Course Description
Topics in mathematics designed for future elementary school teachers. Problem solving. Number systems: whole numbers, integers, rational numbers (fractions) and real numbers (decimals), and the relationships between these systems. Understanding multiplication and division, including why standard computational algorithms work. Properties of arithmetic. Applications of elementary mathematics.
Additional Requirements for Graduate Students:
Graduate students will be required to do additional challenging problems or projects and to write additional essays. These problems, projects, and essays will focus on depth of conceptual understanding of elementary mathematics, as opposed to mere procedural understanding.
Athena Title
Arithmetic and Problem Solving
Equivalent Courses
Not open to students with credit in MATH 5001E, EMAT 5001E, MATH 5001W or MATH 7001E, EMAT 7001E, MATH 7001W
Semester Course Offered
Offered fall and spring
Grading System
A - F (Traditional)
Course Objectives
To strengthen and deepen knowledge and understanding of arithmetic, how it is used to solve a wide variety of problems, and how it leads to algebra. In particular, to strengthen the understanding of and the ability to explain why various procedures from arithmetic 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.
Topical Outline
Problem solving: Polya's principles. Numbers: The natural numbers, the whole numbers, the rational numbers, and the real numbers. The decimal system and place value. Scientific notation and powers. Why the standard algorithms for adding and subtracting whole numbers work. Fractions. Percent. Properties of arithmetic. Use of properties in mental arithmetic. Multiplication: The meaning of multiplication. The grouping, array, area, and tree diagram models for multiplication, including an introduction to applications in probability. The distributive property, the commutative and associative properties of multiplication, and their relationships to areas of rectangles and volumes of boxes. Why the standard procedure for multiplying whole numbers works. Why the procedure for multiplying fractions works. Division: The meaning of division. Why dividing by zero is undefined. Understanding measurement conversions. Why the standard longhand procedure for dividing whole numbers works. Why the procedure for dividing fractions works. Ratio and proportion and applications, including the Consumer Price Index. Divisability tests. How arithmetic leads to algebra.
Syllabus
Public CV