Conceptual Algebra
Spring 2005
Other resources
Syllabus
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.
Course Objectives
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 teaching grades 4-8. Specific topics include
the (sometimes surprisingly deep) mathematics underlying factoring,
divisibility, fractions, ratios, functions, congruence, similarity,
and geometric transformations. A common theme will be finding
relationships between algebra and geometry.
Another goal is for you to become adept at, and comfortable with,
analyzing, solving, and explaining rich mathematical problems that you
do not necessarily immediately know how to solve.
Textbook:
Mathematics for Elementary Teachers via
Problem Solving, Masingila, Lester, Raymond, Chs. 4, 6-10.
Note that there is both a Student Activity Manual and a Student
Resource Handbook. Bring the Activity Manual to every class; you may
leave the Resource Manual at home, if you like.
Class Activities:
Classes will be structured around selected activities from the
Activity Manual. The Resource Manual will serve primarily as a source
for background material (introduction, definitions, examples) for you
to consult. The activities are engaging and conceptually rich, and
are designed to force you to confront the relevant mathematical
concepts.
I will briefly introduce each activity. Then, working in small groups
with your classmates, you will engage each problem or situation in the
activity, and will attempt to describe and explain the results of that
engagement first to each other, and then to the rest of the class in a
classwide discussion.
Grades
- Participation (10%):
- Your active engagement with the material
is required throughout the activity process, from introduction to
class discussion. Active engagement does not require knowing all the
answers all the time. Active engagement does require an honest
effort, and contributing to the ongoing conversation (at the group and
classwide levels) at all times.
You will not be able to get a good participation grade if you are
absent too much.
- Homework (30%)
- Individual homework, directly related to
material relevant to the class activities, will be assigned regularly,
and due approximately weekly. You are allowed to work together on
homework (in fact, I strongly encourage you to do so), but the paper
you turn in you must write yourself. Homework is due at the
beginning of class (12:00 sharp); if you cannot make it to
class, arrange to either deliver the homework to me early, or have
someone else bring it to class for you.
Your lowest homework score will be dropped.
- Activity Reports (60%)
-
You will write written reports for selected activities (approximately
six throughout the semester), after we complete them (including the
classwide discussion) in class.
Reports will be graded not only for answers, but also for
explanations, and descriptions of the process by which you arrived at
your answers (see separate handout for details).
You must write your report yourself, except for
occasional projects that will require group reports (one report for
the whole group). You may not consult any outside resources
(including the internet) without my approval.
Attendance:
On-time attendance at all classes is required.
Classes will begin promptly at the starting time. Though there is no
direct grade penalty for absence or tardiness, it will affect your
participation grade. Furthermore, reports and homework will likely
make little sense without fully participating in the class activities.
Drop date:
The deadline for student-initiated drops with a
W is Fri., 18 Mar. 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, so please exercise the drop option judiciously.