Text: Burger, W. F., & Musser, G. L. (1997). Mathematics for elementary
teachers: a contemporary approach (4th. ed.) . Simon & Schuster, Englewood
Welcome to MAT 205, Mathematics for Elementary Teachers. I'd like to begin by having you read a few paragraphs from the Curriculum and Evaluation Standards: Kindergarten book (NCTM, 1991).
Many people, including students, believe that mathematics is for the privileged few. It is time to dispel that myth. All children, regardless of sex, socioeconomic background, language, race, or ethnic origin, can and must succeed in school mathematics. With proper instruction, encouragement, and high expectations, all students can do mathematics.
All elementary teachers are teachers of mathematics. Thus, your role is to build your student's self-confidence and nurture their natural curiosity; to challenge them with rich problems through which they will learn to value mathematics and appreciate the order and beauty of mathematics; to provide them with a strong foundation for further study; and to encourage their mathematical ability and power.
The elementary school years are crucial in a child's cognitive and affective development, and you are the central figure. You structure classroom experiences to implement the curriculum and create a supportive environment for learning to take place. In most activities you are the guide, the coach, the facilitator, and the instigator of mathematical explorations.
I whole-heartedly believe in these statements. I hope that as your preparation for teaching continues, you'll realize just how important elementary teachers are in setting the stage for their student's academic success. So where does this course fit in?
As of this moment, you will be taking four courses to prepare you to teach mathematics to elementary students. Two of these will be math courses (MAT 205, MAT 206) and two of these will be methods courses(EMT 441, EMT 442). The purpose of the two sequences are quite different. MAT 205 and 206 are mathematics courses designed to ensure that you understand and can work with certain mathematical concepts in a clear, confident and correct manner. They are not designed to teach you how to implement these concepts in the classroom. This will be the main purpose of EMT 441 and 442.
In every mathematics course, the main purpose of the instructor is to teach the students the knowledge and skills necessary to work effectively with mathematics. I am no exception. The following is a list of abilities I hope you will develop while taking this course.
- the ability to understand mathematical concepts
- the ability to solve and pose problems
- the ability to reason mathematically
- the ability to correctly communicate mathematics, both orally and in writing
- the ability to perform skills quickly, correctly and confidently
I will discuss these abilities in more detail when I discuss my method of assessment.
The mathematical content of this course will be taken from the first eight chapters of the textbook. Below, I have provided a brief outline of the topics covered in each chapter. I would hope that many of these topics are familiar to you.
Chapter 1: Problem Solving. We discuss the very important art of problem solving, based on George Polya's method.
Chapter 2: In this chapter, we discuss the basic foundations of numeration. Topics includes sets, the whole numbers, the decimal system, and a brief introduction to functions.
Chapter 3: Here we discuss the basic operations (addition, subtraction, multiplication, division) of the decimal system and their properties. The chapter concludes by introducing ordering and exponents.
Chapter 4: This is where we discuss the algorithms associated with the four basic operations and apply them to other bases.
Chapter 5: The concepts here deal with prime numbers, the GCF, and LCM.
Chapter 6: We talk about fractions and their properties in this chapter.
Chapter 7: Decimals, ratio, proportion, and percent are the focus of this chapter.
Chapter 8: This chapter gives us our first look at negative numbers as we discuss the integers.
Finally, we get to the part that all students seemed to be most concerned with, the manner in which I will determine your grade. As we go through this course, I will be assessing six different areas that I think determine your ability to work effectively in mathematics.
Communication: Communication of mathematics is particularly important to teachers. In the future, you will need to be able to express these ideas in a clear and mathematically correct manner to students who may never have seen the ideas before. Teachers must be able to do this both orally and in writing.
Memorization of Facts: This assesses the student's ability to recall certain facts, definitions, theorems and algorithms completely and correctly. It is much easier and quicker to access one's memory for information than it is to search for information in a book.
Mathematical Reasoning: This area deals with student's ability synthesize mathematical ideas in a logical and correct order. Do the steps used by a student to solve a problem proceed in a logical manner? Are they mathematically correct? Do they form a valid argument for the solution obtained? Are any steps left out?
Skills: Skills include following simple algorithms, computing answers, and performing operations in mathematical systems. They are often assessed by easy and straight forward exercises. Generally, skills in and of themselves are not important, HOWEVER, they often play a huge role in problem solving, which is important. The course is not designed to concentrate on skills, but it is necessary to make sure that students can perform the skills associated with concepts in this course.
Problem Solving: The ability to solve problems, mathematical or otherwise, is a key skill for success in the world. Problems are more involved and require more thinking than the exercises. They often require students to combine knowledge of the world, knowledge of mathematics and ability to perform skills in order to obtain a reasonable solution. This will be a key component of this course.
Understanding of Concepts: This course will cover many concepts that are the foundations for most of mathematics. These are the basic building blocks of mathematics. Without a complete understanding of these concepts, the student will most likely struggle with mathematics in the future. This is a key component of the course.
These will be assessed through homework, tests, in-class assignments and class participation. Not all assignments will be assessing all of the six areas. For each area assessed by a task the student will receive a point total. At the end of the course, the student will have a point total for each of the six areas. This will then determine how much of the allotted percentage the student will receive for that aspect. Some of these areas are considered to be more important in this class than others and will therefore be worth more towards the final grade. The break down in percentages is as follows:
MEMORIZATION OF FACTS 10%
MATHEMATICAL REASONING 15%
PROBLEM SOLVING 25%
UNDERSTANDING OF CONCEPTS 25%