PREFACE
Welcome t o th e secon d volum e i n th e Research in Collegiate Mathematics
Education (RCME) series . Fo r a general introductio n t o th e series , see the pref -
ace to RCME I; and fo r a genera l introductio n t o th e field see the first chapte r
by Alan Schoenfel d i n that volume . I n thi s prefac e w e will simply introduc e th e
papers, bu t wit h a n orientatio n t o futur e research . Sinc e th e field o f researc h
in collegiat e mathematic s educatio n i s very young, most studie s wil l raise man y
more question s tha n the y answer . Som e wil l ope n wid e ne w avenue s fo r inves -
tigation, an d a fe w wil l offe r a n avenu e alread y wel l pave d an d traveled . Suc h
variation i s the cas e with th e paper s i n thi s volum e a s well as those i n prepara -
tion fo r the third volume . The y exhibit larg e diversity in methods an d purposes ,
ranging from historica l studies, t o theoretica l examination s o f the rol e of gender
in mathematic s education , t o practica l evaluation s o f particula r practice s an d
circumstances.
Parallel t o RCME J , thi s collectio n begin s wit h a pape r tha t attend s t o
methodology an d close s with a lis t o f questions . Th e lead-of f paper , fro m a re -
search group led by Ed Dubinsky, describe s a distinctive approach to research on
key concept s i n th e undergraduat e mathematic s curriculum . Thi s approac h i s
distinguished fro m other s i n several ways, key among these being its integratio n
of research an d instruction . Th e metho d begin s with a careful "genetic " (i n th e
sense of Piaget) preliminar y analysi s of the concept' s epistemologica l structure .
This analysis is applied to build a first approximation instructional treatment in -
tended t o enabl e a student t o buil d thi s knowledg e structure. A variety of dat a
are gathere d an d analyze d regardin g th e cognitiv e impac t o f th e interventio n
with a view to refinin g bot h th e theoretica l analysi s an d th e instructiona l inter -
vention i n preparation fo r anothe r instructiona l cycle . Th e typica l instructiona l
treatment involve s interactiv e compute r environment s an d som e collaborativ e
learning; an d th e researc h dat a typicall y involv e a mix of open-response writte n
tests an d clinica l interviews. Amon g the topics addressed throug h thi s approac h
are functions , grou p theory , calculus , discret e mathematics . Thi s wor k ha s be -
gun t o revea l som e underlyin g concept-developmen t invariant s i n th e for m o f a
sequence o f progressions tha t move s fro m actio n t o proces s t o objec t statu s fo r
Vll
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