Reference framework for describing and assessing students’ understanding in first year calculus

References

References

• Anderson , J . 1996 . Learning and teaching with understanding . International Journal of Mathematical Education in Science and Technology , 25 : 813
   Google Scholar
• Kannemeyer L 2003 The Development of a Reference Framework for measuring Students’ Understanding in a First Year Calculus Course Unpublished PhD thesis University of the Western Cape Capetown
   Google Scholar
• Bruner J 1996 The Culture of Education London Harvard University Press
   Google Scholar
• Galbraith , P and Haines , C . 2000 . Conceptual mis(understandings) of beginning undergraduates . International Journal of Mathematical Education in Science and Technology , 31 : 651
   Google Scholar
• Bassey M 1999 Case Study in Educational Settings Buckingham Open University Press
   Google Scholar
• Stake RE 1994 Case studies In: N.K. Denzin and Y.S. Lincoln (Eds) Handbook of Qualitative Research London Sage Publications pp. 236–247
   Google Scholar
• Yin RK 1994 Case Study Research: Design and Methods 2nd Edn Thousand Oaks Sage Publications
   Google Scholar
• Byers , V and Erlwanger , S . 1984 . Content and form in mathematics . Educational Studies in Mathematics , 15 ( 1 ) : 259
   Google Scholar
• Skemp , RR . 1976 . Relational understanding and instrumental understanding . Mathe-matics Teaching , 77 : 20
   Google Scholar
• Skemp , RR . 1982a . Symbolic understanding . Mathematics Teaching , 99 : 59
   Google Scholar
• Skemp , RR . 1982b . Communicating mathematics: surface structures and deep structures . Visible Language , 16 : 281
   Google Scholar
• Tall , D . 1978 . The dynamics of understanding mathematics . Mathematics Teaching , 84 : 50
   Google Scholar
• Hiebert J Carpenter TP 1992 In: D. Grouws (Ed.) Handbook of Research on Mathematics Teaching and Learning New York Macmillan pp. 65–97
   Google Scholar
• Prawat , RS . 1989 . Promoting access to knowledge, strategy, and disposition in students: a research synthesis . Reviews in Education Research , 59 ( 1 ) : 1 – 41 .
   Web of Science ®Google Scholar
• Sierpinska A 1994 Understanding in Mathematics London Falmer Press
   Google Scholar
• Leinhart G 1989 Development of an expert explanation: an analysis of a sequence of subtraction lessons In: L.B. Resnick (Ed.) Knowing, Learning, and Instruction Hillsdale NJ Lawrence Erlbaum Associates pp. 67–124
   Google Scholar
• Morgan C 1998 Writing Mathematically: The Discourse of Investigation London Falmer Press
   Google Scholar
• Shield , M and Galbraith , P . 1998 . The analysis of student expository writing in mathematics . Educational Studies in Mathematics , 36 ( 1 ) : 29 – 52 .
   Google Scholar
• Van Dormolen J 1986 Textual analysis In: B. Christiansen, A.G. Howsen and M. Otte (Eds) Perspectives on Mathematics Education Dordrecht D. Reidel pp. 141–171
   Google Scholar
• Fourali , C . 1997 . Using fuzzy logic in educational measurement . Evaluation and Resources in Education , 11 ( 3 ) : 129 – 148 .
   Google Scholar
• Dreyfus , T . 1999 . Why Johnny can't prove . Educational Studies in Mathematics , 38 : 85 – 109 .
   Google Scholar