Math 1331: Geometrical Inference and Reasoning

This is a problem-solving course in geometry, measurement and reasoning, originally designed to meet the needs of prospective mathematics teachers (and the standards to which they are held accountable in the state certification exams). Its prerequisite is Math 1330 (q.v.).

The rest of this page contains some information specific to the sections of Math 1331 taught by Dr. Kribs Zaleta. Some data may vary by instructor.

The page below contains essentially the same information as the syllabus handed out on the first day of class. Click here for a list of web links related to this course.

To see the data on the symmetries of regular polyhedra, click here.

To go to our class bulletin board and read or post messages, click here, select Math 1331-105 from the pull-down menu, and click on the "Enter the BBS" button below it.

Instructor Info:

Dr. Christopher Kribs Zaleta
Office: 483 Pickard Hall
Phone: (817) 272-5513
Fax: (817)272-5802
Personal home page:
Office Hours: Sorry, I'm on sabbatical in Mexico until fall 2004.

Course Info:

Where & When: days and times vary (check the online timetables), but usually in Room 304 Pickard Hall
Prerequisites: Math 1330 (q.v.)
Text materials: A course packet, available at Bird's Copies (on S. East St., 459-1688)
Course home page: (this page)
Syllabus: An approximate schedule with topics is given below (dates are for spring 2003).

Dates are from 2003 -- will be updated for spring 2004.
UnitTopic# HoursApproximate Dates
1The Basics 4Jan 13 - Jan 22
2Constructions 5Jan 24 - Feb 03
3Polygons 4Feb 05 - Feb 12
4Tessellations 4Feb 14 - Feb 21
5Polyhedra 3Feb 24 - Feb 28
Midterm exam 1Mar 12, in class
6Symmetry 7Mar 03 - Mar 26
-Spring break -Mar 17 - Mar 21
7Rigid Motions 2Mar 28 - Mar 31
8Non-Euclidean Geometries6Apr 02 - Apr 14
9Measurement 5Apr 16 - Apr 25
10Discovering Theorems 2Apr 28 - Apr 30
Final review 1May 02, in class
Final exam Wed May 07, 8 OR 11 AM

Last day for automatic withdrawal: February 21
Last day for withdrawal if passing: April 11
Class policy on drops, withdrawals, academic honesty, and accommodating disabilities follows the University policy on these matters. Copies can be obtained upon request.


This course is designed to prepare future elementary school teachers mathematically to teach math (as opposed to pedagogically, which is the goal of ECED 4311/EDML 4372). It does this in two main ways: by teaching math which is relevant (not identical) to the math they will be teaching, and by modeling a math classroom through problem-solving activities, cooperative groups, and holding students responsible for deciding (reasoning) what is correct.


There will be almost no lecturing in this course. To help you develop your intuitive reasoning and problem-solving skills, we will spend most of our class time working in small groups on problems from the course packet. An important part of learning to solve problems is being willing to struggle with a problem even after you get stuck, and this is one of the first things you will face this term. You may be surprised by how much you can do if you just keep at it!

We will usually discuss the problems in a large group after most groups have finished them. Sometimes you will be asked to write up your ideas and solutions, but always you are expected to think about the problems, participate in solving them, and communicate your ideas with others. Communicating your ideas clearly to others is as important as developing them in the first place.

Note that this is a math content course, and not a pedagogy course. We hope that taking this course will help you be a better teacher, but more by setting an example rather than teaching you math methods. Students who come out of this course generally feel a lot more comfortable about teaching math, and about being a mathematical authority in the classroom. Hang in there!


Your grade for the course will be determined by two exams (20% each), by attendance and participation (20%), and in large part by written work you will turn in (40%).

The exams will be similar in nature to the problems we work in class, but short enough that you should be able to complete them in the time given. A sample exam will be distributed before the actual exam in order to give you a closer feel for it, though you should not expect it to serve as an exact blueprint for the real thing. There will be a midterm and a final exam (both in our usual room); the dates are given above. Please mark these dates and times on your calendar now so as to avoid conflicts. In the event that a conflict arises, please see me as soon as possible so that we can resolve it.

Attendance and participation are a significant part of your grade because this course is more an experience than a set of material to be learned. Most of what I hope will happen for you in this course will take place inside the classroom, working in groups and talking with others. You may miss up to 3 days (excused or not) without penalty; after that it starts affecting your grade. Arriving late (after we have started class) or leaving early counts as half an absence. If you come late frequently or repeatedly, it will affect your attendance grade; you will also miss important announcements! Students with special needs, or who develop a medical condition or other situation which affects their attendance for several consecutive classes should consult with the instructor as soon as possible. Unless I tell you otherwise, every absence counts, even if you tell me about it.

It is also in your interest to participate in the group problem solving sessions since active learning is better than passive learning. Participation includes both small and large group work. If you don't feel comfortable answering questions, ask some of your own: that spurs discussion as much as an answer, and you won't be the only one with that question. Participation also includes coming to class prepared: bringing requested materials to class or completing a problem at home.

Daily homework apart from the write-ups (see below) will also be assigned regularly, checked, and included in the participation grade. Assignments will typically involve working on some specific part of the problem currently under study, and bringing the results to class ready for discussion.

Grading: This component of the grade is somewhat subjective, but here are some rules of thumb which I use in determining it. Your attendance acts as a multiplier: if you miss 5 classes, for instance, and we have 43 class periods during the semester, this part of your grade will be multiplied by (43-5)/43, or about 89\%. Your participation grade includes both large group (I expect everyone to speak up in large group discussion [or write on the blackboard, or post a message on the electronic bulletin board] at least a dozen days during the semester; that's less than once per week) and small group (in addition to observing small group dynamics, this includes daily homework). Besides the write-ups and reflections assigned roughly weekly (see below), I will usually ask everyone to do work on the current problem outside of class, and bring some tangible evidence of it to our next meeting, for me to check. This is necessary in order to ensure that all group members are prepared to discuss it. I will keep a running tally of whether people have done these. They don't have to be correct to be checked, but they do have to be complete. This means that if you have trouble, you need to get help before class, and not wait until class to ask questions about it.

The written work will have two components: write-ups (also called problem reports) and reflections. A write-up is a detailed solution to a problem we discussed in class. These write-ups should be readable independently of any worksheet on which they are based, in good English and either legibly handwritten in ink or word-processed. They should always include the following (although you need not use this form): 1. a statement of the problem at hand, 2. any strategies you used to attack the problem, 3. the solution you obtained, with an explanation of how you got it (and how you know it is complete), and 4. a conclusion that says what we can take with us from the problem. Communication of what you understand (even if it's not a complete understanding) is at least as much the point as finding the solution.

Write-ups in Math 1331 differ in some important ways from Math 1330 write-ups. Perhaps most significantly, they will typically involve more pictures (with careful attention to detail, accuracy and labeling) and fewer words -- even though the need for clarity and solid justifications remains.

I will also sometimes ask you to write a reflection on a rather less concrete issue, like "What does it mean to get stuck?" These essays, usually a page or two in length, will be graded more loosely, more on how much thought went into it than on organization and content.

I will let you know at the time I assign written work when it is due, but typically it will be due in class a week from the time it is assigned, and you will have roughly one assignment due per week.


Class Links Page: Click here.

Library: Barbara Howser is the Mathematics Librarian. She can be reached at (817)272-3000 and by e-mail at You can find useful research information for mathematics on the UTA library page.

Textbooks: In the past, students have asked about reference texts since we don't use a traditional textbook. The following texts may be helpful at times, though they do not follow our syllabus, nor are they in the least necessary for the course. I have a copy of these and other texts in my office which you may come browse.

O'Daffer, Charles, Cooney, Dossey and Schielack, Mathematics for elementary school teachers. Menlo Park, CA: Addison-Wesley (1998).

Billstein, Libeskind and Lott, A problem solving approach to mathematics. Sixth edition. Menlo Park, CA: Addison-Wesley (1998).

Alice F. Artzt & Claire M. Newman, How to use cooperative learning in the mathematics class. Reston, VA: NCTM (1990). (available in library)

These are your blackboards. Own the classroom.

Last revised September 3, 2003