Student perspectives on equation: The transition from school to university

Mathematics Education Research Journal

Volumn 20, Issue 2, 2008, Pages 71-92

  Thomas, Michael O J ^a   Godfrey, David ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77649320178     PISSN: 10332170     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03217478     Document Type: Article

References (36)

1. Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24-35
2. Baroody, A. J., & Ginsburg, H. P. (1983). The effects of instruction on children's understanding of the equals sign. Elementary School Journal, 84(2), 199-212
3. Booth, R. D. L., & Thomas, M. O. J. (2000). Visualisation in mathematics learning: Arithmetic problem-solving and student difficulties. Journal of Mathematical Behavior, 18(2), 169-190
4. Borowski, E. J., & Borwein J. M. (1989). Dictionary of mathematics, London: Collins
5. Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, Massachusetts: Harvard University Press
6. Denmark, T., Barco, E., & Voran, J. (1976). Final report: A teaching experiment on equality. PMDC Technical Report No. 6, Florida State University. (ERIC Document Reproduction Service No. ED144805)
7. Euclid (1933). The elements of Euclid. I. Todhunter (Ed.). London: J. M. Dent and Sons Ltd
8. Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24, 139-162
9. Gattegno, C. (1974). The common sense of teaching mathematics. New York: Educational Solutions
10. Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge: Harvard University Press
11. th Mathematics Education Research Group of Australasia Conference, pp. 396-403). Geelong: MERGA
12. Gray, E. M., & Tall, D. O. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. The Journal for Research in Mathematics Education, 26(2), 115-141
13. th Conference of the International Group for the Psychology of Mathematics Education, Honolulu, Hawaii, 3, 25-32
14. Herscovics, N., & Kieran, C. (1980). Constructing meaning for the concept of equation. The Mathematics Teacher 73, 572-580
15. Jones, I., & Pratt, D. (2006). Connecting the equals sign. International Journal of Computers for Mathematical Learning, 11, 301-325
16. Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317-326
17. Küchemann, D. E. (1981). Algebra. In K. M. Hart (Ed.), Children's understanding of mathematics: 11-16 (pp. 102-119). London: John Murray
18. th annual conference of the Mathematics Education Research Group of Australasia, Auckland, pp. 15-33). Sydney: MERGA
19. Lacey, R. (2004). Great tales from English history. London: Little, Brown
20. Mason, J, (1987). What do symbols represent? In C. Janvier (Ed.) Problems of representation in the teaching and learning of mathematics, LEA, Hillsdale, NJ
21. Mason, J. (1995). Less may be more on a screen. In L. Burton & B. Jaworski (Eds.), Technology in mathematics teaching: A bridge between teaching and learning (pp. 119-134). London: Chartwell-Bratt
22. thconference of the Mathematics Education Research Group of Australasia, Vol. 2, pp. 418-425). Sydney, Australia: MERGA
23. Recorde, R. (1557). The whetstone of witte. Page used available at http://www-history. mcs. st-andrews. ac. uk/Bookpages/Recorde4. jpeg
24. Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 7, 20-26
25. Tall, D. O. (2004). Building theories: The three worlds of mathematics. For the Learning of Mathematics, 24(1), 29-32
26. th Conference of the Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education, Feb 22-27, 2007, San Diego, California, USA. [Available from electronic proceedings http://cresmet. asu. edu/crume2007/eproc. html. Downloaded 10 October 2007]
27. Tall, D. O., Thomas, M. O. J., Davis, G., Gray, E., & Simpson, A. (2000). What is the object of the encapsulation of a process? Journal of Mathematical Behavior, 18(2), 223-241
28. th Mathematics Education Research Group of Australasia Conference, pp. 599-606). Lismore, Australia: MERGA
29. Thomas, M. O. J. (2001). Building a conceptual algebra curriculum: The role of technological tools. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.) International Congress of Mathematical Instruction (ICMI) The Future of the Teaching and Learning of Algebra Proceedings (pp. 582-589). Melbourne: The University of Melbourne
30. Thomas, M. O. J. (2006). Developing versatility in mathematical thinking. In A. Simpson (Ed.) Proceedings of Retirement as Process and Concept: A Festshcrift for Eddie Gray and David Tall (pp. 223-241). Prague, Czech Republic: Charles University
31. th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 257-264). Utrecht, The Netherlands: IGPME
32. Vergnaud, G. (1997). The nature of mathematical concepts. In T. Nunes and P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 5-28). Hove, UK: Psychology Press
33. Vinner, S. (1997). The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning. Educational Studies in Mathematics, 34, 97-129
34. th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 399-406). Utrecht, The Netherlands: IGPME
35. th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 249-256). Seoul, Korea: IGPME
36. th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 262). Honolulu, Hawaii: IGPME