The role of arithmetic structure in the transition from arithmetic to algebra

Mathematics Education Research Journal

Volumn 15, Issue 2, 2003, Pages 122-137

  Warren, Elizabeth ^a  

^a AUSTRALIAN CATHOLIC UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 63649149182     PISSN: 10332170     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03217374     Document Type: Article

References (40)

1. AustralianCouncfl for Educational Research. (1998). Australian year 12 students 'performlce in the Third International MattJematics and Science Study: TIMSS Australian Monograph No. 3. Melbourne: Author.
2. Booth, L. (1989). A question of structure a reacton to: Earlylearning of algebra: A smJctural perspective. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teactflngof algebra (pp 20-32). Virginia, VA: Lawrence Erlbaum.
3. Booth, L. R (1984). Algebra: Children's strategies and en'ors. Windsor, UK: NFER Nelson.
4. Boukon Lewis, G., Coop, T. J, Atweh, B., Pillay, H, & Wilss, L. (1998). Pre-algebra: A cognitive perspective. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22 nd International Conference for Psychology of mathematics Education (Vol 2, pp. 144-151). Stefienbosch, SoLCh Africa: Program Committee.
5. Braufield, P. (1973). The role of algebra in modern K12 cu'ricuhJm. International Journal of Matbematics Education inScience & Technology, 4(2), 175-185.
6. Carpenter, T., & Franke, M. (2001). Developing algebraic reasoning in the ellentary school: Genalisaton atfi proof. In Chick, K. Stacey, J. Vincent, & J. Vincent. (Eds.), The future of the teaching and learning ofalgeta (Proceedings of the 12 th International Commission on Mathematics Instruction study conferlce, Vol. 1, pp. 155-162). Melbourne: University of Melbourne.
7. Collis, K. F. (1974). Cognitive development ofmatbentics learning. Paper presented for tie Psychology of Mathematics Education Workshol Shell Mathmatics Unit Cultre for Scilce Education, Chelsea College, University of Lotflon, England.
8. Falluler, K, Levi, L., &Carpenter, T. (1999). Children'sunderstanding of equality: A foutflation for algebra. Teaching Cbildren Matbentics. Decmber, 232-236.
9. Filloy, E., & Sutherland, R. (1996). Designing curricula for teaching and learning algebra. In A. Bisijp, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (Vol. 1, pp. 139-160). Dordecht, The Netherlatfls: Kluwer.
10. Gallardo, S., & Rojano, T. (1987). Common difficulties in the learning of algebra by dlildrl displayinglow atfi medium pre algebraic proficiency levels. In L Bergs'on, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11 th Annual Cofference of the IntemationM Grottp for the Psychology of Mathematics Education (Vol. 2, pp. 301-307). Montreal, Canada: Program Committee.
11. Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mthematics, 27, 59-78.
12. Kaptt, J. (1998). Transformingalgebra froman engine of inequity to anengine of mathematical powa by algebrafying the K 12 curriculum. In National Coumil of Teachs of Mathematics The Nate and role of algell'ain theN14 curriculum. WasIington, DC: National Academy Press.
13. Kaput, J. (1999). Teaching atfl learning algebra. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms tbat promote understanding. Mahwah, NJ: Lawrence Erlbaum.
14. Kieran, C. (1990). Cognitive processes involved in learning school algebra. In P. Nester & J. Kilpatrick (Eds.), Mathmatics and cognitiorz A research synthesis by the International Group for the Psychology of Mathematics Education (pp 97-136). Cambridge: Cambridge University Press.
15. Kieran, C. (1992). The learning and teaching of school algebra. In T. D. Grouws (Ed), Handbook of research on mathematics teaching and learning (pp 390-419). New York Macmillan.
16. Kieran, C. (1996). The changing face of school algebra. In Alsina et al. (Ed.) Selected lectures from the 7t h International Congress on Mathematical Education, Sevflla, Spain: FESPM. http//www. math. uqam. ca/kier an/ar t/algebr a. html.
17. Kieran, C., & Chalouh, L. (1992). Prealgebra: The transition from arithmetic to algebra. In T. D. Owens (Ed.), Research ideas for the dassroam: Middle grades mathematics. New York: Macmillan.
18. Lamon, W, & Scott, L. (1970). An investigation of elemeltary structure in elementary school matbs: Isomorphism. Educational Studies in Mahthematics, 3(1), 95-110.
19. Lee, L., & Wheela, D. (1989). The arithmetic connection. Education Studiesin Mathematics. 20, 4-54.
20. Lindlevski, L., & Herscovics, N. (1994). Cognitive obstacles in t: re algcbra. Proceedings of the 18 th conferenceof the lnternational Groupfor the Psychologyof Mathematics Education (Vol. 3, t: P. 176-183). Lisbon, Portugal: Program Committee.
21. Lindlevski, L., & Herscovics, N. (1996). Crossing the cognitive gap between arithmetic altalgebra: Operating on the unknown in the cottext of equations. Educational Studies in Mathematics, 30, 39-65.
22. Lindlevski, L., & Livneh, D. (1999). Structure slse: The relationship between algebraic and numa'ical contexts. Educational Studies in Mahthematics, 40, 173-196.
23. Lodholz, R. D. (1993). The transilion from arithmetic to algebra. In E. L. Edwards Jr. (Ed.), Algebra for everyone. Richmond, VA: Departmelt of Education.
24. MacGregor, M, & Price, E. (1999). Aspects of language proficiency and algebra learning. Journal forResearch in Mahthematics Educatiot 30 (4), 449-467.
25. MacGregor, M, & Stacey, K. (1995). The effect of different approaches to algebra on slndents' perceptions of arctional r elalionships. Mathematics Education Research Journal, 7(1), 69-85.
26. Morris, A. (1999). Developing concepts of mathematical structure: Pre arithmetic reasoning versus extelded arithmetic reasoning. Focm on Learning Problems in Mathematics, 21 (1), 44-67.
27. National Council of Teacher of Mathematics. (1998). The nature and role of algebra in the K 14 curriculum. Washington, DC: National Academy Press.
28. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
29. Pillay, H., Wflss, L., & Boulton Lewis, G. (1998). Sequltial development of algebra knowledge: A cognitiveanalysis. Mathematics Education Research Journal, 10(2), 87-102.
30. Quinlan, C. (1994). Comt: nrison of teaching methods in early algebra. InG. Bell andN. Lesson (Ed), Challenges in mathematical education: Constraints on construction. (Proceedings of 1?th annual conference of the Mathematics Education Research Group of Australasia, Vol. 2, (pp. 515-522). Lismore, NSW: MIGA.
31. Raj, L., & Malone, J. (1997). The effects of a computa-algebra system on the learning of, and attitudes towards mathmatics, amongst engineeringstudlts inPapua New Guinea. InF. Biddalph &K. Cart (Eds), People inm athematics education (Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia Vol. 2, pp. 429-435). Rotcua, NZ: MERGA.
32. Redden, E. (1996). WouMn't it be good if we had a symbol to stand for any number: The relationship between nanaral language and symbolic notation in t: nttern description. In L. Puig & A. Gutierrez (Ed), Proceedings of the 2(7 h annual conference of the International Group for the Psychology of Mathematics Education (Vol. 4, t: P. 195-202). Valencia, Spain: Program Committee.
33. Slavitt, D. (1999). Therole of operation sease in transitions from arithmetic to algebra flloughL Educational Studies in Mathematics, 37, 251-274.
34. Steffe, L. P., &Olive, J. (1996). Symbolising as a constructive activity ina compter microworld. Journal of Educational Computing Research, 14(2), 113-138.
35. Sullivan, P., & Clarke, D., (1991). Catering for all abilities throughgood questions. Arithmetic Teacher, 39 (2), 14-18.
36. Sullivan, R, Wanen, E., & White, P. (2000). Students' responses to open ended mathematical tasks. Mathematics Education Research Journal, 21 (1), 2-17.
37. Thorpe, J. (1989). Algebra: What should we teach afl how shouldwe teach it? In S. Wagner & C. Kieran eds.), Research issues in the learning and teaching of algeh'a (PD 11-24). NewJersey, NJ: Lawrence Erlbaum.
38. Wagner, S., & Parker, S. (1993). Advancing algebra. In P. S. Wilson (Ed), Research ideas for the classroom: High school mathematics (PD 120-139). New Yorlc Macmillan.
39. Warren E. (2000). Primary children's knowledge of ariflnetic structure. In J. Bana & A. Chapman (Eds.), Mathematics education beyond 2000 (Proceedings of the 24 th annual conference of the Mathematics Education Research Group of Australasia vol. 2, pp. 624-631). Sydney: M ERGA.
40. Warren, E. (1997). Gemralising from and transferring between algebraic representation systems. In F. Biddlph & K. Can (FAs), People in mathematics education (Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia Vd. 2, tV. 560467). Rotcrua, NZ MERGA.