MA150 MATHEMATICS FOR THE ELEMENTARY SCHOOL TEACHER I (4 Cr.)

COURSE DESCRIPTION

Prerequisite: MA100 (passing with a C or better) or equivalent

Offered:  Fall, Winter

General Introduction and Goals

This course is designed to examine elementary school mathematics from an advanced standpoint. The emphasis is on the development of the system of real numbers and the language, models, concepts, and operations associated with it. Quantitative thinking skills are developed through applications and problem solving situations. In this course the students will:

1. compare the characteristics of different numeration systems from a historical perspective;
2. examine the structure and properties of whole numbers, integers, rational numbers, and real numbers;
3. develop concrete and conceptual models for each of the operations and their algorithms;
4. focus on problem solving and a variety of strategies for solving problems;
5. develop skills for applying number theory to elementary school mathematics;
6. use mental computation and estimation in appropriate situations;
7. use technology as a tool in problem solving;
8. extend the process of mathematical proof through logical, intuitive reasoning.

Course Content

1. Problem Solving
   1. The role of problem solving in K-12 mathematics
   2. Problem solving strategies, skills, and reasoning
   3. Appropriate use of the hand-held calculator at all levels
2. Set Theory
   1. The language of sets
   2. Operations on sets
   3. Venn diagrams and logical thinking
   4. Relations and functions
3. Numeration Systems
   1. Symbols, rules, and properties
   2. Hindu-Arabic, Roman, and other systems
   3. Representing and naming numbers
   4. Other number groups and bases
4. Natural and Whole Numbers
   1. Operations and models for whole numbers
   2. Algorithms, mental computations, and estimation
   3. Applications and problem solving
5. The Integers
   1. Development of the integers
   2. The need for and use of integers
   3. Operations, models, and algorithms
   4. Using integers to solve equations and inequalities
6. Number Theory
   1. Intuitive development of divisibility rules
   2. Prime numbers and factorization leading to GCF and LCM
   3. Clock and modular arithmetic
   4. Applications and problem solving
7. The Set of Rational Numbers
   1. Models for fractions and decimals
   2. Equivalence of fractions and decimals: ratios and proportions
   3. Operations and models for fractions, decimals, and percents
   4. Applications and problem solving
8. The Set of Real Numbers
   1. Development of irrational numbers
   2. Radicals and approximation
   3. Scientific notation
   4. Properties and proofs