Can x=3 be the solution of an inequality? A study of Italian and Israeli students
Tipo de documento
Autores
Lista de autores
Tsamir, Pessia y Bazzini, Luciana
Resumen
This paper describes a study regarding Israeli and Italian students’ solutions to algebraic inequalities. The findings presented here show similarities in students’ correct and incorrect solutions, in both countries. Fischbein’s notions of algorithmic, intuitive and formal knowledge are used co analyze the data. The findings indicate that students generally worked in an algorithmic manner, intuitively drawing analogies to the solutions of related equations. We conclude by suggesting some educational implications.
Fecha
2001
Tipo de fecha
Estado publicación
Términos clave
Contextos o situaciones | Ecuaciones e inecuaciones | Estrategias de solución | Otro (álgebra)
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Referencias
ARZRELLO, F.; BAZZINI, L. and CHIAPPINI, G. (1993). Cognitive Processes in algebraic thinking: Towards a theoretical framework. Tsukuba, Japan. Proceedings of PME 17, v. 1, pp. 138-145. BAZZINI, L. (2000). Cognitive processes in algebraic thinking and implications for teaching. Paper presented at ICME 9. Tokyo, Japan. CHAKRABARTI, A. and HAMSAPRIYE, A. (1997). On corrected summation of alternating series. International Journal of Mathematical Education in Science and Technology, v. 27, 0. 4, pp. 565-582. DOBBS, D. and PETERSON, J. (1991). The sign-chart method for solving inequalities. Mathematics Teacher, n. 84, pp. 657-664. DREYFUS, T. and EISENBERG, T. (1985). A graphical approach to solving inequalities. School Science and Mathematics, a. 85, pp. 651-662. FISCHBEIN, E. (1987). Intuition in Science and Mathematics — An Educational Approach. Reidel. LINCHEVSKI, L. and SFARD, A. (1991). Rules without reasons as processes without objects — The case of equations and inequalities. Assisi, Italy. Proceedings of PME 15, v. Il, pp. 317-324. MAHMOOD, M. and EDWARDS, P. (1999). Some inequalities and sequences converging to e. International Journal of Mathematical Education in Science and Technology, v. 30, n. 3, pp. 430-434. MAUREL, M. and SAKUR, C. (1998). Les inéquations en classe de seconde et l'expérience de la nécessité. Nice. Proceedings of SFIDA XI, pp. 35-46. McLAURIN, S. C. (1985). A unified way to teach the solution of inequalities. Mathematics Teacher, n. 78, pp. 91-95. NCTM - National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, Virginia. NCTM - National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, Virginia. PARISH, C.R. (1992). Inequalities, absolute value, and logical connectives. Mathematics Teacher, v. 85, pp. 756-757. PIEZ, C. M. and VOXMAN, M. H. (1997). Multiple representations — using different perspective to form a clear picture. Mathematics Teacher, v. 90, n. 2, pp. 164-166. PROJECT GROUP 1 (1999). “Algebra: Epistemology, cognition and new technologies”. In: DROUHARD, J. P and BELL, A. (coords.). Proceedings of PME 23. Haifa, Israel, v. I. STAVY, R. and TIROSH, D. (2000). How students (mis-)understand science and mathematics: Intuitive rules. Teachers College Press, USA. TSAMIR, P. and ALMOG, N. (1999). “No answer” as a problematic response: The case of inequalities. Proceedings of PME 23. Haifa, Israel, v. I. TSAMIR, P; TIROSH, D. and ALMOG, N. (1998). “Students” solutions of inequalities. Proceedings of PME 22. Stellenbosch, South Africa, v. VI, pp. 129-136. VANDYK, R. P. (1990). Expressions, equations and inequalities. Mathematics Teacher, n. 83, pp. 41-42. WORKING GROUP 2 (1998). “Algebra: Epistemology, cognition and new technologies”. In: DROUHARD, J. P and VALROSE, P (coords.). Proceedings of PME 22. Stellenbosch, South Africa, v. I.