Conceptual Mathematics II
Please feel free to come by my office any time during scheduled
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
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
as soon as possible.
The purpose of this course is for you to
become involved with a wide variety of situations and contexts which
give rise to geometrical concepts essential for teaching mathematics
in grades 4-8. Specific topics focus on the (sometimes surprisingly
deep) mathematics underlying plane and solid geometry, including the
concepts of: measurement; length, area, and volume; congruent and
similar figures; and transformations and symmetry. A common theme
will be finding relationships between geometry and other areas of
You will continue to develop your skill at, and comfort with,
analyzing, solving, and explaining rich mathematical problems that you
do not necessarily immediately know how to solve. You will be able to
use software such as Geometer's Sketchpad to explore and explain
Mathematics for Elementary Teachers, Sybilla
Beckmann, Chs. 8-11
We will skip some sections, as announced in
class. Note that there is both a textbook and Activities Manual.
Bring the Activities Manual to every class; you may leave the textbook
at home, if you like, though it may prove useful in class.
Classes will be largely structured around
selected activities from the Activities Manual. I will briefly
introduce each activity, including any necessary background
information. 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
- 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 (15%)
- 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 (9:00 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 (40%)
You will submit written reports for selected activities (approximately
four 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.
- Quizzes (15%)
There will be approximately ten short (10- to 15-minute) quizzes
throughout the semester, each one announced a week in advance. Topics
will be taken from recent in-class activities, and questions will
generally be conceptual, and ask you to explain why things
work. Quizzes are closed-book, closed-notes. Missed quizzes
cannot be made up, but your two lowest quiz scores
will be dropped.
- Final Exam (20%)
The final exam will be comprehensive over
all topics we discuss in class. Questions will be both procedural and
conceptual. I will distribute sample questions in advance for you to
master in preparation for the final exam. The final exam will be:
Tue. 8 May, 10:00 a.m.-12:45 p.m.
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 Friday, March 23. After this date, you can only drop with the
Dean's approval, which is granted only under extenuating
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.