Algebraic generalisation strategies: Factors influencing student strategy selection

Mathematics Education Research Journal

Volumn 18, Issue 3, 2006, Pages 3-28

  Lannin, John K ^a   Barker, David D ^b   Townsend, Brian E ^c  

^a UNIVERSITY OF MISSOURI   (United States)

^b ILLINOIS STATE UNIVERSITY   (United States)

^c UNIVERSITY OF NORTHERN IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957720571     PISSN: 10332170     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03217440     Document Type: Article

References (35)

1. Australian Education Council. (1994). Mathematics: A curriculum profile for Australian schools. Melbourne: Curriculum Corporation
2. Bednarz, N., Kieran, C., & Lee, L. (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht, The Netherlands: Kluwer Academic
3. Booth, L. R. (1984). Algebra: Children's strategies and errors. Windsor, UK: NFER-Nelson
4. Carpenter, T., & Franke, M. (2001). Developing algebraic reasoning in elementary school: Generalization and proof. In H. Chick, K. Stacey, Jill Vincent, & John Vincent (Eds.), The future of the teaching and learning of algebra, Proceedings of the 12th ICMI study conference (Vol. 1, pp. 155-162). Melbourne: The University of Melbourne
5. Carpenter, T. R, Franke, M. L., & Levi, L. (2003). Thinking mathematically. Portsmouth, NH: Heinemann
6. Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In R. Lesh (Ed.), Handbook of research design in mathematics and science education (pp. 307-334). Mahwah, NJ: Lawrence Erlbaum
7. Demby, A. (1997). Algebraic procedures used by 13-15-year-olds. Educational Studies in Mathematics, 33(1), 45-70
8. Department for Education and Skills. (2001). Frameworks for teaching mathematics: Years 7, 8, and 9. London: DfES Publications
9. Fujii, T. (2003). Probing students' understanding of variables through cognitive conflict problems: Is the concept of a variable so difficult for students to understand? In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th annual conference of the international group for the Psychology of Mathematics Education (Vol. 1, pp. 49-66). Honolulu, HI: PME
10. Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. New York: Aldine De Gruyter
11. Healy, L., & Hoyles, C. (1999). Visual and symbolic reasoning in mathematics: Making connections with computers. Mathematical Thinking and Learning, 2(1), 59-84
12. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., Olivier, A., Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann
13. Kaput, J. (1995). Long term algebra reform: Democratizing access to big ideas. In C. Lacampagne, W. Blair, & J. Kaput (Eds.), The algebra initiative colloquium (Vol. 1, pp. 33-49). Washington, DC: U. S. Department of Education
14. Kaput, J. (1999). Teaching and learning a new algebra. In T. Romberg & E. Fennema (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Hillsdale, NJ: Lawrence Erlbaum
15. Kaput, J. J., & Blanton, M. L. (2001). Algebrafying the elementary mathematics experience. In H. Chick, K. Stacey, Jill Vincent, & John Vincent (Eds.), The future of the teaching and learning of algebra. Proceedings of the 12th ICMI study conference (Vol. 1, pp. 344-352). Melbourne: The University of Melbourne
16. Kenney, P. A., Zawajewski, J. S., & Silver, E. A. (1998). Marcy's dot pattern. Mathematics Teaching in the Middle School, 3(7), 474-477
17. Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan
18. Lannin, J. K. (2001). Developing middle school students' understanding of recursive and explicit reasoning. Unpublished doctoral dissertation, Illinois State University
19. Lee, L., & Wheeler, D. (1989). The arithmetic connection. Educational Studies in Mathematics, 20(1), 41-54
20. Lins, R., & Kaput, J. (2004). The early development of algebraic reasoning: The current state of the field. In K. Stacey, H. Chick, & M. Kendall (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 47-70). Norwood, MA: Kluwer Academic
21. Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). Dordrecht, The Netherlands: Kluwer Academic
22. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks, CA: Sage
23. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author
24. National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press
25. Piaget, J. (1970). Piaget's theory. In P. H. Mussen (Ed.), Carmichael's manual of psychology (pp. 703-732). New York: Wiley
26. Schliemann, A., Carraher, D., Brizuela, B., Earnest, D., Goodrow, A., Lara-Roth, S., & Peled, I. (2003). Algebra in elementary school. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th annual conference of the international group for the Psychology of Mathematics Education (Vol. 4, pp. 127-134). Honolulu, HI: PME
27. Stacey, K. (1989). Finding and using patterns in linear generalizing problems. Educational Studies in Mathematics, 20(2), 147-164
28. Stacey, K., & MacGregor, M. (2001). Curriculum reform and approaches to algebra. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 141-153). Dordrecht, The Netherlands: Kluwer Academic
29. Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267-306). Mahwah, NJ: Lawrence Erlbaum
30. Swafford, J. O., & Langrall, C. W. (2000). Grade 6 students' preinstructional use of equations to describe and represent problem situations. Journal for Research in Mathematics Education, 32(1), 89-112
31. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. (Original work published 1934)
32. Warren, E. (2000). Visualisation and the development of early understanding in algebra. In M. van de Heavel-Panhuizen (Ed.), Proceedings of the 24th conference of the international group for the Psychology of Mathematics Education (Vol. 4, pp. 273-280). Hiroshima, Japan: PME
33. Warren, E. (2004). Generalizing arithmetic: Supporting the process in the early years. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the international group for the Psychology of Mathematics Education (Vol. 4, pp. 417-424). Bergen, Norway: PME
34. Warren, E. (2005). Young children's ability to generalise the pattern rule for growing patterns. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the international group for the Psychology of Mathematics Education (Vol. 4, pp. 305-312). Melbourne: PME
35. Zazkis, R. (2001, December). From arithmetic to algebra via big numbers. In H. Chick, K. Stacey, Jill Vincent, & John Vincent (Eds.), Proceedings of the 12th ICMI study conference: The future of the teaching and learning of algebra (Vol. 2, pp. 676-681). Melbourne: University of Melbourne