Sequential development of algebra knowledge: A cognitive analysis

Mathematics Education Research Journal

Volumn 10, Issue 2, 1998, Pages 87-102

  Pillay, Hitendra ^a   Wilss, Lynn ^a   Boulton Lewis, Gillian ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17144362624     PISSN: 10332170     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03217344     Document Type: Article

References (29)

1. Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning; The SOLO taxonomy (Structure of the Observed Learning Outcome). New York: Academic Press.
2. Biggs, J. B., & Collis, K. F. (1989). Towards a model of school-based curriculum development and assessment: Using the SOLO Taxonomy. Australian Journal of Education, 33, 149-161.
3. Booth, L. R. (1988). Children's difficulties in beginning algebra. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra, K-12 (pp. 20-32). Reston, VA: National Council of Teachers of Mathematics.
4. Booth, L. R. (1989). Grade 8 students' understanding of structural properties in mathematics. In B. Vergnaud, J. Rogalski, & M. Artigue (Eds.), Proceedings of the 13th conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 141-148). Paris, France: Program Committee.
5. Boulton-Lewis, G. M., Cooper, T. J., Atweh, B., Pillay, H., Wilss, L. A., & Mutch, S. J. (1995). Concrete representations and strategies for solving linear equations. In B. Atweh & S. Flavel, (Eds.), Galtha (Proceedings of the 18th annual conference of the Mathematics Education Research Group of Australasia, pp. 121-127). Darwin: MERGA.
6. Collis, K. F. (1974). Cognitive development and mathematics learning. Paper prepared for the Psychology of Mathematics Education Workshop, Shell Mathematics Unit Centre for Science Education, Chelsea College, University of London, England.
7. Collis, K. F. (1975). The development of formal reasoning (Report of a Social Science Research Council sponsored project (HR 2434/1) carried out at the University of Nottingham). Newcastle, NSW: University of Newcastle.
8. Cortes, A., Vergnaud, G., & Kavafian, N. (1990). From arithmetic to algebra: Negotiating a jump in the learning process. In G. Booker, P. Cobb, & T. De Mendicuti (Eds.), Proceedings of the 14th conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 27-34). Oaxtepec, Mexico: Program Committee.
9. Demana, F., & Leitzel, J. (1988). Establishing fundamental concepts through numerical problem solving. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra, K-12 (pp. 61-69). Reston, VA: National Council of Teachers of Mathematics.
10. Ericsson, K. A., & Polson, P. G. (1988). An experimental analysis of the mechanisms of a memory skill. Journal of Experimental Psychology: Learning, Memory and Cognition, 14, 305-316.
11. Filloy, E., & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9 (2), 19-25.
12. Gott, S., Kane, M., & Lesgold, A. (1994). Tutoring for transfer of technical competence: Coached apprenticeship as a form of constructivist training. Texas: Brooks Airforce Base.
13. Halford, G. S., & Boulton-Lewis, G. M. (1992). Value and limitations of analogs in teaching mathematics. In A. Demetriou, A. Efklides, & M. Shayer (Eds.), Neo-Piagetian theories of cognitive development: Implications and applications for education (pp. 183-209). London: Routledge.
14. Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27, 59-78.
15. Janvier, C. (1996). Modeling and the initiation into algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 225-236). Dordrecht, The Netherlands: Kluwer.
16. Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326.
17. Kieran, C. (1990). Cognitive processes involved in learning school algebra. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition: A research synthesis by the International group for the psychology of mathematics Education (pp. 96-112). New York: Cambridge University Press.
18. Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), The handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
19. Linchevski, L. (1995). Algebra with numbers and arithmetic with letters: A definition of pre-'algebra. Journal of Mathematical Behaviour, 14, 113-120.
20. Linchevski, L., & Herscovics, N. (1994). Cognitive obstacles in pre-algebra. In J. Matos (Ed.), Proceedings of the 18th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 176-183). Lisbon, Portugal: Program Committee.
21. Linchevski, L., & Herscovics, N. (1996). Crossing the cognitive gap between arithmetic and algebra: Operating on the unknown in the context of equations. Educational Studies in Mathematics, 30, 39-65.
22. MacGregor, M. (1996). Curricular aspects of arithmetic and algebra. In J. Gimenez, R. C. Lins & B. Gomez (Eds.), Arithmetics and algebra education: Searching for the future (pp. 50-54). Barcelona, Spain: Universitat Rovira I Virgili, Department d' Encanteria Informatica.
23. MacGregor, M., & Stacey, K. (1993). What is x? The Australian Mathematics Teacher, 49 (4), 28-30.
24. Richards, T., & Richards, L. (1994). QSR NUD. IST. Palo Alto, CA: Alladin Systems.
25. Rosnick, P., & Clements, J. (1980). Learning without understanding: The effect of tutoring strategies on algebra misconceptions. Journal of Mathematical Behavior, 3 (1), 3-27.
26. Scandura, J. M. (1971). Mathematics: Concrete behaviouralfoundations. New York, NY: Harper and Row.
27. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.
28. Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra. Educational Studies in Mathematics, 26, 191-228.
29. Ursini, S., & Trigueros, M. (1997). Understanding of different uses of variable: A study with starting college students. In E. Pehkonen (Ed.) Proceedings of the 21st conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 254-261). Lahti, Finland: Program Committee.