MATH 5003/7003 Algebra and Problem Solving 3 hours

Oasis Title: ALG & PROB SOLV.

Prerequisite: MATH 5002

A deep examination of topics in mathematics that are relevant for elementary school teaching. Number theory, algebra and functions, including ratio and proportion, probability and statistics. Posing and modifying problems.

Course Objectives: To strengthen and deepen knowledge and understanding of probability and statistics, elementary number theory and algebra, and how they are used to solve a wide variety of problems. In particular, to strengthen the understanding of and the ability to explain why various procedures and formulas in mathematics work. To strengthen the ability to communicate clearly about mathematics, both orally and in writing. To promote the exploration and explanation of mathematical phenomena. To show that many problems can be solved in a variety of ways. To learn to pose and modify mathematical problems.

Topical outline:

Fractions, ratio and proportion: Division of fractions: why the "invert and multiply" procedure is valid. Division of decimals. Understanding ratio and proportion in terms of fractions and in terms of multiplication and division.

Number Theory: Factors and multiples, greatest common divisor and least common multiple. Prime numbers. Divisibility tests. Even and odd.

Algebra and functions: patterns, sequences, formulas, and equations. Functions and their graphs. Relating qualitative descriptions of functions to their graphs.

Basic descriptive statistics: Designing investigations and gathering data. Common ways to display data. The average and the median. Percentiles.

Probability: Basic principles of probability. Using tree diagrams and using the meaning of fraction multiplication to understand simple probability calculations.

Solving, posing and modifying problems. Because fractions, decimals, and percents are traditionally difficult topics to teach, it is recommended that part of the course be devoted to solving, posing, and modifying problems involving fractions, decimals, and percents, especially problems that are relevant to and helpful for the teaching of these topics.

Critique of mathematics lessons: students should critique several mathematics lessons that they taught to elementary school children and discuss ways that the lessons could be improved or extended. The critique should focus on mathematics content.

Text: Mathematics for Elementary Teachers volumes I and II, preliminary edition, by Sybilla Beckmann, Addison-Wesley, 2003

Chapter 5 Division, sections 5.5 - 5.7 only, Chapter 6 More About Numbers, Chapter 10 Functions and Algebra, Chapter 11 Statistics, Chapter 12 Probability.

Math 7003: for graduate credit, students must complete an additional course project. The project could consist of several essays, or a longer paper, in which the student discusses some aspect of the course material in depth, or in which the student relates the course material to their future teaching (e.g., with a collection of lesson plans or with a discussion of some lesson plans). However, other creative ideas could also be acceptable. For example, students might think of a creative way to tie their course project for math 7003 to something they will be doing for one of their other courses.