Teaching and learning group theory

Making the Connection: Research and Teaching in Undergraduate Mathematics Education

Volumn , Issue , 2008, Pages 139-152

  Weber, Keith ^a   Larsen, Sean ^b  

^a RUTGERS UNIVERSITY   (United States)

^b PORTLAND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84862981137     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.5948/UPO9780883859759.012     Document Type: Chapter

References (21)

1. Asiala, M., Dubinsky, E., Mathews, D.W., Morics, S., and Oktac, A. (1997). Development of students’ understanding of cosets, normality, and quotient groups. Journal of Mathematical Behavior, 16, 241–309.
2. Dubinsky, E. (Ed.). (1997). An investigation of students’ understanding of abstract algebra (binary operation, groups and subgroups) and The use of abstract structures to build other structures (through cosets, normality and quotient groups) [Special Issue]. The Journal of Mathematical Behavior, 16(3).
3. Dubinsky, E., Dautermann, J., Leron, U., and Zazkis, R. (1994). On learning the fundamental concepts of group theory, Educational Studies in Mathematics, 27 (3), 267–305.
4. Dubinsky, E. and McDonald, M. (2001). APOS: a constructivist theory of learning in undergraduate mathematics education. In D. Holton (ed.) The teaching and learning of mathematics at the undergraduate level. Dordrecht: Kluwer.
5. Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. Kelly & R. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 307–334). Mahwah, NJ: Erlbaum.
6. Findell, B. (2002). The operation table as metaphor in learning abstract algebra. In D. Mewborn (ed.) Proceedings of the 24th Conference for the North American chapter of the Psychology of Mathematics Education. 233–245. Athens, GA.
7. Freudenthal, H. (1991). Revisiting mathematics education: The China lectures. Dordrecht, The Netherlands: Kluwer.
8. Gravemeijer, K. (1998). Developmental research as a research method. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics Education as a Research Domain: A Search for Identity (pp. 277–296). Dordrecht, The Netherlands: Kluwer.
9. Hannah, J. (2000). Visual confusion in permutation representations. Research in Collegiate Mathematics Education IV, 8, 188–209.
10. Hart, E.W. (1994). A conceptual analysis of the proof-writing performance of expert and novice students in elementary group theory, In J. J. Kaput and E. Dubinsky (Eds.) Research Issues in Undergraduate Mathematics Learning: Preliminary Analysis and Results, Washington, D.C.: MAA.
11. Hazzan, O. (1999). Reducing abstraction levels when learning abstract algebra concepts. Educational Studies in Mathematics, 40, 71–90.
12. Hazzan, O. (2001). Reducing abstraction: The case of constructing an operation table for a group. Journal of Mathematical Behavior, 20, 163–172.
13. Larsen, S. (2004). Supporting the guided reinvention of the concepts of group and isomorphism: A developmental research project (Doctoral dissertation, Arizona State University, 2004) Dissertation Abstracts International, B 65/02, 781.
14. Larsen, S. (2002). Progressive mathematization in elementary group theory: Students develop formal notions of group isomorphism. Proceedings of the Twenty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Athens, Georgia. 307–316.
15. Leron, U. and Dubinsky, E. (1995). An abstract algebra story. American Mathematical Monthly, 102, 227–242.
16. Leron, U., Hazzan, O., and Zazkis, R. (1995). Learning group isomorphisms: A crossroad of many concepts. Educational Studies in Mathematics, 29, 153–174.
17. Selden, A. and Selden, J. (1987). Errors and misconceptions in college level theorem proving. In Proceedings of the 2nd International Seminar on Misconceptions and Educational Strategies in Science and Mathematics. Cornell University, NY.
18. Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48, 101–119.
19. Weber, K. (2002). The role of instrumental and relational understanding in proofs about group isomorphisms. In Proceedings from the 2nd International Conference for the Teaching of Mathematics. Hersonisoss, Greece.
20. Weber, K. (2006). Investigating and teaching the thought processes used to construct proofs. Research in Collegiate Mathematics Education, 6, 197–232.
21. Weber, K. and Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56, 209–234.