About the University: Transforming Calculus

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>> Arek Goetz: San Francisco State's Transforming Calculus is an
ambitious project that combines active group work,
online presentations, and automatic homework grading.
Along the way we'll be guiding MA level lecturers
and graduate students in contemporary methods
of college-level instruction.
>> Eric Hsu: In the Transforming Calculus course, we plan to spend most
of class time problem solving.
The way I've taught calculus in the past,
students spend the majority of class time working
in small groups on difficult problems.
They work on blackboards which allows them
to easily collaborate, show their work to me,
and present to the rest of the class.
I give mini lectures after they've had a chance
to work on the problems.
I'll reflect on difficulties that they're having,
consolidate key concepts, and look ahead to new material.
There are rewards and challenges to teaching like this.
You have an immediate sense
of what this class understands and what they don't.
It's really rewarding to be there when they have great ideas
or when they have difficult challenges
so you can help them right away.
It's also very satisfying to see students helping each other,
especially at a place like SF State
which can be large and isolating.
Students also get practice using math as a language
to express their ideas and convince each other
that their answer's right.
One of the challenges of teaching this way is
to get enough time to cover all the material.
You want to give the students time to absorb ideas
and to really think about the math,
but there is a syllabus to get through.
We always want more time to discuss topics or for students
to practice math mechanics.
Arek Goetz and David Meredith are working on technology
to help us use time more efficiently.
>> Arek Goetz: I've been experimenting with some success
on distance learning and using the Internet to stream lectures
and to allow students to collaborate on homework.
In the Transforming Calculus project,
we will have students watching and interacting with lectures
and multimedia at home or in labs.
Students go to the website
and they can view the streamed lectures right to their computer
and can pause or rewind the lecture depending
on if they've missed an important segment
or just simply had trouble understanding a problem.
The lectures will have short comprehension quizzes.
These quizzes pause the lecture so students will be able to get
that immediate feedback to see
if they understood the main points.
We are essentially moving the lectures
out of the class meetings and onto the Internet
where they can watch them at their own pace.
The lectures will be archived so they can go back for review;
this leaves time in live class meetings for difficult problems,
group work, and other activities.
We are also attempting to use computers
to streamline homework submission and grading.
>> David Meredith: Computers today have the capability
to grade most homework questions even those
with symbolic answers.
This gives the students immediate feedback
on their work, a key learning tool
and saves the labor of grading homework.
Because of this,
our Transforming Calculus course will have the students doing
most of their homework through Webwork.
A computer can't grade really deep and rich calculus problems
that involve analysis and argument, but computer grading
of exercises will allow the teacher to focus
on assessing the harder problems.
There have also been advances
in computer visualization in recent years.
A lot of calculus is dynamic and graphical, and we would
like to use computers to make these aspects
of calculus visible to our students.
>> Eric Hsu: One other challenge for teaching a class with lots
of active learning is just getting
around to all the students.
Even 25 students is a challenge, so you can imagine working
with 30 to 40 or sometimes even more;
it can really tire you out.
I've often thought I'd love
to have a graduate student co-teaching the course with me
so we can give students more individual attention.
>> David Meredith: As a former department chair, I can say it's very tempting
to use graduate students or lecturers to teach courses
because they work for a lot less money
than tenured-track faculty, but you have to be responsible
and find situations
where inexperienced teachers can get a lot of support
and learn more about teaching.
Our experimental course provides a golden opportunity
for graduate students and lecturers to help teach calculus
in a cutting edge way while working closely
with skilled faculty members.
We will have a lead faculty member working
with graduate instructors and lecturers who will
in turn lead their own classes.
In the first iteration, the lead faculty will actually teach
discussion sections alongside the graduate students
and lecturers.
>> Eric Hsu: We don't think we have all the answers.
We need to work with other instructors who have experience
or just plain enthusiasm for these ideas.
We want this to be an experiment whose results will
benefit others.
The Transforming Calculus project will try out new
and promising ideas, and we expect some wonderful things
to happen, and at the same time, expect the unexpected.
But we promise to work hard, track the results honestly
in a way that will benefit others,
and to help others make the most of what we learn.
Thank you.
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