Bher M. J., Lesh R., Post T. R. and Silver E. A.: 1983, ‘Rational number concepts’, in Lesh R. and Landau M. (eds.),

*Acquisition of Mathematical Concepts and Processes*, Academic Press, New York, pp. 92–128.

Google ScholarBell, A.: 1988, ‘Algebra-choices in curriculum design’, in Borbas, A. (ed.), *Proceedings of the 12th International Conference for the Psychology of Mathematics Education*, 1, 147–153.

Bell A., Malone J. A. and Taylor P. C.: 1987,

*Algebra—an Exploratory Teaching Experiment*, Nottingham, England: Shell Center for Mathematics Education.

Google ScholarBooth L. R.: 1988, ‘Children's difficulties in beginning algebra’, in

*The Ideas of Algebra, K-12*, 1988 NCTM Yearbook, National Council of Teachers of Mathematics: Reston, Virginia, pp. 20–32.

Google ScholarBoyer C. B./ Merzbach V. C.: 1991,

*A History of Mathematics*, 2nd edition, revised by Merzbach, John Wiley & Sons, New York, pp. 228–9.

Google ScholarBruner J.: 1967,

*The Process of Education*, New York: Random House.

Google ScholarCarpenter T. P., Corbin M. K., Kepner H. S., Montgomery Lindquist M. and Reys R. E.: 1981,

*Results from the Second Mathematics Assessment of the National Assessment of Educational Progress*, NCTM: Reston, Virginia.

Google ScholarCauzinille, E., Mathieu, J. and Resnick, B.: 1984, ‘Children's Understanding of Algebraic and Arithmetic Expressions’, paper presented at the annual meeting of the American Educational Research Association, New Orleans, La.

Chaiklin, S. and Lesgold, S.: 1984, ‘Pre-Algebra Students’ Knowledge of Algebraic Tasks with Arithmetic Expressions’, paper presented at the annual meeting of the American Educational Research Association, New Orleans, La.

Chalouh L. and Herscovics N.: 1988, ‘Teaching algebraic expressions in a meaningful way’, in

*The Ideas of Algebra, K-12*, 1988 NCTM Yearbook, National Council of Teachers of Mathematics: Reston, Virginia, pp. 33–42.

Google ScholarChalouh, L. and Herscovics, N.: 1984, ‘From letter representing a hidden quantity to letter representing an unknown quantity’, in Moser, J. M. (ed.), *Proceedings PME-NA VI*, Madison, Wisconsin, pp. 71–76.

Collis K. F.: 1975,

*The Development of Formal Reasoning*, Report of a Social Science Research Council sponsored project (HR2434/1) carried out at the University of Nottingham, University of Newcastle, NSW, Australia.

Google ScholarCollis K.F.: 1974, ‘Cognitive Development & Mathematics Learning’, paper prepared for the Psychology of Mathematics Education Workshop, published at the Shell Mathematics Unit Center for Science Education, Chelsea College, University of London, UK.

Google ScholarCooney T. J.: 1985, ‘A beginning teacher's view of problem solving’,

*Journal for Research in Mathematics Education*
**16**, 324–336.

Google ScholarDavis R. B.: 1985, ‘Algebraic thinking in the early grades’,

*Journal of Mathematical Behavior*
**2**, 310–320.

Google ScholarDavis R. B.: 1975, ‘Cognitive processes involved in solving simple algebraic equations’,

*Journal of Children's Mathematical Behavior*
**1**, (3), 7–35.

Google ScholarDemana F. and Leitzel J.: 1988, in

*The Ideas of Algebra, K-12*, 1988 NCTM Yearbook, National Council of Teachers of Mathematics: Reston, Virginia, pp. 61–69.

Google ScholarFilloy E. and Rojano T.: 1989, ‘Solving equations: the transition from arithmetic to algebra’,

*For the Learning of Mathematics*
**9**, (2), 19–25.

Google ScholarFilloy E. and Rojano T.: 1985a, ‘Obstructions to the acquisition of elemental algebraic concepts and teaching strategies’, in Streefland L. (ed.),

*Proceedings of PME-9*, OW & OC, State University of Utrecht: The Netherlands, pp. 154–158.

Google ScholarFilloy, E. and Rojano, T.: 1985b, ‘Operating the unknown and models of teaching’, in Damarin, S. and Shelton, M. (eds.), *Proceedings of PME-NA-7*, Columbus, Ohio, pp. 75–79.

Filloy, E. and Rojano, T.: 1984, ‘From an arithmetical to an algebraic thought’, in Moser, J. M. (ed.), *Proceedings of PME-NA-6*, Madison, Wisconsin, pp. 51–56.

Greeno, J.: 1982, ‘A Cognitive Learning Analysis of Algebra’, paper presented at the annual meeting of the American Educational Research Association, Boston, MA.

Harper E.: 1987, ‘Ghosts of Diophantus’,

*Educational Studies in Mathematics*
**18**, 75–90.

Google ScholarHerscovics N.: 1989, ‘Cognitive obstacles encountered in the learning of algebra’, in Wagner S. and Kieran C. (eds.),

*Research Issues in the Learning and Teaching of Algebra*, Reston, Virginia: NCTM, and Hillsdale, N.J.: Erlbaum, pp. 60–68.

Google ScholarHerscovics N. and Kieran C.: 1980, ‘Constructing meaning for the concept of equation’,

*The Mathematics Teacher*
**73**, (8), 572–580.

Google ScholarHerscovics N. and Linchevski L.: 1994, ‘The cognitive gap between arithmetic and algebra’,

*Educational Studies in Mathematics*
**27**, (1), 59–78.

Google ScholarHerscovics, N. and Linchevski, L.: 1992, ‘Cancellation within-the-equation as a solution procedure’, in Geeslin, W. and Graham, K. (eds.), *Proceedings of the XVI PME Conference*, University of New Hampshire, Durham, 1, pp. 265–272.

Kieran C.: 1992, ‘The learning and teaching of school algebra’, in Grouws D. A. (ed.),

*Handbook of Research on Mathematics Teaching and Learning*, Macmillan Publishing Company, New York, pp. 390–419.

Google ScholarKuchemann D.: 1981,

*Children's Understanding of Mathematics: 11–16*, London: John Murray, pp. 102–119.

Google ScholarKuchemann D.: 1978, ‘Children's understanding of numerical variables’,

*Mathematics in School*
**7**, (4), 23–26.

Google ScholarLinchevski, L. and Sfard, A.: 1991, ‘Rules without reasons as processes without objects-the case of equations and inequalities’, in Furinghetti, F. (ed.), *Proceedings of PME XV*, Assisi, Italy, pp. 317–325.

Lodholz R.: 1990, ‘The transition from arithmetic to algebra’, in Edwards E. L.Jr. (ed.),

*Algebra for Everyone*, NCTM: Reston, Virginia, pp. 24–33.

Google ScholarMenchinskaya N. A.: 1969, ‘The psychology of mastering concepts: Fundamental problems and methods of research’, in Kilpatrick J. and Wirszup I. (eds.),

*Soviet Studies in the Psychology of Learning and Teaching Mathematics*, V1, SMSG, Stanford, pp. 75–92.

Google ScholarPeck D. M. and Jencks S. M.: 1988, ‘Reality, arithmetic, algebra’,

*Journal of Mathematical Behavior*
**7**, 85–91.

Google ScholarSfard 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.

Google ScholarSfard A. and Linchevski L.: 1994, ‘The gains and pitfalls of reification: The case of algebra’,

*Educational Studies in Mathematics*
**26**, 191–228.

Google ScholarSteinberg R. M., Sleeman D. H. and Ktorza D.: 1991, ‘Algebra students’ knowledge of equivalence of equations’,

*Journal for Research in Mathematics Education*
**22**, (2), 112–121.

Google ScholarStreeter J. and Hutchison D.: 1989,

*Intermediate Algebra*, McGraw-Hill, New York, p. 75.

Google ScholarUsiskin Z.: 1988, ‘Children's difficulties in beginning algebra’, in

*The Ideas of Algebra*, K-12, 1988 NCTM Yearbook, National Council of Teachers of Mathematics: Reston, Virginia, pp. 8–20.

Google ScholarYerusalmy M.: 1988,

*Effects of Graphic Feedback on the Ability to Transform Algebraic Expressions when Using Computers*, The University of Haifa, Haifa, Israel.

Google Scholar