

Introduction
Teaching is a significant component of most mathematicians' careers. Just
as future lawyers and doctors must study and train to become more
proficient in the skills needed for their professional careers, future
mathematicians must study and train to improve their teaching skills.
The goal of the Teaching Undergraduate Mathematics Seminar is to provide
opportunities during the semester to discuss and reflect on teaching
philosophies and practices in order to become better teachers now
and to prepare for the teaching activities which will be part of
future professional careers.
The seminar presentations and discussions are
designed primarily for mathematics graduate students, but anyone
interested in mathematics teaching is welcome to attend.
Please direct any comments or questions about the seminar to Mathematics
Preceptor Derek Bruff (bruff [at] fas.harvard.edu).
Upcoming Sessions

InquiryBased Calculus
with John Neuberger,
Regents Professor of Mathematics at the University of North Texas
April 22, 2005, 2 to 3 p.m., SC 316
Is it possible to teach calculus in a such a way that the students feel
that they are discovering the fundamental ideas of calculus for themselves?
Inquirybased calculus is an approach to teaching calculus that can do just
that and, by doing so, give students a deep understanding and appreciation
of the calculus.
At this week's TUMS session, we are honored to have
John Neuberger, Regents Professor of Mathematics at the University of North Texas,
show us how inquirybased calculus works by holding a mock class with
undergraduate students. Please join us to welcome Professor Neuberger and to
learn about an interesting, nontraditional way of teaching calculus.

How to Organize a Lively Lecture:
A Class Visit and Luncheon Discussion
with Benedict Gross,
George Vasmer Leverett Professor of Mathematics and Dean of Harvard College
April 29, 2005
Lecture: 10 to 11 am, Jefferson 250
Lunch and Discussion: 11:15 am to 12:30 pm, SC 317
Want to square the circle? Well, you can't. But you can find out how
Galois Theory proves you can't while also finding out more about how to
organize a lively lecture.
Just come to an open house held by Dean Benedict Gross in Math 123 as part
of the Bok Centers Faculty Lecture and Lunch Series.
Everyone is welcome to attend the Math 123 class Dean Gross will teach on
Friday, April 29, from 10:00 to 11:00 in Jefferson 250. A discussion of
the pedagogy will follow over lunch in the Bok Center (Science Center 317)
from 11:15 to 12:30.
No mathematical knowledge is necessary to use this open house as a point
of departure for discussing pedagogy in general and lecturing in
particular. Dean Gross will provide a brief introduction to Galois Theory
for nontechnical visitors at the beginning of his lecture.
Past Sessions

Motivating Students
with Angela VierlingClaassen,
and Derek Bruff,
Preceptors in Mathematics
April 15, 2005, 2 to 3 p.m., Science Center 316
How do you motivate your students to learn mathematics, particularly students who are taking your course as a requirement and may not be that interested in mathematics? To what extent can we motivate our students, and how much responsibility do we have for doing so? What strategies can we employ to motivate our students, and in what ways do we inadvertently demotivate our students? In this TUMS session, we will discuss these questions and look at what educational research tells us about motivating students.

Understanding What Your Students Are Thinking
with Angela VierlingClaassen,
and Derek Bruff,
Preceptors in Mathematics
March 11, 2005, 2 to 3 p.m., Science Center 316
Just what are your students thinking during class? Do they understand
the example you just went over or are they still confused? Is your
teaching having an impact on their learning? If you have ever felt
like you were teaching to a room full of blank stares or if you would
just like to understand your students a little better, then this
session is for you. We will introduce you to several useful techniques
for finding out what your students understand, what they don't understand,
and how you can teach them more effectively and more efficiently.

Seeking Points: A Case Study
with Matt Leingang, Preceptor in
Mathematics
March 4, 2005, 1:30 to 3 p.m., Science Center 316
Note that this session will begin at 1:30 pm instead of the usual starting time.
"Can I talk to you about my grade?" one of your students says as he enters your office shortly after you've handed back an exam. You might not describe the conversation that is likely to follow as pleasurable, yet assessing students and talking about grades with students are important parts of teaching. Can we change the adversarial nature of such events and make them teachable moments?
The meeting this week will take the form of a case study. Participants will read a short story about a student seeking points on a recently graded test. Following this, participants will discuss as a group the issues and problems the story raises as well as possible solutions to these problems. Thinking and talking about these issues will prepare you to face them when they arise in your own teaching.

Managing an Interactive Classroom
with Kathy Paur, Mathematics Graduate Student,
and Robin Gottlieb, Senior Preceptor in Mathematics
February 25, 2005, 2 to 3 p.m., Science Center 316
There's a lot of hype here about running an interactive classroom; it
is said that's why we teach in small classes. BUT... we have a
syllabus to teach and material to get through... the students don't
always know the answers... sometimes they say the wrong thing...
sometimes they don't like to talk... some of them talk too much...
confused students can't ask clear questions... if students are
running the classroom, why is the teacher getting paid?
Bring your questions and concerns.

Caught on Tape: Clips of Teachers in Action
with Derek Bruff, Preceptor in
Mathematics
February 11, 2005, 2 to 3 p.m., Science Center 222
Watching someone else teach is a great way to reflect on and improve one's
own teaching. In this session, we'll watch and discuss several video clips
of experienced teachers in action. We'll focus on the choices the teachers
made both before and during class and how you can think critically about
the choices you make as you teach.

Making Lesson Plans
with Matt Leingang
and Derek Bruff, Preceptors in
Mathematics
February 4, 2005, 2 to 3 p.m., Science Center 222
"Before anything else, preparation is the key to success." When Alexander
Graham Bell, inventor of the telephone, said that, he probably wasn't talking
about teaching, but his maxim holds true for teaching nonetheless. In this
session, we'll look at the preparation that precedes a successful class.
We'll analyze the components of a good lesson plan, discuss ways to plan
lessons quickly, and practice our lesson planning skills.

Grading 102: More Nuts and Bolts of Good Grading
with Andy Engelward,
Preceptor in Mathematics
December 17, 2004, 2 to 3 p.m., Science Center 222
This second session on grading will feature a number of grading
examples selected to illustrate POGGs (Principles of Good Grading) and PORCs
(Principles of Rubric Construction). One main goal of doing this is to
help you become more efficient in your own grading, an especially timely
goal as we head into finals season in January! Feel free to bring in
examples of questions you might have graded from earlier this semester, if
you want to share your own grading experiences in this discussion meeting.

Grading 101: The Nuts and Bolts of Good Grading
with Tom Judson
and Andy Engelward,
Preceptors in Mathematics
November 19, 2004, 2 to 3 p.m., Science Center 316
In this session, we will investigate how it's possible to grade
successfully without spending an outrageous amount of time on it.
We'll go through several grading demonstrations to explore the ins and
outs of good grading, and figure out techniques that everyone can use
to make their grading go well.

The Act of Teaching
with Nancy Houfek,
Head of Voice and Speech for the
American Repertory Theater at Harvard University (via tape)
November 12, 2004, 2 to 3 p.m., Science Center 316
"The Act of Teaching: Theater Techniques
for Classroom Presentations" is a video featuring Nancy Houfek, the head of
Voice and Speech for the American Repertory Theater here at Harvard,
demonstrating how we can use our voices and body language to communicate
ideas more effectively and improve our presentation skills. The video
discusses how to engage an audience and well as ways to overcome "stage
fright" when teaching.
