyze common error patterns in students’ computations and demonstrate how alternative algorithms can reduce those errors.