No Tests, No Tears:
A Model for a Liberal Arts Mathematics Course
Joint Meetings
· Three challenges for a liberal arts
math course
· Main features of the course design
· How well did it work? Pros, cons, and
some variations on the theme…
Three Challenges
1.
Students are generally comfortable with writing and discussion.
2.
Students are generally uncomfortable with anything quantitative,
especially equations and notation.
3.
Students want autonomy but feel safer with structure.
The Plan
Design
a course that
· Plays to students’ strengths by using
writing and discussion to learn
· De-emphasizes notation and special
vocabulary
· Fosters intellectual independence
without complete chaos
Main Features
Course materials:
A
packet of 150 standard problems from Combinatorics and Graph Theory, in five
sections:
· General counting problems
· Binomial coefficients
· Partitions, permutations and probability
· Recurrences
· Graph theory
Audience:
Honors
program students, primarily in the humanities and fine arts (18 students,
thirty-four 70 minute classes)
In class –
Students
worked in groups of three on problems chosen by the group
I
circulated to check on progress and make encouraging noises
Outside of class –
Students
worked on additional problems of their own choice and recorded progress on all
problems in a portfolio. (Problems could
be revised, extended, updated, or abandoned.)
I
evaluated the portfolios, providing extensive commentary on both mathematics
and writing, and a tentative grade on each problem designated by the student as
“ready to read”.
Every two
weeks …
Each group gave an
informal progress report to the rest of the class on “the problem we love to
hate”.
I introduced a new section
of the course packet by describing a typical problem and giving a
“mini-lecture” as needed.
The last two
weeks…
Students worked in groups
on a major project, made a formal presentation to the class and created a
written report for me.
There were…
No lectures
No exams
No quizzes
No daily homework
No tears!
Evaluation
· Oral communication
skills including informal presentations
(My observations, students’
evaluations of their own group, and student self-evaluation)
· Portfolios
(Progress on problems,
mathematical correctness, ability to make an effective argument and to use
language precisely and appropriately)
· Final Project
(Formal oral presentation
and written report)
What students liked…
*Not your typical math course*
·
· Autonomy – students had significant
ownership
· No “meaningless” formulas to memorize
· Lots of different problems to work on
· Excitement about discovering patterns
for oneself
· Collaboration leads to progress
and didn’t
like…
*
“The price of autonomy is self-discipline”*
· Changing groups
· Not changing groups
· Some problems were too hard
Pros…
· No lectures, no tests, no daily
homework …
· More direct contact and conversation
with students
· Students developed their own notation
and vocabulary as they needed it
· Students learn more, and solve deeper
problems, when they own the course
Cons…
· Evaluating portfolios is
time-consuming
· Evaluating discussion skills is
unfamiliar territory
· Dealing with procrastination
Variations on the theme
for non-honors students
· January term (28 Nursing
majors, fifteen 2 hour classes)
Daily mini-lecture with
“problem of the day”; specified minimum daily progress; weekly quizzes; no
final project.
· Semester course (Two sections,
56 students, thirty-six 70 minute classes)
D. Farmer and T. Stanford,
Knots and Surfaces (AMS) plus a
packet of additional problems; most
problems assigned, but some choice; six quizzes; final project presentations in
poster sessions.
More info…
http://www.employees.csbsju.edu/jgalovich/no_tests.htm