Math Camp: A Language Immersion Class
Each
Spring, two mathematics faculty members and approximately thirty students at
Bates College join together. They have
embarked upon a class that will consume them for five weeks, the successful
completion of which they will later refer to as a badge of honor. During the five weeks, they meet daily: five
hours Monday through Thursday, with Friday devoted to an untimed exam, and
weekends free. This class has the formal
name Introduction to Abstraction, but around campus, students and
faculty know it more fondly as Math Camp.
Bates
has a scheduling system that affords Math Camp full attention while students
take it. In addition to our regular
Fall and Winter Semesters, we have a five-week Short Term which starts in late
April and continues through most of May.
Students take two or three Short Term units in the course of their
studies at Bates, and may not enroll in more than one unit at a time. Some faculty use this opportunity to
incorporate week-long field trips, travel abroad, or other activities which
demand a lot of students' time. In Math
Camp, we use our time to introduce students to the language of mathematics, and
particularly the structure of proofs.
Five
hours a day, five weeks, for four days of the week, not including tests, all
add up to more than double the amount of time we would meet with students
during the span of a regular semester class.
Additionally, our time becomes very flexible, rather than broken into 55
or 80 minute chunks. Clearly a
lecture-style class does not work! The
students realize this quickly, and take an active part in their study. They work in small groups, reading new
material and working through exercises together. These groups then compare their results with the class as a
whole. Pairs write proofs together,
then confer with neighboring pairs, checking each others' statements for
accuracy and clarity. Sometimes the
entire class works through a new proof together, calling out statements to an
appointed scribe at the chalkboard. The
scribe has the job of writing, and writing only; other students must instruct
the scribe in what to write, as well as where and when to include the various
pieces of the proof. Periodically, individual
students write out proofs for the faculty facilitators to check, then rewrite
to correct any errors. Some of these
proofs later become LaTeX exercises for students to typeset, giving us yet
another period of improvement. By the
time students typeset a proof, they typically have higher skill and
understanding than when they first crafted that proof, and can produce an even
more detailed and carefully organized result.
By
the end of the five weeks, we see clearly that students have progressed, from
first- or second-year students with some interest in mathematics, to
mathematicians with a much clearer understanding of the vocabulary and logic
processes required for higher-level mathematics. They have a clear mathematical advantage in their later classes
over students who have not yet participated in Math Camp, with particular
excellence in concepts relating to proofs and abstraction. As a final note, the entire experience helps
to form cohesion within our newest group of math majors, and to help them get
to know two faculty members well. These
results contribute to the pleasant, social atmosphere we like to have in the
Mathematics Department at Bates.