Description

Topics from algebra and number theory, designed to provide insight into arithmetic; problem solving heuristics; inductive and deductive proof; the natural number system; systems of numeration; the system of integers; the system of rational numbers; sets and functions.

Prerequisites

One year of college preparatory algebra. Required for majors in elementary education, and open only to students in this field.

Topics

Problem Solving
     Polya's four steps
     Strategies
Sets and Functions
     Sets and set notation
     Function Representations
Numeration Systems
     Characteristics of numeration systems
     Hindu-Arabic system
Number Theory
     Primes and composites
     Tests for divisibility
     Counting factors
     Greatest common factor
     Least common multiple
Natural Number System
     Models for operations
     Properties of operations
     Mental math
     Estimation
System of integers
    Models for operations
    Properties of operations
    Negative exponents and scientific notation
System of rational numbers
    Models for operations
    Properties of operations
    Rational numbers as exponents
    Decimal representations
    Ratio and proportion
    Percent models
    Solving percent problems

Text

Mathematics for Elementary School Teachers, by Tom Bassarear
Mathematics for Elementary School Teachers: Explorations, by Tom Bassarear