Text

Course topics

Course objectives

How your grade will be calculated

Types of assignments and grading criteria

Class work and attendance policies

Materials needed

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

Text: Mathematics for Elementary Teachers , volumes I and II, preliminary edition, and the accompanying Class Activities manuals by Sybilla Beckmann, published by Addison-Wesley. These can be purchased from the UGA bookstore. For now, please bring the volume I activity manual to class. I will let you know when to bring the volume II activity manual to class.

Course topics:

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, 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.

Critique of mathematics lessons.

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.

How your grade will be calculated:

We will grade all your work on a 5 point scale, and we 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 careful and thorough
4 points	competent	good, solid work that is largely correct
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

Please also see the more detailed grading criteria below.

Your grade will be based on tests, homework, 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

Types of assignments and grading criteria:

You will work on several different types of assignments throughout the semester: don't hand in assignments, checked assignments, scored assignments, and your field experience assignment.

When you write up assignments, please refer to Elizabeth Edward's writing tips. I will take off points for sloppy writing.

I encourage you to work on assignments with your classmates. Of course, you should adhere to UGA's Academic Honesty Policy, as described in http://www.uga.edu/ovpi/honesty/main.html. 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.

Field experience assignment is due Wednesday, April 2. In completing this 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.

Don't hand in assignments: Most sections in the text include a number of exercises that have detailed solutions. The exercises will be assigned for you to solve without handing in your work. Read the solutions only after you have seriously attempted to solve the exercises: by grappling with the exercises you will learn much more than if you simply read the solution right away. The exercises will help prepare you to solve the problems, so do not skip them. The solutions to the exercises provide you with many examples of good mathematical explanations: use them as models for your own writing of mathematical explanations. In many cases, there is more than one way to solve an exercise. Therefore your solution need not be identical to the given solution in order to be correct. If in doubt, please check with me or with the teaching assistant.

Checked assignments will give you an opportunity to develop ideas and deepen your thinking without holding you to the polished level of performance that is expected on the scored assignments. Some checked assignments may ask you to solve a problem in the book and some may ask for exploratory writing. A checked assignment will receive a grade of check, of check-minus, or of 0 as follows.

A score of check, which counts as 5 points, will be given to work with the following characteristics:

• The work addresses the problem that was posed and makes significant progress.
• The work was done with care and effort: it is neatly written and is understandable.

A score of check-minus, which counts as 3 points, will be given to work that represents a serious attempt but that fails to meet the standards set for a check.

A score of 0 will be given to work that was not handed in or that does not represent a serious attempt.

A checked assignment may be re-assigned as a scored assignment, or there may be a test question related to the checked assignment. Therefore, you should make your best effort on these assignments, and you should follow class discussions on them closely.

Scored assignments will ask you to produce polished writing. Usually, a scored assignment will either ask for an explanation of a fact or phenomenon in elementary mathematics or it will ask you to produce an example of a problem or activity that could help children learn a mathematical concept, and a discussion of how and why that problem or activity would be useful for teaching the concept in question. I will determine your score on such an assignment by the extent to which your work meets the following criteria:

• The work is factually correct, or nearly so, with only minor flaws (for example, a minor mistake in a calculation).
• The work addresses the specific question or problem that was posed. It is focused, detailed, and precise. There are no irrelevant or distracting points.
• The work is clear, convincing, and logical. In the case of an explanation, the explanation should have the following characteristics:
  • The explanation could be used to teach another (college) student, possibly even one who is not in the class.
  • The explanation could be used to convince a skeptic.
  • The explanation does not require the reader to make a leap of faith.
  • Key points are emphasized.
  • If applicable, supporting pictures, diagrams, and/or equations are used appropriately and as needed.
  • The explanation is coherent.
  • Clear, complete sentences are used.

Class work: We will frequently work in small groups during class. When you work in a group, please make sure that everyone in your group has a chance to think about the question and has an opportunity to discuss and debate it. At times, this may mean that you should "hold back" a little, at other times you may need to ask your group to wait a moment for you to think about something. Although it can be tempting to listen to someone else's solution before thinking deeply about a problem, the process of grappling actually helps us learn and understand. Therefore please be sensitive to each other and allow everyone time to think.

Attendance is required. Unexcused absences will result in a lowering your course score by .25 for each unexcused absence beyond 1. After 3 or more unexcused absences, your grade may be lowered even further, or you may be dropped from the course. You are responsible for all information and announcements given in class, even if your absence is excused. Please make every effort to arrive in class on time. Late arrivals can be disruptive, and can cause you to miss important material or announcements. Two tardy arrivals will count as one absence.

Materials needed: Please have a calculator available for your use.