Properties of the Real Numbers I

Spring 2001

During spring break, the computer lab in the Education building will not be open. Also, the computer lab in Bell Hall will not generally be open, but if you arrange for a group of at least two students to come at a specified time (Mon-Thu, 8:30-4:30), I can open the lab for you. So let me know if you and at least one friend want to use the lab, and during what time.

Also, I will be available in my office (BELL 303) during spring break, at least Mon-Thu 8:30-4:30. If you turn in resubmissions during this time, I will generally be able to get them back to you within 2-3 days.


Instructor: Dr. Art Duval

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 sending e-mail.

You may also ask any questions directly via phone or e-mail. 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 respond to your phone or e-mail message as soon as possible.

Block IA:

This course is being team-taught with ELED 3302 and ELED 3310, the other two courses in the block. You will teach some of the projects from this class to students at Wiggs Middle School once per week, as part of ELED 3302. Additionally, our class will model some of the techniques you will learn in ELED 3310, and the content for these two courses is somewhat aligned.


The problems in the course are intended to acquaint you with the following concepts in roughly the following order: Counting and Whole Numbers, Integers, 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 systematic inquiry; this dialogue is what constitutes mathematics.

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 sun. 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.

Course Expectations

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. You are expressly prohibited from consulting with anyone who has taken this course before, or seeing their notes or reports.

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, etc.

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 contact me as soon as possible if some emergency prevents you from attending class and turning in your report.

Reports will 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. Do not just resubmit the parts of your report that there were questions on; each resubmission must be able to stand on its own. Thus, you are required to use computer word-processors to produce your reports.

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.

Some projects will have final due dates, after which there can be no more resubmissions, so that we may have a final discussion before you teach that project to the Wiggs students.

Each project will be returned with one of three marks:

"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.
More specific details of what is required for these grades will be available with each project.

Additionally, there will be three common assignments for all three courses in the block: a journal; a lesson plan and a videotape of that lesson (together treated as a single assignment for this course) being taught at Wiggs; and a final essay. I will be looking especially for math content in each of these. Each will count as one project grade for this course, and there are no resubmissions for any of them.

There will be a total of 15 project grades. If you eventually achieve at least 12 "check"s, you will get a grade of C; if you eventually achieve at least 8 "check plus"s and 6 "check"s, you will get a B; and if you eventually achieve at least 13 "check plus"s and 2 "check"s, you will get an A.

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 no more than two resubmitted projects will be accepted after the beginning of class, Mon., Apr. 23. Your final grade will depend on a portfolio of all your submissions for the semester; therefore, keep all your submissions (even after turning in subsequent resubmissions for the same project). Your portfolio will be due on Thu., May 3.


Because of the experimental nature of this class, on-time attendance is mandatory at all times. If you have more than two 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 Plus Calculator, since that is what is widely available in most schools.

Final Word

"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