Math 67-319
Syllabus
Fall 2007
Instructor: Dr. Carol Seaman
Office: 111 Swart
E-mail contact: seaman@uwosh.edu
Phone: 424-1059
Office hours: 11:30am–12:30 MWF, 12:30–1:45pm T, or by appointment (don’t hesitate to ask –
we will find a time that works!)
Textbook and Materials: BIG Ideas in Mathematics for Future Middle Grades Teachers and
Elementary Math Specialists: Big Ideas in Infinite Processes, Carol Seaman & Jennifer Szydlik
TI-83+ Graphics Programmable Calculator, Texas Instruments (Other graphing calculators are fine
too), graphing paper, compass, and straightedge
Prerequisite: Math 104 (or equivalent), Math 211 and 217, each with a grade of C or better.
Website: You will find the course site on D2L. Please check it regularly for course information,
assignments, announcements, and grades.
Welcome to Math 319, Infinite Processes for Elementary and Middle School Programs. We meet
MTWF from 1:50 to 2:50 pm in Swart 3.
Course Outline and Goals
This course is designed to provide you with an appreciation for the beauty and power of the
mathematics of infinite processes, an historical perspective on the development of the calculus, and a
conceptual understanding of the mathematical ideas involved in that development. We begin with a
look at the infinite in our number system (primes, rational and irrational numbers, the number pi, etc.)
and then consider the size of infinite sets. Next we take a careful look at functions and their graphical
representations and use them to model data sets. Then we investigate the mathematical concept of a
limit and the application of that concept to graphical representations of functions and to infinite
series. Finally, we take an intuitive look at the main ideas of the calculus – the derivative and the
integral – and culminate with the Fundamental Theorem of Calculus!
Our guiding principle can be expressed in the words of John Cotton Dana, "Who dares to teach must
never cease to learn." Our approach will be investigative and will center on problem solving.
Successful students will be involved in investigating, questioning, conjecturing, reasoning, and
communicating about the major ideas of the calculus and pre-calculus. Reading, writing, and oral
presentations will also be important components.
Another goal for this course is for students to become literate in the mathematical language of
models, change, and the infinite; and confident in tackling large problems and in assessing the quality
of their arguments independently (of the instructor). The problems you will work on in this class will
not be exactly like examples you’ve seen, and will not be immediately solvable. You will need to
spend more time than you might expect simply understanding what a problem is asking for. Most
problems will require you to collect data from several examples that you will choose yourself, or to
investigate the definitions of concepts word by word. You will need to create mathematical models,
as well as to represent them by graphs, and interpret properties of these models and their graphs in the
context of the original problem. We will make use of technology (through graphing calculators) to
assist in this visualization and investigation.
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In this course you will have the opportunity to develop the ability to distinguish problem solving and
critical thinking from exercises and routine thinking. We will identify attitudes and beliefs that are
conducive to success in problem solving and critical thinking (and those which are not).
In addition (as in other classes as well) I hope you continue to develop: (1) effective written and oral
communication skills; (2) skills related to critical thinking, problem solving and creativity; (3) the
ability to understand symbol systems and use quantitative methods; and (4) reasoning skills,
including rational inquiry, data collection, analysis, conjecture formulation, and making mathematical
arguments.
Class time will be a combination of problem solving, teaching presentations, group activities, lecture,
and discussion of pre-assigned readings and exercises. Students will be expected to present solutions
to problems and summaries of activities for their classmates. We will use the TI-83+ calculator
regularly in the classroom. It is important that you come to class prepared and participate regularly.
Assessment
We will have three exams – each worth 75 points, which is 15% of your course grade. The tentative
dates for the exams will be: October 4-5, November 8-9, and December 13-14. These exams will be
offered over a two-day period in the Testing Center, allowing you some flexibility in scheduling and
unlimited time for test taking. Do not schedule travel or appointments that conflict with these dates.
In cases of extreme emergency, serious illness, or school-sponsored activity, if I am notified by the
scheduled exam day, you may make-up one missed exam. I will give these make-up exams on
Friday, December 7, 2007 only.
Every non-exam week you will have a written assignment (which may be a problem set, a group
project write-up, a quiz, and/or a short paper) to turn in for evaluation on Friday. These assignments
will come from problems found in your packet and occasionally from outside sources. Expect these
written assignments to take 8 to 10 hours to prepare! Problem solutions must be well written,
organized, and prepared according to the guidelines that accompany this syllabus. Each written
assignment collected will be worth 25 points. I will not accept assignments after the due date.
However, assignments (including announced quizzes) may be turned in (or taken) early if your
absence is unavoidable. Together, the written assignments are 30% of your course grade.
You are highly encouraged to work together on the problem sets (and you will work with other
students on the group projects) - work together, learn from each other, discuss the problems and
concepts, investigate proposed solutions, but then write the paper on the solutions on your own and in
your own words. You may choose your own groups for the group project assignments. It will be
your responsibility to ensure that each member contributes a reasonable share of the work toward the
completed write-up, and that each member understands the solution completely. All students in a
particular group will receive the same grade for a group project assignment.
Each of you (in pairs) will be required to present a curriculum teaching project in which you will
teach a middle school lesson on mathematics related to our course. (We will use Tuesdays,
beginning October 16th, for these presentations.) This project will compose another 15% of your
course grade (75 points). Guidelines for this project and its oral presentation and a schedule for the
presentations will be provided at a later date. More information about signing up for a presentation
date will be provided in class.
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The final component (50 points – 10%) of your course grade will be for class participation, which
includes regular attendance, asking and answering questions based on reading assignments, class
presentation of homework problems, active involvement in classroom group work, feedback on oral
presentations, open-notes quizzes, attending office hours, and completion of non-graded assignments.
The grading scale will be approximately as follows:
A:
93 – 100%
AB: 88 – 92%
B:
80 – 87%
BC: 77 – 79%
C:
68 – 76% (68 – 70% will revert to CD if participation is not close to 50 pts.)
D:
60 – 67%
F:
0 – 59%
You are expected to attend all classes. Excessive (more than three) absences will affect your
participation grade. You are responsible for all material covered and all activities in class and for all
assignments (including readings), whether present or absent from a particular class meeting. You
may always contact me by email regarding these assignments and class activities.
You should expect to spend significant time outside of class working on the various assignments of
this course. In addition, I encourage you to spend time reflecting on the ideas we are discussing.
You should be reflecting on what you’re doing and why you’re doing it. What is the process or
concept? How did we develop the process or concept? In what contexts does the process make
sense? How is this process or concept related to the other ideas in the course? Thinking and doing is
more effective than just doing. Mathematics is a subject that requires work, practice, reflection, and
concentration. Expect to spend a minimum of eight to twelve hours per week outside of class
engaged with the wonders of infinite processes in mathematics.
An Invitation
I welcome your feedback on how the course is going for you and I encourage each of you to spend
time with me during office hours. Good students take advantage of the opportunity for one-on-one
time with their instructors. We can talk about your course concerns, about problem assignments,
about quizzes and exams, or explore some aspect of mathematics or teaching you find exciting or
challenging or frustrating! My time is your time during office hours and we set up individual
appointments outside of office hours. Each of you is welcome! At other times, take advantage of email. I promise to check and answer e-mail each day - provided the system is “up!”
I am looking forward to an exciting semester pondering the infinite together.
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