One Size Does Not Fit All: the Capstone Program in Mathematics at CC

Marlow Anderson

The Colorado College

March 6, 2006

The Obligatory Block Plan Slide

Year is divided into 8 blocks (3.5 weeks) Students take one course at a time Faculty teach 6 of 8 blocks There are semester-long half unit

courses – but they require time-stealing from the block course

Scheduling a major requirement for seniors in a single block is problematic

CC Math Department

Ten tenure-track faculty – one Ph.D. Computer scientist

15-20 majors per year Strong traditional math major, with

enlarged interest in applied math (two new hires)

Brand new computer science major

Distinction in Mathematics

A program traditionally for only the best students

Requires high grades, extra coursework and a faculty vote

Includes an independent expository or research component with an oral presentation to students and faculty

Math Department Distinction

We’ve been too lax, and too stringent – what are our standards

Students with lesser records still can benefit from independent projects!

Great recent idea: decrease the length of the talks, and have them all on one day – great camaraderie and mutual support among the candidates

The Handwriting on the Wall

The new college president Richard Celeste puts senior capstones on his CC2010 trip-tix

Other departments in the sciences have a capstone

The external review of the math department recommends capstones for all majors

FYI --

Dick

FYI --

Dick

Capstones in the Sciences at CC

Biology: ETS subject test & 5 talk abstracts Chemistry: seminar on lab or library research Geology: senior seminar strongly urged Psych: final project: empirical, literature or

field study EV: a practicum, integrative experience or

thesis Physics: required seminar talk – now with a

block course too

External Review Statement, April 2005

All students majoring in mathematics would benefit from some type of capstone experience completed before graduation.

For students who participate in the distinction program, completing the complex analysis course and the distinction project and presentation forms an effective such experience.

External Review Statement, April 2005

Distinction students interviewed indicated that they appreciate from that experience the drawing together of separate mathematical strands and the resulting better sense of how the distinct areas of mathematics fit together.

External Review Statement, April 2005

For mathematics majors not in the distinction program, we encourage the department faculty to consider developing as a capstone experience a history of mathematics seminar taken as an adjunct course in the senior year. Such a course could reveal the contextual relevance of various mathematical ideas and topics to the students and allow them to pursue projects and give presentations.

Some Thoughts Masonry

A capstone is the last course of fancy brickwork at the corner

This is not what I’m thinking about! I’m thinking about a keystone--- Something that holds the arch

together (this observation belongs to someone else – I can’t remember who)

The New Plan – Fall 2006

The goal is to bring together disparate ideas and subdisciplines – to see mathematics as the unified subject we believe it is

Some of our students barely make it through our senior level courses – others are ready for independent work

Particular interests make for different hooks

Option 1: The Project

Based on our traditional distinction model

Independent project (expository or research) with one faculty sponsor

Talk in the spring as part of a math day

Option 1: The Project

Open to students whether they pursue distinction or not – we don’t have to discourage students without the grades

The project might not provide the cross connections we look for in the other options

The independence of the work can compensate for the last point

Option 2: History of Mathematics For some students, history is an

attractive way to see interconnections We have had 300-level history course

for some time (offered in alternate years), but students often took it too soon

The new version requires algebra & analysis, and senior status

Option 2: History of Mathematics

A block course instead of alternate format – it must be offered every year, and this is a cost

Original sources still appropriate Good options for relatively independent

research Non-seniors miss out on taking history

Option 3: Semester-long Seminar We have had a semester-long seminar

course on a topic chosen by the faculty member – often at a lower level

We replace this with a seniors-only seminar with analysis & algebra required

We need topics (perhaps applications) which illustrate the interconnectedness of various subdisciplines

General Comments

We have no idea yet what the distribution will be like among students!

More projects means more uncompensated faculty work, especially when working with weaker students who did not do distinction

We need to figure out what the upgrades in the level of the seminar and the history course really mean

Computer Science Major

We have just added this major (replacing math with CS emphasis)

We’ve built a program we can staff Enrollment and number of majors

uncertain Distinction program in place We’re not ready to put the capstone in

place!

Special Thanks

To Sheldon Wettack To Marlene field To my friend, Janet Andersen