Celebratio Mathematica

In the late 1970s and early 80s I got in­volved in “fac­ulty gov­ernance”. I had served on the ex­ec­ut­ive com­mit­tee of the Gradu­ate School and even­tu­ally served on and be­came chair of the Ex­ec­ut­ive Com­mit­tee of the Uni­versity Fac­ulty Gov­ernance. Later, as a “re­ward”, the math chair en­lis­ted me as As­so­ci­ate Chair for Edu­ca­tion. The pre­vi­ous As­so­ci­ate Chair, Peter Hin­man and I found that our de­part­ment’s cal­cu­lus pro­gram ser­i­ously needed re­pair. Fail­ure/dro­pout rates were high. Gradu­ate teach­ing as­sist­ants, who taught the bur­den of cal­cu­lus and pre-cal­cu­lus courses at Michigan were giv­en in­ad­equate train­ing. In­terest in teach­ing was giv­en low pri­or­ity in the de­part­ment (of­ten none at all) in the hir­ing of fac­ulty. Al­though classes were not very large, courses were lec­ture-style, syl­labus was for­mu­laic and in prac­tice (i.e., tests) re­quired little con­cep­tu­al un­der­stand­ing, of­ten just ap­ply­ing mem­or­ized for­mu­las. At one time, the col­lege con­sidered re­mov­ing Cal­cu­lus 1 as sat­is­fy­ing the Col­lege’s Quant­it­at­ive Reas­on­ing re­quire­ment!

Dur­ing the 1986 Berke­ley ICM, I had a con­ver­sa­tion with Dick An­der­son who told me about the Sloan-fun­ded Tu­lane Con­fer­ence, and Ron Douglas’s re­port (“To­ward a Lean and Lively Cal­cu­lus”, 1986) which was in agree­ment with my (and their) con­cerns about the teach­ing of cal­cu­lus, and its fu­ture in the math­em­at­ics ele­ment­ary cur­riculum. Dick or­gan­ized a group of math­em­aticians (Martha Siegel, Tom Tuck­er, Wayne Roberts, Dick An­der­son, and I) and ar­ranged for us to in­form­ally vis­it vari­ous math pro­grams around the coun­try. Al­though math­em­at­ics, stu­dent cap­ab­il­it­ies and needs, de­pend­ent sci­ence courses, and tech­no­logy had vastly changed over the pre­vi­ous 50 years, cal­cu­lus teach­ing had not. The ef­fect­ive­ness of cal­cu­lus teach­ing seemed to be pretty much a mess. (Our group was even­tu­ally form­ally le­git­im­ized by the Math­em­at­ics As­so­ci­ation of Amer­ica as the CRAFTY (Cal­cu­lus Re­form And the First Two Years) Com­mit­tee). Around this time, the cri­tique of ele­ment­ary math­em­at­ics in­struc­tion be­came a na­tion­al is­sue cul­min­at­ing in a ma­jor na­tion­al col­loqui­um on cal­cu­lus held in Wash­ing­ton D.C. (some 800 at­tendees), jointly sponsored by the MAA and Na­tion­al Re­search Coun­cil.

In the winter of 1992, I was giv­en a quarter time re­lease to de­vel­op a “cal­cu­lat­or-based cal­cu­lus course”. This res­ul­ted in my be­com­ing the PI (with Pat Shure) for an NSF-DUI grant to de­vel­op a new cal­cu­lus pro­gram at the Uni­versity of Michigan. The main fea­tures of our pro­gram were these:

• lec­tur­ing was min­im­ized (stu­dents were re­spons­ible for read­ing the text ma­ter­i­al be­fore class);

• stu­dents par­ti­cip­ated at tables of four for dis­cus­sions with each oth­er and with the in­struct­or;

• graph­ing cal­cu­lat­ors were used in class and with home­work;

• aside from in­di­vidu­al home­work as­sign­ments, stu­dents sub­mit­ted team home­work as­sign­ments weekly, which were graded and re­turned by the in­struct­or;

• a new cur­riculum based on the, new at the time, Har­vard text­book;

• ex­tens­ive train­ing for all new cal­cu­lus in­struct­ors on teach­ing is­sues.

As part of my grant agree­ment, between 1992 and 1996 I gave about 40 in­vited talks, col­loquia, present­a­tions, etc. de­scrib­ing the pro­gram to vari­ous math­em­at­ics de­part­ments, na­tion­al math­em­at­ics meet­ings, etc.

The pro­gram has re­mained es­sen­tially un­changed over the past 20 years. Michigan cur­rently has one of the low­est D,D,F rates for cal­cu­lus of ma­jor Uni­versit­ies, and scored at (or near?) the top of the re­cent na­tion­al Cal­cu­lus Concept In­vent­ory.

For about a year I was a Fac­ulty As­so­ci­ate of the Uni­versity’s Cen­ter on Learn­ing and Teach­ing.

In 1994, for “ex­em­plar­ity teach­ing activ­it­ies”, I was named Ar­thur F. Thurnau Pro­fess­or of the Col­lege of Lit­er­at­ure, Sci­ence and the Arts.

Em­ploy­ing the ideas of co­oper­at­ive learn­ing, I later de­signed an ad­vanced cal­cu­lus course and a lin­ear al­gebra/dif­fer­en­tial equa­tions course, both of which are still offered at Michigan.

After re­tire­ment I de­signed and taught for 6 years “Com­bin­at­or­i­al Com­bat”, a two-week 60-hour course in com­bin­at­or­i­al games for high­school stu­dents at­tend­ing the Michigan Math­em­at­ics and Sci­ence Schol­ars camp.