Fundamentals of Math from an Advanced Standpoint
TuTh 1:30-2:50, LART 207; 3 credit hours
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MATH 3325, or an equivalent course where you learn the basics of writing proofs. I further recommend that you take this course only after taking several other advanced (proof- based) courses.
This course was designed as a capstone experience to your mathematical preparation to teach high school math, by being the connection between your college courses and the topics you will teach in high school. However, this is not a pedagogy course, or even a math methods course, and it is not a repeat or review of high school math (though you may find yourself understanding better some of the topics and ideas you first saw in high school); in particular, you will have to prove theorems.
Upon successful completion of this course, you will be able to find for yourself the deeper mathematics underlying topics from high school. In particular, you will be able to explain why the rules and procedures of high school math work as they do, and why the definitions are set as they are. You will be able to place high school math problems in larger context; you will be able to show how they generalize, and what other problems they relate to.
Particular topics include real and complex numbers, functions, algebraic structures and solving equations, natural numbers, divisibility properties of integers and polynomials, and number fields. (Note that geometry is part of a different course at UTEP.)
Mathematics for High School Teachers -- An Advanced Perspective, Usiskin, Peressini, Marchisotto, and Stanley, Part I (Chs. 2-5).
We may skip some chapters, as announced in class.
The textbook is required at all class meetings.
You will spend a substantial amount of time outside of class reading
the textbook. The course will be structured to encourage and support
you in this endeavor. In-class activities will center around our
making use of what you have read outside of class.
Homework and Participation:
For each section of material we encounter, there will be three kinds of homework, as follows (more details are on a separate handout):
- Advance preparation (10%):
You will read the section carefully, write responses to reading questions, create some of your own questions, and reflect. The written part of this assignment will be due before we discuss the material in class.
- Warmup exercises (10%):
On the day of our class
discussion over the material, we will discuss easier warmup exercises.
You will prepare your answers, in writing, before class, and the class
will share answers in small groups or whole class discussions.
I expect everyone to attend and participate actively in class, in
particular to speak up during class discussion with questions and
ideas, and to work well with others. Your active participation in
class will constitute a substantial part of this part of your grade
for the course.
- Main exercises (10%):
After our class discussion over
the material, you will turn in clearly-written solutions to harder
homework problems. These will generally be due weekly.
Written assignments (for all three kinds of homework) will not be
accepted after they are due, except in extenuating circumstances that
you explain to me as soon as possible. Incomplete homeworks will be
accepted, though, so please turn in whatever work you have completed
when homework is due. You are encouraged to work together on your
homework, but you must write up your solutions by yourself.
Class presentation (20%)
Small groups of students will design and conduct all classroom activities for part of one class session and will be responsible for the content covered in those sessions. Each group will also create homework assignments.
Final project (20%)
There are mathematics problems that require more attention than just one day. Some of these problems are found at the end of the chapters in the textbook. Small student groups will complete one of these problems and present the results in class and in a written report during our scheduled final exam period:
Thu., 13 Dec., 1:00-3:45 p.m.
Exams (15% each)
There will be two in-class, closed-book exams on the following days:
Thu., 4 Oct.
Thu., 15 Nov.
Each exam will cover material from the beginning of the semester, though the second exam will focus more on material since the first exam. Makeup exams can be given only in extraordinary and unavoidable circumstances, and with advance notice. There will be no final exam (but note the final project presentations scheduled during finals week, above).
Academic dishonesty: It is UTEP's policy, and mine, for all suspected cases or acts of alleged scholastic dishonesty to be referred to the Dean of Students for investigation and
appropriate disposition. See Section 1.3.1 of the Handbook of Operating Procedures.
Due to the course structure, attendance is mandatory. There is no particular penalty
for missing a particular class, but you cannot get a good participation grade if you miss too many classes. I will usually "excuse" an absence if you tell me about it in advance, or, in cases of emergencies, as soon as possible afterwards.
My goal is for class meetings and activities to complement, rather than echo, the textbook, and thus for every class to be worth attending.
Drop date: The deadline for student-initiated drops with a W is Friday, November 2. After this date, you can only drop with the Dean's approval, which is granted only under extenuating circumstances.
I hope everyone will complete the course successfully, but if you are having doubts about your progress, I will be happy to discuss your standing in the course to help you decide whether or not to drop. You are only allowed three enrollments in this course, and students enrolled after Fall 2007 are only allowed six withdrawals in their entire academic career, so please exercise the drop option judiciously.
Courtesy: We all have to show courtesy to each other, and the class as a whole, during class time. Please arrive to class on time (or let me know when you have to be late, and why); do not engage in side conversations when one person (me, or another student) is talking to the whole class; turn off your cell phone (or at least set it to not ring out loud), and do not engage in phone, email, or text conversations during class.
Disabilities: If you have, or suspect you have, a disability and need an accommodation, you should contact the Center for Accommodations and Support Services (CASS) at 747-5148, firstname.lastname@example.org, or Union East room 106. You are responsible for presenting to me any CASS accommodation letters and instructions.
Exceptional circumstances: If you anticipate the possibility of missing large portions of class time, due to exceptional circumstances such as military service and/or training, or childbirth, please let me know as soon as possible.