CBMS Issue s i n Mathematic s Educatio n
Volume 6 , 1996
A Framewor k fo r Researc h an d
Curriculum Developmen t i n
Undergraduate Mathematic s Educatio n
MARK ASIALA, ANNE BROWN, DAVID J. DEVRIES,
ED DUBINSKY, DAVID MATHEWS, AND KAREN THOMAS
ABSTRACT. Ove r th e pas t severa l years , a communit y o f researcher s ha s
been usin g an d refinin g a particula r framewor k fo r researc h an d curriculu m
development i n undergraduate mathematic s education . Th e purpos e o f thi s
paper i s t o shar e th e result s o f thi s wor k wit h th e mathematic s educatio n
community a t larg e b y describin g th e curren t versio n o f the framewor k an d
giving som e example s o f it s application .
Our framewor k utilize s qualitativ e method s fo r researc h an d i s based o n
a ver y specifi c theoretica l perspectiv e tha t i s bein g develope d throug h at -
tempts t o understan d th e idea s o f Piage t concernin g reflectiv e abstractio n
and reconstruc t the m i n th e contex t o f college leve l mathematics . Ou r ap -
proach ha s thre e components . I t begin s wit h a n initia l theoretica l analysi s
of what i t mean s t o understan d a concep t an d ho w tha t understandin g ca n
be constructe d b y th e learner . Thi s lead s t o th e desig n o f a n instructiona l
treatment tha t focuse s directl y o n tryin g t o ge t student s t o mak e th e con -
structions calle d fo r b y th e analysis . Implementatio n o f instructio n lead s
to th e gatherin g o f data , whic h i s the n analyze d i n th e contex t o f th e the -
oretical perspective . Th e researcher s cycl e throug h th e thre e component s
and refin e bot h th e theor y an d th e instructiona l treatment s a s needed .
In thi s repor t th e author s presen t detaile d description s o f eac h o f thes e
components. I n ou r discussio n o f theoretica l analyses , w e describ e cer -
tain menta l construction s fo r learnin g mathematics , includin g actions , pro -
cesses, objects , an d schemas , an d th e relationship s amon g thes e construc -
tions. Unde r instructiona l treatment , w e describ e th e component s o f th e
ACE teachin g cycl e (activities , clas s discussion, an d exercises) , cooperativ e
learning an d th e us e of a mathematica l programmin g language . Finally , w e
describe th e methodolog y use d i n dat a collectio n an d analysis . Th e pape r
concludes wit h a discussio n o f issue s raise d i n th e us e o f thi s framework ,
followed b y a n extensiv e bibliography .
(c) 1996 America n Mathematica l Societ y
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http://dx.doi.org/10.1090/cbmath/006/01
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