Learning binary operations, groups, and subgroups

Journal of Mathematical Behavior

Volumn 16, Issue 3, 1997, Pages 187-239

  Brown, Anne ^b   DeVries, David J ^c   Dubinsky, Ed ^c   Thomas, Karen ^a  

^a UNIVERSITY OF WISCONSIN PLATTEVILLE   (United States)

^b INDIANA UNIVERSITY SOUTH BEND   (United States)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040517060     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0732-3123(97)90028-6     Document Type: Article

References (33)

1. Asiala, Mark, Brown, Anne, DeVries, David J., Dubinsky, Ed, Mathews, David & Thomas, Karen. (1996). A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education, 2, 1-32.
2. Asiala, Mark, Brown, Anne, Kleiman, Jennifer, & Mathews, David. (in press). The development of students' understanding of permutations and symmetries. International Journal of Computers for Mathematical Learning.
3. Asiala, Mark, Cottrill, Jim, Dubinsky, Ed, & Schwingendorf, Keith. (1997). The development of students' graphical understanding of the derivative. Journal of Mathematical Behavior, 16.
4. Barbut, Erol. (1987). Abstract algebra for high school teachers: An experiment with learning groups. Journal of Mathematical Education in Science and Technology, 18(2), 199-203.
5. Branca, Nicholas A. (1974). Learning mathematical structures. Paper presented at the annual meeting of the American Educational Research Association, Chicago, 1974. (ERIC document ED092384).
6. Breidenbach, Danny, Dubinsky, Ed, Hawks, Julie, & Nichols, Devilyna. (1992). Development of the process conception of function, Educational Studies in Mathematics, 23, 247-285.
7. Burn, Bob. (1996). What are the fundamental concepts of group theory? Educational Studies in Mathematics, 31, 371-378.
8. Clark, Julie, Cordero, Francisco, Cottrill, Jim, Czarnocha, Broni, DeVries, David, St. John, Dennis, Tolias, Georgia, & Vidakovic, Draga (1997). Constructing a schema: The case of the chain rule. Journal of Mathematical Behavior, 16.
9. Clark, Julie, Hemenway, Clare, St. John, Dennis, Tolias, Georgia, & Vakil, Roozbeh. (in press). Student attitudes about abstract algebra: a comparative research study. PRIMUS.
10. Dutermann, Jennie. (1992). Using ISETL 3.0: A Language for Learning Mathematics. St. Paul: West.
11. Dienes, Zoltan P. (1959). Concept formation and personality. Leicester, U.K.: Leicester University Press.
12. Dienes, Zoltan P., & Jeeves, Malcolm A. (1965). Thinking in Structures. London: Hutchinson Educational.
13. Dubinsky, Ed, Dautermann, Jennie, Leron, Uri, & Zazkis, Rina. (1994). On learning fundamental concepts of group theory, Educational Studies in Mathematics, 27, 267-305.
14. Dubinsky, Ed, & Leron, Uri. (1994). Learning Abstract Algebra with ISETL. New York: Springer-Verlag.
15. Freedman, Haya. (1983). The teaching of mathematics: A way of teaching abstract algebra. American Mathematical Monthly, 90(9), 641-644.
16. Gray, Eddie, & Tall, David. (1993). Success and failure in mathematics: the flexible meaning of symbols as process and concept, Mathematics Teaching, 142, 6-10.
17. Halford, Graeme. (1982). How do we define the limits to children's understanding? Paper presented at the 20th International Congress of Applied Psychology, Edinburgh, Scotland, 1982 (ERIC document 258726).
18. Hart, Eric. (1994). A conceptual analysis of the proof-writing performances of expert and novice students in elementary group theory. In E. Dubinsky and J. Kaput (Eds.), Research issues in mathematics learning: Preliminary analyses and results (pp. 49-62), MAA Notes, E. Washington: The Mathematical Association of America.
19. Hazzan, Orit, & Leron, Uri. (1994). Students' use and misuse of mathematical theorems: the case of Lagrange's Theorem . For the Learning of Mathematics, 16(1), 23-26.
20. Hirsch, Christian R. (1981). An exploratory study of the effectiveness of a "Didactical Shadow" seminar in abstract algebra. School Science and Mathematics, 81(6), 459-466.
21. Johnson, Wells. (1983). A note on Lagrange's Theorem. American Mathematical Monthly, 90(2), 132-133.
22. Kraines, David P., Kraines, Vivian Y., & Smith, David A. (1990). Classroom computer capsules Binary operations. College Mathematics Journal, 21(3), 240-241.
23. Lant, Rainier M.C. (1980). A comparative study of the learning and understanding of a mathematica group structure in different representations. ERIC document ED190405.
24. Leskow, Sonia, & Smock, Charles D. (1970). Developmental changes in problem-solving strategies Permutation. Developmental Psychology, 2(3), 412-422.
25. Leron, Uri, Hazzan, Orit, & Zazkis, Rina. (1995). Learning group isomorphism: A crossroad of many concepts. Educational Studies in Mathematics, 29, 153-174.
26. Leron, Uri, & Dubinsky, Ed. (1995). An abstract algebra story. American Mathematical Monthly 102(3), 227-242.
27. Maruszewski, Richard F., Jr. (1991). ADA in a theoretical mathematics course. Mathematics and Computer Education, 25(2), 131-143.
28. Sfard, Anna. (1991). On the dual nature of mathematical conceptions. Educational Studies in Mathematics, 22, 1-36.
29. Sfard, Anna, & Linchevski, Liora (1994). The gains and pitfalls of reification - the case of algebra Educational Studies in Mathematics, 26, 191-228.
30. Simmonds, Gail. (1982). Computer discovery of a theorem of modern algebra. Mathematics and Computer Education, 16(1), 58-61.
31. Thomas, Karen. (1995). The fundamental theorem of calculus: An investigation into students' constructions. Unpublished doctoral dissertation, Purdue University, West Lafayette, IN.
32. Vidakovic, Draga. (1993). Cooperative learning: Differences between group and individual processes of construction of the concept of inverse function. Unpublished doctoral dissertation Purdue University, West Lafayette, IN.
33. Vidakovic, Draga. (unpublished manuscript). Learning the concept of inverse function in a group versus individual environment.