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 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