t g r undme@c a lpo l y . edu.ABSTRACT: A survey was administered to calculus stude nts who had pr eviously been exposed to a course on int egr al calc ulus. T he pur pose of t he survey was to explore st udents ' understanding of t he definit ion of a definite integra l, t hei r abilit ies to evaluate definite integrals , and their gra phica l interpret ations of definite integrals. The analysis of par ti cipants' sur vey responses develop ed insi ght into their concepti ons of integration. Survey results sugges t that understanding the definiti on of a definite integral did not imply pro cedural fluency and t hat these students d id not make connect ions between definit ions and procedures in integral calculus. ] paper , First-year Uni versi ty Students' Understan ding of Rate of Change, he poses the qu estions: "Do calculus st udents in general achieve t he desir ed level of underst anding? Do these st udents develop relia ble intuiti ve ideas and the mathematical competence ... to find counter-examples, to use t he meaning of concepts to ana lyze pr oblem situat ions, to penetrat e from t he sur face to the central idea and to express t hemse lves in clear and conc ise mathem ati cal lan guage?" [1, p . 378] These inquiries were not t he resul t of a new concern. For some t ime, mathem ati cs 178

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