No Tests, No Tears:
A Model for a Liberal Arts Mathematics Course
· 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…
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.
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
A packet of 150 standard problems from Combinatorics and Graph Theory, in five sections:
· General counting problems
· Binomial coefficients
· Partitions, permutations and probability
· Graph theory
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.
No daily homework
· Oral communication skills including informal presentations
(My observations, students’ evaluations of their own group, and student self-evaluation)
(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
· 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
· 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.