CBMS Issue s i n Mathematic s Educatio n Volume 13 , 200 6 An Imag e o f Calculu s Reform : Students ' Experience s o f Harvard Calculu s Jon R. Star and John P. Smith III ABSTRACT. Thi s pape r examine s students ' experience s o f calculu s refor m a t one majo r researc h universit y tha t ha s implemente d an d maintaine d th e Har - vard Consortiu m calculu s progra m fo r man y years . Ou r focu s i s o n students ' experiences wit h th e ne w course , particularl y o n whic h feature s student s no - ticed a s differen t fro m traditiona l expectation s an d assumption s abou t th e teaching an d learnin g o f mathematics . Ninetee n first-yea r student s wh o wer e enrolled i n refor m calculu s course s a t th e Universit y o f Michiga n participate d in thi s study . Thes e student s wer e interviewe d multipl e times , kep t mathe - matics journals , an d reporte d thei r grade s i n al l o f thei r courses . I n addition , research staf f observe d thei r mathematic s classes . Ou r result s indicate tha t th e "taught" curriculu m di d no t diffe r muc h fro m traditiona l practic e i n calculus . However, student s di d notic e significan t difference s betwee n th e traditiona l mathematics course s the y ha d take n i n hig h schoo l an d Harvar d calculus , most notabl y th e presenc e o f group homewor k assignments , th e accompanyin g requirement t o provid e writte n explanation s fo r one' s problem-solvin g step s and a n increas e i n th e percentag e o f applicatio n o r stor y problem s assigned . We di d no t fin d an y relationshi p betwee n repeate d mentionin g o f thes e differ - ences an d change s i n students ' achievemen t i n mathematics . Th e relevanc e o f our result s t o thos e implementin g o r considerin g implementin g refor m calculu s programs i s discussed . 1. Introductio n This pape r examine s students ' experience s o f calculu s refor m a t on e majo r research university . Th e Universit y o f Michiga n ha s implemente d an d maintaine d the Harvard Consortiu m calculus program for many years. Afte r nearl y two decades of design, development, an d implementation, fundamenta l change s have taken plac e in both th e conten t an d th e pedagogy of calculus at man y college s and universities . Mathematicians an d educator s continu e t o reflec t upo n th e succes s o f such refor m efforts, wit h a n ey e towar d furthe r improvin g learnin g an d engagemen t i n thi s pivotal course . The Tulan e Conferenc e i n 198 6 is commonly recognize d a s the beginning of the reform calculu s movement in the U.S., although its roots can be traced to the 1950' s (Tucker & Leitzel, 1994) . I n general , refor m calculu s i s characterized b y a scalin g back in the number o f topics covered and an enrichment o f the pedagogy used in in- struction, includin g attentio n t o graphical , symbolic , an d numeri c representations ©2006 America n Mathematica l Societ y 1 http://dx.doi.org/10.1090/cbmath/013/01
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