This page
describes a general plan for the course. Changes may be necessary.
Text: Mathematics for
Elementary Teachers , second edition, (purple with zebras) and the accompanying Class
Activities
manual by Sybilla Beckmann, published by Addison-Wesley. These can be purchased
from the UGA bookstore and other bookstores. Please bring the
activity manual to class.
Course
topics:
Problem solving (chapter 1), numbers and the decimal system (chapter 2), fractions
(chapter 3), addition and subtraction (chapter 4), multiplication (chapter 5),
multiplication of fractions, decimals, and negative numbers (chapter 6),
division (chapter 7 only through section 7.2 or 7.3). The course focuses on the
arithmetic taught in elementary school and a little bit beyond elementary
school and goes deeply into this material.
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.
Preparation
for your teaching:
This course is part of your preparation to become an elementary school teacher who
will teach math. The importance of understanding the math you will teach well
cannot be overstated. Teacher quality is known to be a major factor in student
achievement. Students who build a good foundational understanding of the
mathematical ideas in elementary school will be ready for middle school math
and beyond. Students who don’t have good mathematical foundations in elementary
school often get stuck at algebra and these students frequently don’t finish
high school, thus limiting their opportunities.
Our focus in
this course is on the mathematics content itself and not the methods by which
you will help children learn math. Even so, a number of the activities we will
do in class can readily be modified for use in elementary school (or middle
school). However, we will often go beyond what is feasible with typical
students in elementary school. This is to help you understand the material more
deeply and to prepare you to guide your students toward “where the math goes
next.”
The
responsibility of teaching math to children may seem daunting and scary, but we
have designed our math and math methods courses here at UGA (MATH 5001, 5002,
5003, and EMAT 3400, 3410) to prepare you for this important responsibility. Of
course, it is up to you to take the opportunities these courses provide and to
study hard and learn the material well for the sake of your future students. We
also hope that you will find the courses interesting and engaging and that you
will seek to develop an enthusiasm for math that you will pass on to your
students.
Class
work:
As a teacher, you will have the important responsibility of helping your
students understand mathematical ideas and ways to solve math problems. To help
prepare you, we will often ask you to explain a mathematical idea, a line of
reasoning, or why a solution method is valid to a classmate or to the whole
class. As a teacher you will also need to determine how your students are
thinking about mathematical ideas so that you can address misconceptions and
build on what your students know. This means you will need to listen carefully
to your students’ mathematical ideas. So in class, we will ask you to listen
carefully to other students’ methods of solution, and we will sometimes ask you
to restate or ask a question about another student’s idea, or whether you agree
or disagree with a statement. Class time is a time for us to think ideas
through and to evaluate the ideas. Even answers that ultimately prove to be
incorrect can provide invaluable learning opportunities when we determine where
the flaws lie. In order to make productive use of our class time, and as part
of your preparation to teach mathematics to children, all students (and the
instructor and teaching assistants too!) are asked to do the following in
class:
Because
our interactive work in class is an important component of this course, class
attendance is required. In the event of an illness or emergency, please contact
Dr. Beckmann as soon as possible. Students with four or more unexcused absences
will be dropped from the course.
Writing
Intensive Program:
This section of MATH 5001 is part of the Writing
Intensive Program. The Writing Intensive Program is designed to help courses
teach the writing process within various disciplines. Although you have taken
English courses on writing, and although these courses will help you with all
your writing, mathematical writing has its own special features. In
mathematics, we seek coherent, logical explanations, in which the desired
conclusion is deduced from starting assumptions.
Our graduate
teaching assistants, Whitney Montgomery and Matt Mastin, have been trained by
the Writing Intensive Program to help you learn to write good mathematical
explanations. Whitney and Matt will give you feedback to help you improve your
explanations over the course of the semester.
Why are we
emphasizing writing in this course? To be an effective teacher of mathematics,
you need to understand the mathematical ideas you will teach well and beyond
the level at which you will discuss them with your students. By writing your
initial thoughts and then revising your writing to produce clear, thorough,
well thought out explanations, you will have a chance to develop and refine
your understanding of the ideas you will teach. Because of the benefits of
writing, we think that the writing intensive format is a perfect fit for this
course.
Types of
assignments:
All assignments will be posted on the links on the main course page. Some
assignments may require that you access WebCT. You should expect to spend at
least 2 to 3 hours outside of class for each hour in class.
Written
homework assignments to turn in: Expect to have a written assignment due at
every class. These assignments must be typed. You may write by hand any equations, pictures,
diagrams, or the like. Pictures and diagrams can be inserted either within the
body of the text or they can be labeled and placed at the end of the document
(and in this case you should refer to them by their label within the text).
Your written assignments will generally be fairly short, but we expect your
work to be highly polished. Turn in only well thought out second or third (or
fourth ...) drafts. Mathematics requires precise language, so attend closely to
the way you express your ideas. When you teach, you will also need to take care
to use correct and precise language, but we will hold you to an even higher
standard of expression than would be realistic all the time in a classroom with
children. In grading your work we will be looking for the extent to which it
meets the following criteria:
Explain all your solutions unless there are explicit instructions not to.
You
are encouraged to form study groups and to work on homework assignments with
your classmates. (Perhaps some of you might like to form facebook groups.) 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. It is not academically honest to simply read someone else’s work
and then put it in your own words. Instead, when you work with others, you must
participate in the development and refinement of the ideas by discussing them.
All partners should “give and take” in the discussion. It is not academically
honest to allow others to copy your work.
Homework is due
at the beginning of class. Because grading late homework adds a significant
time burden, late homework cannot be accepted, even with a valid excuse. Please contact Dr. Beckmann
as soon as possible if you are unable to hand in an assignment due to an
illness or emergency. We will drop up to 3 assignments for which you have a
valid excuse.
Please save
returned homework since we expect to allow you to revise and resubmit a few
selected assignments.
Reading
and “don’t hand in” assignments: Expect to have a reading assignment due after
every class. The reading is designed to help you shore up the ideas discussed
in class and be ready for the topic to be discussed in the next class. The
“don’t hand in” assignments will consist mainly of problems whose solutions are
given in the book. You should work the problems first without looking at the
solutions and then read the solutions and compare them with your own. It’s a
good idea to discuss the “don’t hand in” problems with a study group. Expect
weekly short quizzes on the “don’t hand in” problems and the reading.
Minute
papers:
Occasional “minute papers” will be assigned to do either at the end of class or
to post on WebCT before the next class. These minute papers are an opportunity
to think through the day’s material by writing freely and quickly about it,
capturing any insights you had or questions and stumbling blocks you hope to
follow up on. Minute papers will be graded only for completion, not for
accuracy.
No
calculators allowed: Since
our focus in this course is on how and why various procedures in arithmetic
work, the use of calculators is not allowed unless explicitly stated otherwise.
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 |
Your course
grade will be based on 3 hour tests, quizzes, homework assignments, and a comprehensive
final exam. The tests and final exam will emphasize problems that require
you to write clear, complete, logical explanations.
|
hour tests, 3 at 13%
each |
39% |
|
quizzes, total |
15% |
|
minute papers |
3% |
|
homework |
18% |
|
final exam |
25% |
Letter grades
are expected to be assigned as follows.
|
for scores from |
up to |
letter grade |
|
4.6 |
5 or above |
A |
|
4.5 |
4.6 |
A- |
|
4.4 |
4.5 |
B+ |
|
4.1 |
4.4 |
B |
|
4.0 |
4.1 |
B- |
|
3.9 |
4.0 |
C+ |
|
3.6 |
3.9 |
C |
|
3.5 |
3.6 |
C- |
|
2.5 |
3.5 |
D |
|
below 2.5 |
|
F |
Materials
needed: Please
bring your activity manual to class.
Observers: You may notice that
some students never turn in any work and never take any tests! How do they get
away with it? These students are graduate students who are observing MATH 5001
in preparation for eventually teaching courses for prospective elementary
teachers.
Research
project:
A research project that is studying the mathematical preparation of elementary
teachers will be videotaping during the semester. Videotaping will focus on the
instructor, not on the students. If you do not want your image captured on the
videotapes you may choose your seating accordingly. The research project will
ask you to complete a pre- and post-test. These tests do not count toward your
grade and are voluntary. We hope you will participate in the research project
since we believe it will provide useful information on how to improve teacher
preparation.