Contents Preface Anne Selden, Ed Dubinsky, Guershon Harel, Fernando Hitt First-year Undergraduates ' Difficultie s i n Workin g with Differen t Use s o f Variabl e Maria Trigueros and Sonia Ursini Cooperative Learnin g i n Calculu s Reform : What Hav e W e Learned ? 3 0 Abbe Herzig and David T. Kung Calculus Refor m an d Traditiona l Students ' Us e o f Calculus i n a n Engineerin g Mechanic s Cours e 5 6 Cheryl Roddick Primary Intuition s an d Instruction : The Cas e o f Actua l Infinit y 7 9 Pessia Tsamir Student Perfomanc e an d Attitude s i n Course s Base d on APO S Theor y an d th e AC E Teachin g Cycl e 9 7 Kirk Weller, Julie M. Clark, Ed Dubinsky, Sergio Loch, Michael A. McDonald, and Robert R. Merkovsky Models an d Theorie s o f Mathematica l Understanding : Comparing Piri e an d Kieren' s Mode l o f th e Growt h o f Mathematical Understandin g an d APO S Theor y 13 2 David E. Meel

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