Writing in calculus and reflective abstraction

Journal of Mathematical Behavior

Volumn 21, Issue 3, 2002, Pages 255-282

  Cooley, Laurel ^a  

^a CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

Calculus; Cognitive theory; Conceptual knowledge; Constructivism; Epistemology; Language and mathematics; Writing and mathematics

Indexed keywords

EID: 0036399334     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0732-3123(02)00129-3     Document Type: Article

References (22)

1. Beth, E., & Piaget, J. (1966). Mathematical epistemology and psychology (W. Mays, Trans.). Dordrecht: D. Reidel Publishing Company.
2. Bishop, A. (1985). The social construction of meaning - a significant development for mathematics education? For the Learning of Mathematics, 5(1), 24-28.
3. Borasi, R. (1984). Some reflections on and criticisms of the principle of learning concepts by abstraction. For the Learning of Mathematics, 4(3), 14-18.
4. Davis, G., & Jones, A. (1990). Reading for comprehension and writing for communication in university mathematics. In: G. Davis, & R. P. Hunting (Eds.), Language issues in learning and teaching mathematics (pp. 112-119). Victoria: Institute of Mathematics Education, La Trobe University.
5. Dienes, Z. P. (1971). Six stages of learning. London: National Foundation for Educational Research.
6. Dienes, Z. P. (1978). Learning mathematics. London: Mathematical Education.
7. Dubinsky, E. (1991a). Constructive aspects of reflective abstraction in advanced mathematics. In: L. P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 160-220). New York: Springer.
8. Dubinsky, E. (1991b). Reflective abstraction in advanced mathematical thinking. In: D. Tall (Ed.), Advanced mathematical thinking (pp. 95-123). Dordrecht: Kluwer Academic Publishers.
9. Dubinsky, E., & Lewin, P. (1986). Reflective abstraction and mathematics education: the genetic decomposition of induction and compactness. The Journal of Mathematical Behavior, 5, 55-92.
10. Eco, U. (1988) The aesthetics of St. Thomas Aquinas (H. Bredin, Trans.). London: Radius.
11. Ellerton, N., & Clements, K. (1990). Language factors in mathematics learning. In: Proceedings of the 13th Biennial Conference of the Australian Association of Mathematics Teachers (pp. 230-258).
12. Mason, J. (1989). Mathematical abstraction as the result of a delicate shift of attention. For the Learning of Mathematics, 9(2), 2-8.
13. Piaget, J. (1975). To understand is to invent: the future of education. New York: Viking.
14. Piaget, J. (1976). The grasp of consciousness (S.Wedgwood, Trans.). Cambridge, MA: Harvard University Press. (Original work published 1974)
15. Piaget, J. (1985). The equilibration of cognitive structures (T. Brown & K. J. Thampy, Trans.). Cambridge, MA: Harvard University Press. (Original work published 1975)
16. Richards, L. (1990). Measuring things in words: language for learning mathematics. Language Arts, 67(1), 14-25.
17. Southwell, B. (1988). Construction and reconstruction: the reflective practice in mathematics education. In: A. Borbas (Ed.), Proceedings of the Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 12, pp. 584-592).
18. Tall, D. (1988, July). The nature of advanced mathematical thinking. Discussion paper for the Working Group on Advanced Mathematical Thinking at the Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 12. Vezprém, Hungary.
19. Thurston, W. P. (1990). Mathematical education. Notices of the American Mathematical Society, 37, 844-850.
20. von Glasersfeld, E. (1996). Aspects of radical constructivism and its educational recommendations. In: P. Cobb, G. Goldin, B. Greer, P. Nesher, & L. Steffe (Eds.), Theories of mathematical learning (pp. 307-313). Mahwah, NJ: Lawrence Erlbaum.
21. Waywood, A. (1992). Journal writing and learning mathematics. For the Learning of Mathematics, 12(2), 34-43.
22. Waywood, A. (1988). Mathematics and language: reflections on students using mathematics journals. In: R. P. Hunting (Ed.), Language issues in learning and teaching mathematics (pp. 37-38). Melbourne: La Trobe University.