Syllabus Fall, 2000
Course: Math 255, Mathematics for Elementary and Middle School Teachers, 4 credits
Instructor
Dr. Larry Krajewski
MC 526
e-mail: llkrajewski@viterbo.edu
Phone: 796-3658 [office]
782-1648 [home] (call before 10 p.m. please)
Hours: 2M, 11W, 8:30F & by appointment
Prerequisites:
Grade of C or better in Math 155
Text
Mathematics for Elementary Teachers, by Tom Bassarear, Houghton Mifflin, 1997.
Final Exam
Section 1 (9:00 class) Section 2 (10:00 class)
Tuesday, December 19 Monday, December 18
7:40 - 9:40 a.m. 12:50 - 2:50 p.m.
Description
This course is designed to introduce the preservice K-9 teacher with ideas,
techniques and approaches to teaching mathematics. Manipulatives, children's
literature, problem solving, diagnosis and remediation, estimation, mental
mathematics, equity issues, and the uses of the calculator are interwoven
throughout the topics presented. The math content areas are the arithmetic
operations and number theory.
The Viterbo College Teacher Education Program has adopted a Teacher As
Reflective Decision Maker Model. Each course is designed to contribute to the
development of one or more of the knowledge bases in professional education.
This course contributes to the development of the knowledge bases: Knowledge of
the Learner, Curriculum Design, Planning and Evaluation, and Instructional and
Classroom Management.
Resources
You may qualify for free tutoring in the Learning Center.
Methodology
Lecture, class discussion, small group work, student presentations.
Todd Wehr Library The following books are on reserve:
Solutions Manual for text
Sample Portfolio by Jennie Schoonover
Goals
To help students:
1. learn to value mathematics;
2. learn to reason mathematically;
3. learn to communicate mathematically;
4. become confident in their mathematical ability; and
5. become problem solvers and posers.
Objectives
Upon successful completion of this course, the student will be able to:
explore, conjecture, reason logically and use a variety of mathematics
methods effectively to solve nonroutine problems.
establish classroom environments so that his or her students can explore,
conjecture, reason logically and use a variety of mathematics methods
effectively to solve nonroutine problems and develop a lifelong appreciation
of math in their lives;
become familiar with educational research on effective teaching of
mathematics.
Student Responsibilities
One cannot benefit from or contribute to a class discussion or activity unless one is
physically present (this a necessary condition, not a sufficient one). Attendance is
required. Call me (796-3658) if you will not be in class. A valid excuse is necessary
to miss class. Unexcused absences may lower your grade for the course.
Assigned readings of the texts and handouts need to be done if meaningful
discussion can occur.
As teachers you should appreciate the importance of class participation. Your active
participation makes the course go.
Math is not a spectator sport. Assigned problems and textbook exercises are ways
for you to develop problem solving skills and reflect on your learning.
Content
I. Foundations for Learning Mathematics
A. Getting Comfortable with Mathematics
B. Problem Solving and Reasoning
C. Patterns
D. Communication
E. Connections
F. Putting It All Together
II. Fundamental concepts
A. Sets
B. Functions
C. Numeration
III. The Four Operations of Arithmetic
A. Addition and Subtraction
B. Multiplication and Division
C. Mental Arithmetic and Estimation
IV. Number Theory
A. Divisibility and Related Concepts
B. Primes and Composites
C. Greatest Common Factor and Least Common Multiple
V. Extending the Number System - Integers <if time permits>
A. Operations With Integers
Requirements
¥ Two math activities, one for K-5, the other for grades 6-8.
¥ A problem-solving portfolio representing your work during the semester.
¥ Learning journal from class
¥ Two exams and a final comprehensive exam
¥ A problem notebook with assigned problems from the text and class. You
must work out the solutions. Merely copying answers from the solutions
manual is not appropriate.
¥ Six summaries of articles in professional journals on the following topics:
Problem Solving <due September 15>
Addition of Whole Numbers <due September 29>
Subtraction of Whole Numbers <due October 13>
Multiplication of Whole Numbers <due November 3>
Division of Whole Numbers <due November 17>
Number Theory <due December 8>
[Some good sources are Arithmetic Teacher, Teaching Children Mathematics,
Mathematics Teaching in the Middle School, AIMS, and School Science and
Mathematics.]
The purpose of this assignment is to acquaint you with some resources outside of
the textbook and to introduce you to some ideas or activities that you may want to
share with the class when we are investigating the appropriate topic.
Please follow these guidelines:
Include a copy of the article with your summary.
Use the reporting form included in your packet.
Articles must be at least two pages long in the original citation.
Articles taken from the internet must be complete (No missing pictures,
diagrams, or equations.)
Articles must have appeared in professional journals.
Evaluation
Points
Class journal 5
Problem notebook 10
Readings 3
Portfolio 20
Math activities 2
tests 60
A Note to You
This is a course for prospective elementary and middle school teachers about
how children learn mathematics and how to create positive, developmentally-
appropriate mathematics instruction. Since we have all gone to elementary school,
we have learned and "know" the mathematics which will be addressed in this course;
in fact, we may know it so well that we have forgotten what it was like to ever not
know it. Or, because of inadequate past instruction, we may feel we "know" certain
mathematical topics but have never really understood them, or we may even dislike
the subject. If this is the case, consider this course an opportunity to break the cycle
of negative, disempowering mathematics teaching. Mathematics can be an
intellectual adventure, a powerful tool, and a creative experience for children. As a
teacher, you can make it so.
Some of you may have had mathematics courses that were based on the
transmission, or absorption, view of teaching and learning. In this view, students
passively ÒabsorbÓ mathematical structures invented by others and recorded in texts
or known by authoritative adults. Teaching consists of transmitting sets of
established facts, skills, and concepts to students. I do not accept this view. I am a
constructivist. Constructivists believe that knowledge is actively created or invented
by the person, not passively received from the environment. No one true reality
exists, only individual interpretations of the world. These interpretations are shaped
by experience and social interactions. Thus, learning mathematics should be
thought of as a process, of adapting to and organizing oneÕs quantitative world, not
discovering preexisting ideas imposed by others. It is one way to make sense of the
world.
Consequently, I have three goals when I teach. The first is to help you develop
mathematical structures that are more complex, abstract, and powerful than the
ones you currently possess so that you will be capable of solving a wide variety of
meaningful problems. The second is to help you become autonomous and self-
motivated in your mathematical activities. You will not ÒgetÓ mathematics from me
but from your own explorations, thinking, reflecting, and participation in discussions.
As independent students you will see your responsibility is to make sense of, and
communicate about, mathematics. Charles Schultz, creator of "Peanuts", compared
people to multispeed bikes and noted that "most of us have gears we do not use."
Hopefully you will see mathematics as an open-ended, creative activity and not a
rigid collection of recipes. And the last is to help you become a skeptical student
who looks for evidence, example, counterexample and proof, not simply because
school exercises demand it, but because of an internalized compulsion to know and
to understand,
I want to help you learn to do something different from and better than what
you have experienced as pupils in previous mathematics classes A mathematics
methods class is about mathematics, about children as learners of mathematics,
about how mathematics can be learned and taught, and about how classrooms can
be environments for learning mathematics. ItÕs a class where the students learn
about learning mathematics while they themselves are learning mathematics.
As a teacher I have come to realize that when I teach mathematics I teach
not only the underlying mathematical structures but I am also teaching my students
how to develop their cognition, how to see the world through a set of quantitative
lenses which I believe provide a powerful way of making sense of the world, how to
reflect on those lenses to create more and more powerful lenses and how to
appreciate the role these lenses play in the development of their understanding.
So I ask your help in establishing a mathematical community where one uses
logic and mathematical evidence as verification rather than the teacher, where
mathematical reasoning replaces the memorization of procedures, and where
conjecturing, inventing, and problem solving are encouraged and supported.
You may find this experience frustrating at times. Persevere! Eventually I
hope you will own personally the mathematical ideas you once knew unthinkingly or
only peripherally (and sometimes anxiously). I want you to become competent and
confident using mathematical ideas and techniques. I want you to be ready to learn
how to get other persons actively involved in problem solving. To nurture a
mathematical idea in the mind of a child might be easier if it first thrived in the mind
of the childÕs teacher.
In training a child to activity of thought, above all things we must beware of what I
will call "inert ideas" - that is to say, ideas that are merely received into the mind
without being utilized, or tested, or thrown into fresh combinations . . . Education
with inert ideas is not only useless: it is, above all things, harmful. Except at rare
intervals of intellectual ferment, education in the past has been radically infected
with inert ideas . . . Let us now ask how in our system of education we are to guard
against this mental dryrot. We enunciate two educational commandments, "Do not
teach too many subjects," and again, "What you teach, teach thoroughly." . . . Let the
main ideas which are introduced into a child's education be few and important, and
let them be thrown into every combination possible. The child should make them his
own, and should understand their application here and now in the circumstances of
his actual life. From the very beginning of his education, the child should experience
the joy of discovery. (Alfred North Whitehead, The Aims of Education)
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Americans with Disabilities Act
If you are a person with a disability and require any auxiliary or other accommodations for this class,
please see me and Wayne Wojciechowski, the Americans With Disabilities Act Coordinator (MC
320 <796- 3085>) within ten days to discuss your accommodation needs.