Text

Course topics

Course objectives

Class work

Assignments

How your grade will be calculated

Materials needed

This document describes a general plan for the course. Changes may be necessary.

Text: Mathematics for Elementary Teachers , first edition, and the accompanying Class Activities manual by Sybilla Beckmann, published by Addison-Wesley. These can be purchased from the UGA bookstore. Please bring the activity manual to class.

Course topics: We will cover chapters 12 - 15 and sections 7.3 - 7.6 of the textbook. The specific topics are:

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. Solving algebra word problems with and without variables. 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, part of the course will 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.

Course objectives: To strengthen and deepen knowledge and understanding of fractions, ratios, 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 solve problems in a variety of ways, including informal methods, such as with pictures, as well as standard methods in mathematics. To learn to pose and modify mathematical problems.

Our focus in this class is on mathematics content, not methods of teaching. In order to be able to teach mathematics well, you must know not only the math you teach, but also how this math progresses and develops. In other words, you must know how the math you teach provides a foundation for your students' future mathematics learning. Therefore, for the topics we study, we will consider simple, concrete approaches and methods of solution as well as more advanced approaches and methods of solution, and we will relate different approaches.

Class work: This class is part of your preparation as a professional. As a professional, you should engage in collegial discussions about professional practice and you should constantly seek to enhance and refine your professional knowledge. To receive a full participation score, your work in class must consistently exhibit several or all of the following:

• interest in mathematical ideas
• interest in different ways of approaching mathematical ideas
• careful listening to different ways of solving a problem
• careful evaluation of proposed methods of solution
• attempts to connect the course material to your experiences with children and teachers at schools
• attempts to connect the course material to your future teaching
• attempts to connect the course material to the Georgia QCCs the Georgia Performance Standards (GPS) (which phases in starting fall 2005 and replaces the QCCs) and to NCTM's Principles and Standards for School Mathematics
• interest in learning with and from others

Assignments:

In addition to regular homework assignments, you will have a field experience assignment. In completing this field experience assignment, please refer to the detailed description on the web site, not the general description of the assignment in the field packets for mentor teachers.

I encourage you to work on homework assignments with your classmates. Of course, you must adhere to UGA's Academic Honesty Policy. Therefore, always write your homework up on your own, using your own words to express the ideas you have discussed with others. Do not allow anyone to copy your work. When you discuss assignments with others, all partners should "give and take" ideas.

Late homework will not be accepted. Please consult with me as soon as possible if you are unable to hand in an assignment due to an illness or emergency.

How your grade will be calculated:

I will grade all your work on a 5 point scale, and will assign points as follows:

# of points	description	characteristics
5.25 points	exemplary	work that could serve as a model for other students
5 points	very good	correct work that is carefully prepared, thorough, and fully meets the grading criteria below
4 points	competent	good, solid work that is largely correct and meets most of the grading criteria below
3 points	basic	work that has merit but also has significant shortcomings
2 points	emerging	work that shows effort but is seriously flawed
0 points	no credit	no work submitted, or no serious effort shown

Grading criteria: I will determine your score on assignments and tests by the extent to which your work meets the following criteria:

• The work is factually correct, or nearly so, with only minor, inconsequential flaws.
• The work addresses the specific question or problem that was posed. It is focused, detailed, and precise. Key points are emphasized. There are no irrelevant or distracting points.
• The work could be used to teach a student: either a child or another college student, whichever is most appropriate.
• The work is clear, convincing, and logical. An explanation should be convincing to a skeptic and should not require the reader to make a leap of faith.
• Clear, complete sentences are used. Mathematical terms and symbols are used correctly. If applicable, supporting pictures, diagrams, and/or equations are used appropriately and as needed.
• The work is coherent.

Your grade will be based on tests, homework, a field assignment, class participation, and a comprehensive final exam. I expect to give 1 test during the semester, right before the field experience. I will calculate your course score using the following percentages.

I expect to assign letter grades as follows.

for scores from	up to	letter grade
4.7	5 or above	A
4	4.7	B
3.5	4	C
2.5	3.5	D
below 2.5		F

Materials needed: Please have a calculator available for your use. Please bring your activity manual to class. You may wish to have colored pencils or markers on hand since we will frequently solve problems with the aid of pictures.