Properties of the Real Numbers I
Please feel free to come by my office any time during scheduled office
hours. You are welcome to come at other times, but in that case you
might want to make an appointment, just to make sure that I will be
there then. You can make an appointment simply by talking to me
before or after class, by calling me at my office or at home, or by
You may also ask any questions directly via phone or email. If I'm
not in when you call, please leave a message on the voice-mail or
answering machine with your name, number, and a good time for me to
call you back. I will try to repond to your phone or e-mail message
as soon as possible.
I will also be available after class in the clasroom for a while
The problems in the course are intended to acquaint you with the
following concepts in roughly the following order: Counting and Whole
Numbers, Integers, Base Representations, Number Theory, Geometric
Congruence and Similarity, Ratio, Proportions, Rational Numbers,
Decimal Representations, Irrational Numbers, Data Analysis, and
Symmetry Transformations. In addition to these mathematical concepts,
you will become familiar with the following computer software:
ClarisWorks (word processor), Divide & Conquer, Geometer's Sketchpad,
and Function Probe.
Guiding Philosophic Principles
The purpose of this course is for you to become involved with a wide
variety of situations and contexts which give rise to mathematical
concepts essential for K-8 teaching. You will be expected to engage
in a dialogue between grounded activity and
Grounded activities will include situations arising from physical
activity with strings, sticks, blocks, cardboard, marbles, dice,
coins, cut paper, models, photographs, and anything else under the
Systematic inquiry will involve the fullest possible use of the tools
that are commonly available in our culture, including both
physical tools, such as rulers, measuring cups, scales,
stopwatches, thermometers, projectors, calculators, and computers; and
linguistic tools, such as words, numbers, symbols, drawings,
diagrams, tables, graphs, along with computer software
which can be considered as both a physical and a linguistic tool.
Mathematics is a dialogue between grounded activity and systematic
inquiry. This dialogue is a deep and essential element of what it
means to be human, and all humans are engaged in some form of this
dialogue. The refinement of one's expression of this dialogue is
achieved through a broader set of physical experiences, and clearer
communication tested in the context of social interaction.
Working in small groups with your classmates, or alone, you will
engage each problem or situation presented in class, and will attempt
to describe and explain the results of that engagement in a written
report. You must write your report yourself
(a private oral
exam is always possible, in case of irregularities). A description,
experiment, explanation or proof is anything which is both
meaningful to you and convinces other people of the
validity of your thoughts, words and activities. Reports may
incorporate any available media including written words, symbols,
pictures, diagrams, models, tables, graphs, videos, computer discs,
There will be an initial due date (approximately weekly), by which
time some work (however partial) must be turned in.
If you do
not turn in a report by the initial due date, you will not be able to
resubmit it; please see me as soon as possible if some emergency
prevents you from attending class and turning in your report
be returned as soon as possible with questions and comments, after
which you may respond, revise, amend, and then resubmit the project.
Resubmitted solutions will again be returned with comments and may
again be revised and resubmitted.
After the initial reports are returned, selected students will be
chosen to present their work in class. After such presentations
others may still continue to resubmit those same projects in their own
personal way making full or partial use of what has been presented.
Originality and diversity of expression will always be encouraged.
Each project will be returned with one of three marks:
If you eventually achieve a "chek" on 10 of the projects, you will get
a grade of C or better. If you eventually achieve a "check plus" on
11 of the projects, you will get an A.
- "check minus"
Some engagement with the project, but substantial questions remain.
A well reasoned explanation, but some questions remain.
- "check plus"
A complete and thorough explanation, no further questions.
Remember to pace yourself in a reasonable way. It is virtually
impossible to turn in well-written resubmissions if you leave them all
until the end of the semester, so the following deadlines will apply:
Your final grade will depend on a portfolio of all your
submissions for the semester; therefore, keep all your
(even after turning in subsequent resubmissions for the
same project). Your portfolio will be due on Wednesday, May 6.
- Resubmission of Projects 2-5 will not be accepted after 3:00
p.m., Thursday, March 5.
- No more than three resubmitted projects will be accepted after
3:00 p.m., Tuesday April 21.
- No more than one resubmitted project will be accepted after
Thursday, April 30.
Because of the experimental nature of this class, on-time attendance
is mandatory at all times. If you have more than four unexcused
absences, you will be dropped from the class with an F. I will
usually excuse an absence if you tell me about it in advance, or, in
cases of emergencies, as soon as possible afterwards.
All students will be required to purchase several computer discs, a
ruler, a compass, scissors, and other incidental supplies as required
by the problems. I recommend the purchase of a Texas Instruments
Math Explorer Calculator, since that is what is widely available in
most schools. A textbook is not required, but many of the
topics that will emerge in this course are discussed in the book
A Problem Solving Approach to Mathematics for Elementary School
Teachers, by Billstein, Libeskind, and Lott, 6th ed. (1997), Addison
Wesley. Students may wish to consult this book at their discretion.
Students who work together might easily share a textbook. The math
department is working on making this book available in the UTEP bookstore.
Mathematics is not a march down any particular road, but
rather a walk in a garden with many branching paths that circle and
wind back onto themselves. Visitors stroll in many different ways,
pausing to look down at a single small flower, or gaze out over an
enchanting vista, or perhaps even to water, weed or plant (for a
garden is a human creation constructed within the constraints of
life). Each new return brings its own special set of views and
experiences. - David Dennis