Research on the learning and teaching of algebra

Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future

Volumn , Issue , 2006, Pages 11-49

  Kieran, Carolyn ^a  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85135996149     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (262)

1. Ainley, J. (1996). Purposeful contexts for formal notation in a spreadsheet environment. Journal of Mathematical Behavior, 15, 405-422.
2. Ainley, J. (Coord.). (2001). Research Forum: Early algebra. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th PME International Conference, 1, 129-159.
3. Ainley, J., Wilson, K., & Bills, L. (2003). Generalising the context and generalising the calculation. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 2, 9-16.
4. Alcock, L., & Weber, K. (2005). Referential and syntactic approaches to proof: Case studies from a transition course. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 2, 33-40.
5. Amit, M., & Fried, M. N. (2005). Multiple representations in 8th grade algebra lessons: Are learners really getting it? In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 2, 57-64.
6. Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24-35.
7. Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241.
8. Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245-274.
9. Arzarello, F., Bazzini, L., & Chiappini, G. (1994). The process of naming in algebraic thinking. In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th PME International Conference, 2, 40-47.
10. Arzarello, F., Bazzini, L., & Chiappini, G. (2001). A model for analysing algebraic processes of thinking. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 61-82). Dordrecht, The Netherlands: Kluwer.
11. Arzarello, F., & Robutti, O. (2001). From body motion to algebra through graphing. In H. Chick, K. Stacey, J. Vincent, & J. Vincent. (Eds.), Proceedings of the 12th ICMI Study Conference: The Future of the Teaching and Learning of Algebra (pp. 33-40). Melbourne, Australia: The University of Melbourne.
12. Balacheff, N. (2001). Symbolic arithmetic vs. algebra: The core of a didactical dilemma. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 249-260). Dordrecht, The Netherlands: Kluwer.
13. Ball, L., Pierce, R., & Stacey, K. (2003). Recognising equivalent algebraic expressions: An important component of algebraic expectation for working with CAS. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 4, 15-22.
14. Barkai, R., Tsamir, P., Tirosh, D., & Dreyfus, T. (2002). Proving or refuting arithmetic claims: The case of elementary school teachers. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 2, 57-64.
15. Bartolini Bussi, M. G. (1995). Analysis of classroom interaction discourse from a Vygotskian perspective. In L. Meira & D. Carraher (Eds.), Proceedings of the 19th PME International Conference, 1 , 95-101.
16. Bazzini, L., Boero, P., & Garuti, R. (2001). Moving symbols around or developing understanding: The case of algebraic expressions. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th PME International Conference, 2, 121-128.
17. Bednarz, N., & Janvier, B. (1996). Emergence and development of algebra as a problem-solving tool: Continuities and discontinuities with arithmetic. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 115-136). Dordrecht, The Netherlands: Kluwer.
18. Bednarz, N., Kieran, C., & Lee, L. (Eds.). (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht, The Netherlands: Kluwer.
19. Behr, M., Erlwanger, S., & Nichols, E. (1976). How children view equality sentences (PMDC Technical Report No. 3). Tallahassee: Florida State University. (ERIC ED144802)
20. Bell, A. (1976). A study of pupils' proof-explanations in mathematical situations. Educational Studies in Mathematics, 7, 23-40.
21. Bell, A. (1996). Problem-solving approaches to algebra: Two aspects. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 167-185). Dordrecht, The Netherlands: Kluwer.
22. Bell, A., O'Brien, D., & Shiu, C. (1980). Designing teaching in the light of research on understanding. In R. Karplus (Ed.), Proceedings of the 4th PME International Conference, 1, 119-125.
23. Bills, L. (1997). Stereotypes of literal symbol use in senior school algebra. In E. Pehkonen (Ed.), Proceedings of the 21st PME International Conference, 2, 73-80.
24. Bills, L. (2001). Shifts in the meanings of literal symbols. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th PME International Conference, 2, 161-168.
25. Bishop, A. J., Clements, K., Keitel, C., Kilpatrick, J., & Laborde, C. (Eds.). (1996). International handbook of mathematics education. Dordrecht, The Netherlands: Kluwer.
26. Blanton, M. L., & Kaput, J. J. (2004). Elementary students' capacity for functional thinking. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 2, 135-142.
27. Bloedy-Vinner, H. (1994). The analgebraic mode of thinking: The case of parameter. In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th PME International Conference, 2, 88-95.
28. Bloedy-Vinner, H. (2001). Beyond unknowns and variables - parameters and dummy variables in high school algebra. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 177-189). Dordrecht, The Netherlands: Kluwer.
29. Boaler, J. (2003). Studying and capturing the complexity of practice: The case of the dance of agency. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 1, 3-16.
30. Boero, P., Bazzini, L., & Garuti, R. (2001). Metaphors in teaching and learning mathematics: A case study concerning inequalities. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th PME International Conference, 2, 185-192.
31. Booth, L. R. (1981). Strategies and errors in generalized arithmetic. In Equipe de Recherche Pédagogique (Eds.), Proceedings of the 5th PME International Conference, 1, 140-146.
32. Booth, L. R. (1982). Developing a teaching module in beginning algebra. In A. Vermandel (Ed.), Proceedings of the 6th PME International Conference, 1, 280-285.
33. Booth, L. R. (1983). A diagnostic teaching programme in elementary algebra: Results and implications. In R. Hershkowitz (Ed.), Proceedings of the 7th PME International Conference, 1, 307-312.
34. Booth, L. R. (1984). Algebra: Children 's strategies and errors. Windsor, UK: NFER-Nelson.
35. Booth, L. R. (1989). A question of structure. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (Volume 4 of Research agenda for mathematics education, pp. 57-59). Reston, USA: NCTM.
36. Borba, M. (1993). Students' understanding of transformations of functions using multi-representational software. Unpublished PhD dissertation, Cornell University, Ithaca, USA.
37. Boulton-Lewis, G., Cooper, T., Atweh, B., Pillay, H., Wilss, L., & Mutch, S. (1997). Processing load and the use of concrete representations and strategies for solving linear equations. Journal of Mathematical Behavior, 16, 379-397.
38. Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, USA: Heinemann.
39. Carry, L. R., Lewis, C., & Bernard, J. (1980). Psychology of equation solving: An information processing study (Final Technical Report). Austin, USA: University of Texas at Austin, Department of Curriculum and Instruction.
40. Cavanagh, M., & Mitchelmore, M. (2000). Student misconceptions in interpreting basic calculator displays. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME International Conference, 2, 161-168.
41. Cedillo, T., & Kieran, C. (2003). Initiating students into algebra with symbol-manipulating calculators. In J. T. Fey (Ed.), Computer algebra systems in secondary school mathematics education (pp. 219-239). Reston, USA: NCTM.
42. Cerulli, M. (2004). Introducing pupils to algebra as a theory: L 'Algebrista as an instrument of semiotic mediation. Unpublished PhD dissertation, Universita degli Studi di Pisa, Italy. Retrieved from http://www-studenti.dm.unipi.it/~cerulli/tesi/.
43. Cerulli, M., & Mariotti, M. A. (2001). L' L'Algebrista: A microworld for symbolic manipulation. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), Proceedings of the 12th ICMI Study Conference: The Future of the Teaching and Learning of Algebra (pp. 179-186). Melbourne, Australia: The University of Melbourne.
44. Chalouh, L., & Herscovics, N. (1988). Teaching algebraic expressions in a meaningful way. In A. Coxford (Ed.), The ideas of algebra, K-12 (Yearbook of the NCTM, pp. 33-12). Reston, USA: NCTM.
45. Chazan, D. (1996). Algebra for all students?. Journal of Mathematical Behavior, 15, 455-477.
46. Chazan, D. (2000). Beyondformulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York: Teachers College Press.
47. Chevallard, Y. (1999). L'analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19, 221-266.
48. Chick, H., Stacey, K., Vincent, J., & Vincent, J. (Eds.). (2001). Proceedings of the 12th ICMI Study Conference: The Future of the Teaching and Learning of Algebra. Melbourne, Australia: The University of Melbourne.
49. Chin, E.-T., & Tall, D. (2000). Making, having and compressing formal mathematical concepts. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME International Conference, 2,177-184.
50. Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13, 16-30.
51. Clement, J. (1985). Misconceptions in graphing. In L. Streefland (Ed.), Proceedings of the 9th PME International Conference, 1, 369-375.
52. Cobb, P. (1994). Where is mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13-20.
53. Cobb, P., & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14, 83-94.
54. Cobb, P., & Yackel, E. (1995). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. In D. T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the 17th PME-NA Annual Meeting, 1, 3-29.
55. Coles, A. (2001). Listening: A case study of teacher change. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th PME International Conference, 2, 281-288.
56. Collis, K. F. (1974). Cognitive development and mathematics learning. Paper presented at the Psychology of Mathematics Workshop, Centre for Science Education, Chelsea College, London, UK.
57. Confrey, J. (1987). The constructivist. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th PME International Conference, 3, 307-317.
58. Cortés, A. (1998). Implicit cognitive work in putting word problems into equation form. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd PME International Conference, 2, 208-216.
59. Da Rocha Falcão, J. T., Brito Lima, A. P., De Araújo, C. R., Lins Lessa, M. M., & Oliveira Osório, M. (2000). A didactic sequence for the introduction of algebraic activity in early elementary school. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME International Conference, 2, 209-216.
60. Davis, R. B. (1975). Cognitive processes involved in solving simple algebraic equations. Journal of Children's Mathematical Behavior, 1 (3), 7-35.
61. Davis, R. B. (1985). ICME-5 report: Algebraic thinking in the early grades. Journal of Mathematical Behavior, 4, 195-208.
62. De Bock, D., Verschaffel, L., & Janssens, D. (2002). The effects of different problem presentations and formulations on the illusion of linearity in secondary school students. Mathematical Thinking and Learning, 4, 65-89.
63. De Bock, D., Verschaffel, L., Janssens, D., & Claes, K. (2000). Involving pupils in an authentic context: Does it help them to overcome the "illusion of linearity"? In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME International Conference, 2, 233-240.
64. Demby, A. (1997). Algebraic procedures used by 13- to 15-year-olds. Educational Studies in Mathematics, 33, 45-70.
65. Dettori, G., Garuti, R., & Lemut, E. (2001). From arithmetic to algebraic thinking by using a spreadsheet. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 191-207). Dordrecht, The Netherlands: Kluwer.
66. Doerr, H. M. (2003). Using students' ways of thinking to re-cast the tasks of teaching about functions. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 2, 333-340.
67. Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41, 143-163.
68. Douek, N. (1999). Argumentative aspects of proving: Analysis of some undergraduate mathematics students' performances. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, 2, 273-280.
69. Dougherty, B. J. (2003). Voyaging from theory to practice in learning: Measure Up. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 1, 17-23.
70. Dougherty, B. J., & Slovin, H. (2004). Generalized diagrams as a tool for young children's problem solving. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 2, 295-302.
71. Dreyfus, T., & Eisenberg, T. (1981). Function concepts: Intuitive baseline. In Equipe de Recherche Pédagogique (Eds.), Proceedings of the 5th PME International Conference, 1, 183-188.
72. Drijvers, P. (2003). Algebra on screen, on paper, and in the mind. In J. T. Fey (Ed.), Computer algebra systems in secondary school mathematics education (pp. 241-267). Reston, USA: NCTM.
73. Drouhard, J.-Ph., & Teppo, A. R. (2004). Symbols and language. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI Study (pp. 227-264). Dordrecht, The Netherlands: Kluwer.
74. Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-123). Dordrecht, The Netherlands: Kluwer.
75. English, L. D. (Ed.). (2002). Handbook of international research in mathematics education. Mahwah, USA: Lawrence Erlbaum.
76. English, L. D., & Doerr, H. M. (2003). Perspective-taking in middle-school mathematical modelling: A teacher case study. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 2, 357-364.
77. Even, R. (1988). Pre-service teachers' conceptions of the relationships between functions and equations. In A. Borbás (Ed.), Proceedings of the 12th PME International Conference, 1, 304-311.
78. Even, R. (1990). The two faces of the inverse function: Prospective teachers' use of undoing. In G. Booker, P. Cobb, & T. N. Mendicuti (Eds.), Proceedings of the 14th PME International Conference, 1, 37-44.
79. Ferrara, F. (2003). Metaphors as vehicles of knowledge: An exploratory analysis. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 2, 373-380.
80. Fey, J. T. (Ed.). (1984). Computing and mathematics: The impact on secondary school curricula. Reston, USA: NCTM.
81. Fey, J. T. (1989). School algebra for the year 2000. In S. Wagner, & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (Volume 4 of Research agenda for mathematics education, pp. 199-213). Reston, VA: NCTM.
82. Fey, J. T., & Good, R. A. (1985). Rethinking the sequence and priorities of high school mathematics curricula. In C. R. Hirsch, & M. J. Zweng (Eds.), The secondary school mathematics curriculum (Yearbook of the NCTM, pp. 43-52). Reston, USA: NCTM.
83. Filloy, E. (1990). PME algebra research: A working perspective. In G. Booker, P. Cobb, & T. N. Mendicuti (Eds.), Proceedings of the 14th PME International Conference, 1, PII 1-33.
84. Filloy, E., Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19-25.
85. Filloy, E., Rojano, T., & Rubio, G. (2001). Propositions concerning the resolution of arithmetical-algebraic problems. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 155-176). Dordrecht, The Netherlands: Kluwer.
86. Filloy, E., Rojano, T., & Solares, A. (2003). Two meanings of the "equal" sign and senses of comparison and substitution methods. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 4, 223-229.
87. Filloy, E., Rojano, T., & Solares, A. (2004). Arithmetic/algebraic problem solving and the representation of two unknown quantities. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 2, 391-398.
88. Fischbein, E., & Kedem, I. (1982). Proof and certitude in the development of mathematical thinking. In A. Vermandel (Ed.), Proceedings of the 6th PME International Conference, 1, 128-131.
89. Fujii, T. (1993). A clinical interview on children's understanding and misconceptions of literal symbols in school mathematics. In I. Hirabayashi, N. Nohda, K. Shigematsu, & F.-L. Lin (Eds.), Proceedings of the 17th PME International Conference, 1, 173-180.
90. Fujii, T. (2003). Probing students' understanding of variables through cognitive conflict problems: Is the concept of variable so difficult for students to understand? In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 1, 49-65.
91. Furinghetti, F., & Paola, D. (1994). Parameters, unknowns and variables: A little difference? In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th PME International Conference, 2, 368-375.
92. Gallardo, A. (2002). The extension of the natural-number domain to the integers in the transition from arithmetic to algebra. Educational Studies in Mathematics, 49, 171-192.
93. Garuti, R., Boero, P., & Lemut, E. (1998). Cognitive unity of theorems and difficulty of proof. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd PME International Conference, 2, 345-352.
94. Gilead, S., & Yerushalmy, M. (2001). Deep structures of algebra word problems: Is it approach (in)dependent? In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th PME International Conference, 3, 41-48.
95. Goldenberg, E. P. (1988). Mathematics, metaphors, and human factors: Mathematical, technical and pedagogical challenges in the educational use of graphical representations of functions. Journal of Mathematical Behavior, 7, 135-173.
96. Gray, E., & Tall, D. (1994). Duality, ambiguity, and flexibility: A "proceptual" view of simple arithmetic. Journal for Research in Mathematics Education, 25, 116-140.
97. Grouws, D. A. (Ed.). (1992). Handbook of research on mathematics teaching and learning. New York, USA: Macmillan.
98. Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3, 195-227.
99. Guin, D., & Trouche, L. (2000). Thinking of new devices to make viable symbolic calculators in the classroom. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME International Conference, 3, 9-16.
100. Guzmán, J., & Kieran, C. (2002). The role of calculators in instrumental genesis: The case of Nicolas and factors and divisors. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 3, 41-48.
101. Hadjidemetriou, C., & Williams, J. (2002). Teachers' pedagogical content knowledge: Graphs from a cognitivist to a situated perspective. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 3, 57-64.
102. Harper, E. W. (1981). Psychological changes attending a transition from arithmetical to algebraic thought. In Equipe de Recherche Pédagogique (Eds.), Proceedings of the 5th PME International Conference, 1 , 171-176.
103. Harper, E. W. (1987). Ghosts of Diophantus. Educational Studies in Mathematics, 18, 75-90.
104. Healy, L., & Hoyles, C. (1999). Visual and symbolic reasoning in mathematics: Making connections with computers? Mathematical Thinking and Learning, 1 , 59-84.
105. Heid, M. K. (1996). A technology-intensive functional approach to the emergence of algebraic thinking. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 239-255). Dordrecht, The Netherlands: Kluwer.
106. Herscovics, N., & Kieran, C. (1980). Constructing meaning for the concept of equation. The Mathematics Teacher, 73, 572-580.
107. Herscovics, N., & Linchevski, L. (1991). Pre-algebraic thinking: Range of equations and informal solution processes used by seventh graders prior to any instruction. In F. Furinghetti (Ed.), Proceedings of the 15th PME International Conference, 2, 173-180.
108. Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27, 59-78.
109. Hershkowitz, R., Dreyfus, T., Ben-Zvi, D., Friedlander, A., Hadas, N., Resnick, T., Tabach, M., & Schwarz, B. (2002). Mathematics curriculum development for computerized environments: A designer-researcher-teacher-learner activity. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 657-694). Mahwah, USA: Lawrence Erlbaum.
110. Hershkowitz, R., & Kieran, C. (2001). Algorithmic and meaningful ways of joining together representatives within the same mathematical activity: An experience with graphing calculators. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th PME International Conference, 1,96-107.
111. Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32, 195-222.
112. Hewitt, D. (2003). Notation issues: Visual effects and ordering operations. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 3, 63-69.
113. Hoch, M., & Dreyfus, T. (2004). Structure sense in high school algebra: The effects of brackets. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 3, 49-56.
114. Hoch, M., & Dreyfus, T. (2005). Students' difficulties with applying a familiar formula in an unfamiliar context. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 3, 145-152.
115. Hoyles, C. (2002). From describing to designing mathematical activity: The next step in developing a social approach to research in mathematics education? In C. Kieran, E. Forman, & A. Sfard (Eds.), Learning discourse: Discursive approaches to research in mathematics education (pp. 273-286). Dordrecht, The Netherlands: Kluwer.
116. Hoyles, C., Sutherland, R., & Evans, J. (1985). The Logo Maths Project: A preliminary investigation of the pupil-centred approach to the learning of Logo in the secondary mathematics classroom, 1983-84. London, UK: University of London, Institute of Education.
117. Huntley, M. A., Rasmussen, C. L., Villarubi, R. S., Sangtong, J., & Fey, J. T. (2000). Effects of standards-based mathematics education: A study of the Core-Plus Mathematics Project Algebra and Functions Strand. Journal for Research in Mathematics Education, 31, 328-361.
118. Iannone, P., & Nardi, E. (2002). A group as a 'special set'? Implications of ignoring the role of the binary operation in the definition of a group. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 3, 121-128.
119. Ishida, J., & Sanjii, A. (2002). Can poor students identify the good features of a demonstrated problem solving method and use it to solve a generalization problem? In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 3, 137-144.
120. Janvier, C. (1981). Difficulties related to the concept of variable presented graphically. In Equipe de Recherche Pédagogique (Eds.), Proceedings of the 5th PME International Conference, 1, 189-192.
121. John-Steiner, V. (1995): Spontaneous and scientific concepts in mathematics: A Vygotskian approach. In L. Meira & D. Carraher (Eds.), Proceedings of the 19th PME International Conference, 1, 30-44.
122. Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In S. Wagner, & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (Volume 4 of Research agenda for mathematics education, pp. 167-194). Reston, USA: NCTM.
123. Kaput, J. J. (1992). Technology and mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515-556). New York, USA: Macmillan.
124. Kaput, J. J. (1995). A research base supporting long term algebra reform? In D. T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the 7th PME-NA Annual Meeting, 1, 71-94. (ERIC ED 389539)
125. Kaput, J. J., & Roschelle, J. (1997). Developing the impact of technology beyond assistance with traditional formalisms in order to democratize access to ideas underlying calculus. In E. Pehkonen (Ed.), Proceedings of the 21st PME International Conference, 1, 105-112.
126. Kerslake, D. (1977). The understanding of graphs. Mathematics in School, 6(2), 22-25.
127. Kieran, C. (1979). Children's operational thinking within the context of bracketing and the order of operations. In D. Tall (Ed.), Proceedings of the 3rd PME International Conference, 1, 128-133.
128. Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326.
129. Kieran, C. (1983). Relationships between novices' views of algebraic letters and their use of symmetric and asymmetric equation-solving procedures. In J. C. Bergeron, & N. Herscovics (Eds.), Proceedings of the 5th PME-NA Annual Meeting, 1, 161-168.
130. Kieran, C. (1984). A comparison between novice and more-expert algebra students on tasks dealing with the equivalence of equations. In J. M. Moser (Ed.), Proceedings of the 6th PME-NA Annual Meeting, 1, 83-91.
131. Kieran, C. (1985). Use of substitution procedure in learning algebraic equation solving. In S. K. Damarin, & M. Shelton (Eds.), Proceedings of the 7th PME-NA Annual Meeting, 1, 145-152.
132. Kieran, C. (1988). Two different approaches among algebra learners. In A. F. Coxford (Ed.), The ideas of algebra, K-12 (Yearbook of the NCTM, pp. 91-96). Reston, USA: NCTM.
133. Kieran, C. (1989). The early learning of algebra: A structural perspective. In S. Wagner, & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (Volume 4 of Research agenda for mathematics education, pp. 33-56). Reston, USA: NCTM.
134. 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). Cambridge, UK: Cambridge University Press.
135. 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, USA: Macmillan.
136. Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde, & A. Pérez (Eds.), 8th International Congress on Mathematical Education: Selected lectures (pp. 271-290). Seville, Spain: S.A.E.M. Thales.
137. Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139-151.
138. Kieran, C., Boileau, A., & Garançon, M. (1989). Processes of mathematization in algebra problem solving within a computer environment: A functional approach. In C. A. Maher, G. A. Goldin, & R. B. Davis (Eds.), Proceedings of the 11th PME-NA Annual Meeting, 1, 26-34.
139. Kieran, C., Forman, E., & Sfard, A. (Eds.). (2001). Bridging the individual and the social: Discursive approaches to research in mathematics education [special issue]. Educational Studies in Mathematics, 46(1-3).
140. Kieran, C., & Saldanha, L. (2005). Computer algebra systems (CAS) as a tool for coaxing the emergence of reasoning about equivalence of algebraic expressions. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 3, 193-200.
141. Kieran, C., & Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI Study (pp. 99-152). Dordrecht, The Netherlands: Kluwer.
142. Kirshner, D. (1989). The visual syntax of algebra. Journal for Research in Mathematics Education, 20, 274-287.
143. Kirshner, D. (2001). The structural algebra option revisited. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 83-98). Dordrecht, The Netherlands: Kluwer.
144. Kirshner, D., & Awtry, T. (2004). Visual salience of algebraic transformations. Journal for Research in Mathematics Education, 35, 224-257.
145. Knuth, E. J. (2000). Student understanding of the Cartesian connection: An exploratory study. Journal for Research in Mathematics Education, 31, 500-508.
146. Kopelman, E. (2002). Misunderstanding of variables by students in an advanced course. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 3, 225-232.
147. Küchemann, D. (1981). Algebra. In K. Hart (Ed.), Children's understanding of mathematics: 11-16 (pp. 102-119). London, UK: John Murray.
148. Kutscher, B., & Linchevski, L. (1997). Number instantiations as mediators in solving word problems. In E. Pehkonen (Ed.), Proceedings of the 21st PME International Conference, 3, 168-175.
149. Lagrange, J.-B. (2000). L'intégration d'instruments informatiques dans l'enseignement: une approche par les techniques. Educational Studies in Mathematics, 43, 1-30.
150. Lagrange, J.-B. (2003). Learning techniques and concepts using CAS: A practical and theoretical reflection. In J. T. Fey (Ed.), Computer Algebra Systems in secondary school mathematics education (pp. 269-283). Reston, USA: NCTM.
151. Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, USA: Basic Books.
152. Lee, L. (1987). The status and understanding of generalised algebraic statements by high school students. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th PME International Conference, 1, 316-323.
153. Lee, L., & Wheeler, D. (1987). Algebraic thinking in high school students: Their conceptions of generalisation and justification (Research Report). Montreal, Canada: Concordia University, Mathematics Department.
154. Lee, L., & Wheeler, D. (1989). The arithmetic connection. Educational Studies in Mathematics, 20, 41-54.
155. Leron, U., Hazzan, O., & Zazkis, R. (1994). Students' constructions of group isomorphism. In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th PME International Conference, 3, 152-159.
156. Linchevski, L. (1995). Algebra with numbers and arithmetic with letters: A definition of pre-algebra. Journal of Mathematical Behavior, 14, 113-120.
157. Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40, 173-196.
158. Linchevski, L., & Vinner, S. (1990). Embedded figures and structures of algebraic expressions. In G. Booker, P. Cobb, & T. N. Mendicuti (Eds.), Proceedings of the 14th PME International Conference, 2, 85-92.
159. Linchevski, L., & Williams, J. (1996). Situated intuitions, concrete manipulations and the construction of mathematical concepts: The case of integers. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th PME International Conference, 3, 265-272.
160. Lins, R. C. (2001). The production of meaning for algebra: A perspective based on a theoretical model of semantic fields. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 37-60). Dordrecht, The Netherlands: Kluwer.
161. MacGregor, M., & Price, E. (1999). An exploration of aspects of language proficiency and algebraic learning. Journal for Research in Mathematics Education, 30, 449-467.
162. MacGregor, M., & Stacey, K. (1993). Seeing a pattern and writing a rule. In I. Hirabayashi, N. Nohda, K. Shigematsu, & F.-L. Lin (Eds.), Proceedings of the 17th PME International Conference, 1, 181-188.
163. Malara, N. (1999). An aspect of a long-term research on algebra: The solution of verbal problems. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, 3, 257-264.
164. Malara, N. (2003). The dialectics between theory and practice: Theoretical issues and practice aspects from an early algebra project. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 1, 31-48.
165. Maracci, M. (2003). Difficulties in vector space theory: A compared analysis in terms of conceptions and tacit models. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 3, 229-236.
166. Markovits, Z., Eylon, B., & Bruckheimer, M. (1986). Functions today and yesterday. For the Learning of Mathematics, 6(2), 18-24, 28.
167. 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.
168. Mason, J. (2002). What makes an example exemplary? Pedagogical and research issues in transitions from numbers to number theory. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 1, 224-229.
169. Mason, J., Graham, A., & Johnston-Wilder, S. (2005). Developing thinking in algebra. London, UK: Sage.
170. Mason, J., Graham, A., Pimm, D., & Gowar, N. (1985). Routes to roots of algebra. Milton Keynes, UK: Open University Press.
171. Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277-289.
172. Mason, J., & Sutherland, R. (2002). Key aspects of teaching algebra in schools (Report prepared for the Qualifications and Curriculum Authority). London, UK: QCA.
173. Meira, L. (1995). Mediation by tools in the mathematics classroom. In L. Meira & D. Carraher (Eds.), Proceedings of the 19th PME International Conference, 1, 102-111.
174. Meira, L. (1998). Making sense of instructional devices: The emergence of transparency in mathematical activity. Journal for Research in Mathematics Education, 29, 121-142.
175. Molyneux-Hodgson, S., Rojano, T., Sutherland, R., & Ursini, S. (1999). Mathematical modeling: The interaction of culture and practice. Educational Studies in Mathematics, 39, 167-183.
176. Moschkovich, J., Schoenfeld, A. H., & Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations and connections among them. In T. A. Romberg, E. Fennema, & T. P. Carpenter. Integrating research on the graphical representation of function (pp. 69-100). Hillsdale, USA: Lawrence Erlbaum.
177. Moss, J. (2005). Integrating numeric and geometric patterns: A developmental approach to young students' learning of patterns and functions. Paper presented at Annual Meeting of the Canadian Mathematics Education Study Group, Ottawa, Canada.
178. Nemirovsky, R. (Coord.). (2003). Research Forum: Perceptuo-motor activity in mathematics learning. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 1, 103-135.
179. Nesher, P., & Kilpatrick, J. (Eds.). (1990). Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education. Cambridge, UK: Cambridge University Press.
180. Noble, T., Nemirovsky, R., Wright, T., & Tierney, C. (2001). Experiencing change: The mathematics of change in multiple environments. Journal for Research in Mathematics Education, 32, 85-108.
181. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings. Dordrecht, The Netherlands: Kluwer.
182. Pawley, D. (1999). To check or not to check? Does teaching a checking method reduce the incidence of the multiplicative reversal error? In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, 4, 17-24.
183. Pence, B. (1994). Teachers' perceptions of algebra. In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th PME International Conference, 4, 17-24.
184. Perrenet, J. C., & Wolters, M. A. (1994). The art of checking: A case study of students' erroneous checking behavior in introductory algebra. Journal of Mathematical Behavior, 13, 335-358.
185. Pierce, R., & Stacey, K. (2001). A framework for Algebraic Insight. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Proceedings of the 24th MERGA Conference, 2, 418-125.
186. Pirie, S. E. B., & Martin, L. (1997). The equation, the whole equation and nothing but the equation! One approach to the teaching of linear equations. Educational Studies in Mathematics, 34, 159-181.
187. Ponte, J. (1985). Geometric and numerical strategies in students' functional reasoning. In L. Streefland (Ed.), Proceedings of the 9th PME International Conference, 1, 413-418.
188. Presmeg, N., & Nenduradu, R. (2005). An investigation of a preservice teacher's use of representations in solving algebraic problems involving exponential relationships. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 4, 105-112.
189. Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics, 42, 237-268.
190. Radford, L. (2004). Syntax and meaning. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 1, 161-166.
191. Radford, L., Bardini, C., Sabena, C., Diallo, P., & Simbagoye, A. (2005). On embodiment, artifacts, and signs: A semiotic-cultural perspective on mathematical thinking. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 4, 113-120.
192. Radford, L., Demers, S., Guzmán, J., & Cerulli, M. (2003). Calculators, graphs, gestures and the production of meaning. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 4, 55-62.
193. Radford, L., & Grenier, M. (1996). Les apprentissages mathématiques en situation. Revue des Sciences de l'Éducation, XXII, 253-275.
194. Robinson, N., Even, R., & Tirosh, D. (1992). Connectedness in teaching algebra: A novice-expert contrast. In W. Geeslin & K. Graham (Eds.), Proceedings of the 16th PME International Conference, 2, 258-265.
195. Robutti, O., & Arzarello, F. (2003). Approaching algebra through motion experiences. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 1, 111-115.
196. Rogalski, M. (1996). Teaching linear algebra: Role and nature of knowledges in logic and set theory which deal with some linear problems. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th PME International Conference, 4, 211-218.
197. Romberg, T. A., Fennema, E., & Carpenter, T. P. (Eds.). (1993). Integrating research on the graphical representation of function. Hillsdale, USA: Lawrence Erlbaum.
198. Ruthven, K., & Hennessy, S. (2002). A practitioner model of the use of computer-based tools and resources to support mathematics teaching and learning. Educational Studies in Mathematics, 49, 47-88.
199. Sackur, C., Drouhard, J.-Ph., Maurel, M., & Pécal, M. (1997). Comment recueillir des connaissances cachées en algèbre et qu'en faire? Repères - IREM, 28, 37-68.
200. Sasman, M. C., Olivier, A., & Linchevski, L. (1999). Factors influencing students' generalisation thinking processes. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, 4, 161-168.
201. Schliemann, A., Carraher, D. W., Brizuela, B. M., Earnest, D., Goodrow, A., Lara-Roth, S., & Peled, I. (2003). Algebra in elementary school. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 4, 127-134.
202. Schmidt, S., & Bednarz, N. (1997). Raisonnements arithmétiques et algébriques dans un contexte de résolution de problèmes: Difficultés rencontrées par les futurs enseignants. Educational Studies in Mathematics, 32, 127-155.
203. Schmittau, J., & Morris, A. (2004). The development of algebra in the elementary mathematics curriculum of V. V. Davydov. The Mathematics Educator, 8, 60-87.
204. Schnepp, M., & Nemirovsky, R. (2001). Constructing a foundation for the fundamental theorem of calculus. In A. A. Cuoco, & F. R. Curcio (Eds.), The roles of representation in school mathematics (Yearbook of the NCTM, pp. 90-102). Reston, USA: NCTM.
205. Schwartz, J., & Yerushalmy, M. (1992). Getting students to function in and with algebra. In E. Dubinsky, & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (MAA Notes, 25, pp. 261-289). Washington, DC, USA: Mathematical Association of America.
206. Schwartz, J., & Yerushalmy, M. (1996). Calculus unlimited [Computer software]. Tel-Aviv, Israel: Center for Educational Technology.
207. Schwarz, B. B., & Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30, 362-389.
208. Schwarz, B. B., Hershkowitz, R., & Dreyfus, T. (2002). Abstraction in context: Construction and consolidation of knowledge structures. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 1, 120-125.
209. Sfard, A. (1987). Two conceptions of mathematical notions: Operational and structural. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th PME International Conference, 3, 162-169.
210. 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.
211. Sfard, A. (1994). Reification as the birth of a metaphor. For the Learning of Mathematics, 14, 44-55.
212. Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communication to learn more about mathematical thinking. Educational Studies in Mathematics, 46, 13-57.
213. Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification - the case of algebra. Educational Studies in Mathematics, 26, 191-228.
214. Shaughnessy, M. (1987). Research reports on projects with in-service teachers: A reaction. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th PME International Conference, 2, 149-162.
215. Sierpinska, A., Trgalová, J., Hillel, J., & Dreyfus, T. (1999). Teaching and learning linear algebra with Cabri. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, 1, 119-134.
216. Simmt, E., Davis, B., Gordon, L., & Towers, J. (2003). Teachers' mathematics: Curious obligations. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 4, 175-182.
217. Solomon, J., & Nemirovsky, R. (1999). "This is crazy, differences of differences!" On the flow of ideas in a mathematical conversation. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, 4, 217-224.
218. Soloway, E., Lochhead, J., & Clement, J. (1982). Does computer programming enhance problem solving ability? Some positive evidence on algebra word problems. In R. J. Seidel, R. E. Anderson, & B. Hunter (Eds.), Computer literacy (pp. 171-185). New York, USA: Academic Press.
219. Stacey, K., Chick, H., & Kendal, M. (Eds.). (2004). The future of the teaching and learning of algebra: The 12th ICMI Study. Dordrecht, The Netherlands: Kluwer.
220. Stacey, K., Kendal, M., & Pierce, R. (2002). Teaching with CAS in a time of transition. The International Journal of Computer Algebra in Mathematics Education, 9, 113-127.
221. Stacey, K., & MacGregor, M. (1997). Multiple referents and shifting meanings of unknowns in students' use of algebra. In E. Pehkonen (Ed.), Proceedings of the 21st PME International Conference, 4, 190-197.
222. Stacey, K., & MacGregor, M. (1999). Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18, 149-167.
223. Steinberg, R. M., Sleeman, D. H., & Ktorza, D. (1990). Algebra students' knowledge of equivalence of equations. Journal for Research in Mathematics Education, 22, 112-121.
224. Streun, A. V., Harskamp, E., & Suhre, C. (2000). The effect of the graphic calculator on students' solution approaches: A secondary analysis. Hiroshima Journal of Mathematics Education, 8, 27-40.
225. Sutherland, R., & Rojano, T. (1993). A spreadsheet approach to solving algebra problems. Journal of Mathematical Behavior, 12, 353-383.
226. Sutherland, R., Rojano, T., Bell, A., & Lins, R. (Eds.). (2001). Perspectives on school algebra. Dordrecht, The Netherlands: Kluwer.
227. Thomas, M. O. J., & Hong, Y. Y. (2005). Teacher factors in integration of graphic calculators into mathematics learning. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th PME International Conference, 4, 257-264.
228. Thomas, M. O. J., & Tall, D. (1986). The value of the computer in learning algebra concepts. In Univ. of London Institute of Education (Eds.), Proceedings of the 10th PME International Conference, 1, 313-318.
229. Thompson, P. W., & Thompson, A. G. (1987). Computer presentations of structure in algebra. In J. C. Bergeron, N. Herscovics, & C. Kieran (Eds.), Proceedings of the 11th PME International Conference, 1, 248-254.
230. Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51-64.
231. Trigueros, M., & Ursini, S. (1999). Does the understanding of variable evolve through schooling? In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, 4, 273-280.
232. Trouche, L. (2000). La parabole du gaucher et de la casserole à bec verseur: Étude des processus d'apprentissage dans un environnement de calculatrices symboliques. Educational Studies in Mathematics, 41 , 239-264.
233. Tsamir, P., & Bazzini, L. (2002). Algorithmic models: Italian and Israeli students' solutions to algebraic inequalities. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 4, 289-296.
234. Ursini, S. (1990). Generalization processes in elementary algebra: Interpretation and symbolization. In G. Booker, P. Cobb, & T. N. Mendicuti (Eds.), Proceedings of the 21st PME International Conference, 2, 149-156.
235. Ursini, S., & Trigueros, M. (1997). Understanding of different uses of variable: A study with starting college students. In E. Pehkonen (Ed.), Proceedings of the 14th PME International Conference, 4, 254-261.
236. Van Amerom, B. A. (2003). Focusing on informal strategies when linking arithmetic to early algebra. Educational Studies in Mathematics, 54, 63-75.
237. Van Dooren, W., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers' content knowledge on their evaluation of students' strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Education, 33, 319-351.
238. Van Dooren, W., Verschaffel, L., & Onghena, P. (2003) Pre-service teachers' preferred strategies for solving arithmetic and algebra word problems. Journal of Mathematics Teacher Education, 6, 27-52.
239. Vergnaud, G. (1984). Understanding mathematics at the secondary-school level. In A. Bell, B. Low, & J. Kilpatrick (Eds.), Theory, research and practice in mathematical education (Report of ICME5 Working Group on Research in Mathematics Education, pp. 27-35). Nottingham, UK: Shell Centre for Mathematical Education.
240. Vergnaud, G. (1988). Long terme et court terme dans l'apprentissage de l'algèbre. In C. Laborde (Ed.), Actes du Premier Colloque Franco-Allemand de Didactique des Mathématiques et de l'Informatique (pp. 189-199). Grenoble, France: La Pensée Sauvage.
241. Vermeulen, N. (2000). Student teachers' concept images of algebraic expressions. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME International Conference, 4, 257-264.
242. Vlassis, J. (2002). The balance model: Hindrance or support for the solving of linear equations with one unknown. Educational Studies in Mathematics, 49, 341-359.
243. Vlassis, J. (2004). Sens et symboles en mathématiques: Étude de l'utilisation du signe «moins» dans les réductions polynomiales et la résolution d'équations du premier degré à une inconnue (doctoral dissertation). Liège, Belgium: Université de Liège, Faculté de Psychologie et des Sciences de l'Éducation.
244. Wagner, S. (1981). Conservation of equation and function under transformation of variable. Journal for Research in Mathematics Education, 12, 107-118.
245. Wagner, S., & Kieran, C. (Eds.). (1989). Research issues in the learning and teaching of algebra (Volume 4 of Research agenda for mathematics education). Reston: NCTM.
246. Wagner, S., Rachlin, S. L., & Jensen, R. J. (1984). Algebra Learning Project: Final report. Athens, USA: University of Georgia, Department of Mathematics Education.
247. Warren, E. (2003). Young children's understanding of equals: A longitudinal study. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 4, 379-386.
248. 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 PME International Conference, 4, 305-312.
249. Whitman, B. S. (1976). Intuitive equation solving skills and the effects on them of formal techniques of equation solving. PhD dissertation, Florida State University, USA. (Dissertation Abstracts International, 36, 5180A. University Microfilms No. 76-2720)
250. Wilson, K., Ainley, J., & Bills, L. (2003). Comparing competence in transformational and generational algebraic activities. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th PME International Conference, 4, 427-434.
251. Yerushalmy, M. (2000). Problem solving strategies and mathematical resources: A longitudinal view on problem solving in a function-based approach to algebra. Educational Studies in Mathematics, 43, 125-147.
252. Yerushalmy, M., & Chazan, D. (2002). Flux in school algebra: Curricular change, graphing, technology, and research on student learning and teacher knowledge. In L. English (Ed.), Handbook of international research in mathematics education (pp. 725-755). Mahwah, USA: Lawrence Erlbaum.
253. Yerushalmy, M., & Schwartz, J. L. (1993). Seizing the opportunity to make algebra mathematically and pedagogically interesting. In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.), Integrating research on the graphical representation of function (pp. 41-68). Hillsdale, USA: Lawrence Erlbaum.
254. Yerushalmy, M., & Shternberg, B. (2001). Charting a visual course to the concept of function. In A. A. Cuoco, & F. R. Curcio (Eds.), The roles of representation in school mathematics (Yearbook of the NCTM, pp. 251-268). Reston, USA: NCTM.
255. Zack, V. (1995). Algebraic thinking in the upper elementary school: The role of collaboration in making meaning of 'generalization'. In L. Meira & D. Carraher (Eds.), Proceedings of the 19th PME International Conference, 2, 106-113.
256. Zack, V. (1997). You have to prove me wrong: Proof at the elementary school level. In E. Pehkonen (Ed.), Proceedings of the 21st PME International Conference, 4, 291-298.
257. Zack, V. (2002). Learning from learners: Robust counterarguments of fifth graders' talk about reasoning and proving. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th PME International Conference, 4, 434-441.
258. Zaslavsky, O., Sela, H., & Leron, U. (2002). Being sloppy about slope: The effect of changing the scale. Educational Studies in Mathematics, 49, 119-140.
259. Zazkis, R., & Campbell, S. (1996). Divisibility and multiplicative structure of natural numbers: Preservice teachers' understanding. Journal for Research in Mathematics Education, 27, 540-563.
260. Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379-402.
261. Zbiek, R. M., & Heid, M. K. (2001). Dynamic aspects of function representations. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), Proceedings of the 12th ICMI Study Conference: The future of the teaching and learning of algebra (pp. 682-689). Melbourne, Australia: The University of Melbourne.
262. Zehavi, N. (2004). Symbol sense with a symbolic-graphical system: A story in three rounds. Journal of Mathematical Behavior, 23, 183-203.