Difficulties in Learning Inequalities
in Students of the First Year of
Pre-University Education in Spain

Lorenzo J. Blanco; Manuel Garrote

doi:10.12973/ejmste/75401

Difficulties in Learning Inequalities in Students of the First Year of Pre-University Education in Spain

Full Text (PDF)

Lorenzo J. Blanco ¹ ^* , Manuel Garrote ²

More Detail

¹ Universidad de Extremadura, Badajoz, SPAIN² Colegio “Ntra Sra del Carmen” Badajoz, SPAIN^* Corresponding Author

Abstract

We present a summary of a study carried out with students of the first year of Bachillerato (the first of two pre-university non-obligatory secondary education courses in Spain) to determine and analyse some of their errors and difficulties in learning inequalities with the aim of improving the teaching-learning process of this topic. The study was based on work on the initiation to algebra, in particular on the observed difficulties and errors relative to algebraic skills.

Keywords

inequalities
students’ misteakes
secondary
algebra
mathematics

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2007, Volume 3, Issue 3, 221-229

https://doi.org/10.12973/ejmste/75401

Publication date: 23 Oct 2007

Article Views: 3549

Article Downloads: 3969

Open Access References How to cite this article

References

Behr, M. et al. (1980). How children view the equal sign. Mathematics Teaching 92. 13-15.
Beltrán, A. (1997). Evolución matemática de nuestros alumnos. [The mathematical evolution of our pupils.] Épsilon, 39. 165-168.
Blanco, L.J. (2001). Errors in the Teaching/Learning of the Basic Concepts of Geometry. International Journal for Mathematics Teaching and Learning. http://www.ex.ac.uk/cimt/ijmtl/ijmenu.htm
Brousseau, G. (1997). Theory of Didactical Situations in Mathematics. Kluwer Academic Publishers. Dordrecht.
Cohen, L. & Manion, L. (1982). Research Methods in Education. Croom Helm. London.
Collis, K.F. (1975). A study of concrete and formal operations in school mathematics: a Piagetian view point. Australian Council for Educational Research. Melbourne.
Coxford, A.F. & Shulte, A.P. (1988). The ideas of algebra, K–12. 1988 Yearbook. N.C.T.M.
Enfedaque, J. (1990). De los números a las letras. [From numbers to letters.] Suma, nº 5. 23-34.
Gallego, J.L. (1995). Errores conceptuales y de procedimientos en las matemáticas. [Conceptual and procedural error in mathematics.] Épsilon, 33. 261-264.
Goldin, G. and Shteingold, N (2001). System of representations and the development of mathematical concepts. In Cuoco, A.A. & Curcio, F.R. The roles of representation in school mathematics. NCTM. 1 – 23
Grupo Azarquiel (1991). Ideas y actividades para enseñar álgebra. [Ideas and activities to teach algebra] Síntesis. Madrid.
Gutiérrez, A. & Jaime, A. (1996). Uso de definiciones e imágenes de conceptos geométricos por los estudiantes de Magisterio. [Use of definitions and images of geometrical concepts by students for primary teachers.] In Giménez, J.; Llinares, S.; & Sánchez, M.V. (eds.): El proceso de llegar a ser un profesor de primaria. Cuestiones desde la educación matemática. [The process of becoming a primary teacher. Questions from mathematics education.] Comares. 143- 170.
Kieran, C. (1979). Children's operational thinking within the context of bracketing and the order of operations. In D. Tall (ed.) Proceeding of the Third International Conference for PME. Coventry, England. Warwick University, Mathematics Eduational Research Centre. 128-133.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12. 317- 326.
Kieran, C. (1992). The learning and teaching of school algebra. In Grouws, D.A. Handbook of Research on Mathematics Teaching and Learning. Macmillan Pub. Co. 390 – 419.
Kücheman, D. (1978). Children’s understanding of numerical variables Mathematics in School, 20. 41-54 20. 41 – 54
Kücheman, D. (1981). Algebra. In K.M. Hart (ed.) Children’s understanding of mathematics. London. John Murray. 102-119.
Lochhead, J. & Mestre, J.P. (1988). From words to algebra: mending misconceptions. In Coxford, A.F. & Shulte, A.P. The ideas of algebra, K-12. 1988 Yearbook. NCYM. 127-135.
MacGregor, M. & Stacey, K. (1997). Students' understanding of algebraic notation: 11-15. Educational Studies in Mathematics, 33(1), 1-19. http://www.edfac.unimelb.edu.au/DSME/staff/ Kaye_Stacey/projects/alg-proj.htm
Marquis, J. (1988). Common mistakes in algebra. In Coxford, A.F. & Shulte, A.P.. The ideas of algebra, K12. 1988 Yearbook. NCTM. 204-205.
Palarea, M.M. (1999). La adquisición del lenguaje algebraico: reflexiones de una investigación. [The acquisition of algebraic language: reflections from an investigation.] Números, nº 40. 3-28.
Palarea, M.M & Socas, M.M. (1999-2000). Procesos cognitivos implicados en el aprendizaje del lenguaje algebraico. Un estudio biográfico. [Cognitive processes involved in learning algebraic language.] El Guiniguada, nº 8/9. 319-336.
Radatz, H (1980). Students' errors in the mathematical learning process: A survey. For the Learning Mathemtaics, 1. 16-20.
Resnick, L. (1983). Mathematics and sciences learning. A new conception. Science, 29. 477-78.
Socas, M.M. (1997). Dificultades, obstáculos y errores en el aprendizaje de las matemáticas en la educación secundaria. [Difficulties, obstacles, and errors in learning mathematics in secondary education.] In Rico, L. et al.: La educación matemáti ca en la enseñanza secundaria. [Mathematics education at the secondary level.] ICE/Horsori. 125-154.
Socas, M.M., Camacho, M., Palarea, M. & Hernández, J. (1989). Iniciación al álgebra. Matemáticas: Cultura y Aprendizaje. [Initiation to algebra. Mathematics: Culture and Learning.] Ed. Síntesis, nº 23. Madrid.
Trigueros, M., Reyes, A., Ursini, S. & Quintero, R.(1996). Diseño de un cuestionario de diagnóstico acerca del manejo del concepto de variable en el álgebra. [Design of a diagnostic questionnaire about the handling of the concept of variable in algebra.] Enseñanza de las ciencias, nº 14(3). 351-363.
Usiskin, Z (1988). Conceptions of school algebra and uses of variables. In Coxford, A.F. & Shulte, A.P. The ideas of algebra, K-12. 1988 Yearbook. NCTM. 8– 19.
Vega, E. (1995). El uso del lenguaje algebraico en alumnos de bachillerato. [The use of algebraic language in pre-university pupils.] Educación matemática, nº 7(3), pp. 27-47.
Woods, P. (1986). Inside schools. Routledge & Kegan, P. London.

How to cite this article

APA

Blanco, L. J., & Garrote, M. (2007). Difficulties in Learning Inequalities in Students of the First Year of Pre-University Education in Spain. Eurasia Journal of Mathematics, Science and Technology Education, 3(3), 221-229. https://doi.org/10.12973/ejmste/75401

Vancouver

Blanco LJ, Garrote M. Difficulties in Learning Inequalities in Students of the First Year of Pre-University Education in Spain. EURASIA J Math Sci Tech Ed. 2007;3(3):221-9. https://doi.org/10.12973/ejmste/75401

AMA

Blanco LJ, Garrote M. Difficulties in Learning Inequalities in Students of the First Year of Pre-University Education in Spain. EURASIA J Math Sci Tech Ed. 2007;3(3), 221-229. https://doi.org/10.12973/ejmste/75401

Chicago

Blanco, Lorenzo J., and Manuel Garrote. "Difficulties in Learning Inequalities in Students of the First Year of Pre-University Education in Spain". Eurasia Journal of Mathematics, Science and Technology Education 2007 3 no. 3 (2007): 221-229. https://doi.org/10.12973/ejmste/75401

Harvard

Blanco, L. J., and Garrote, M. (2007). Difficulties in Learning Inequalities in Students of the First Year of Pre-University Education in Spain. Eurasia Journal of Mathematics, Science and Technology Education, 3(3), pp. 221-229. https://doi.org/10.12973/ejmste/75401

MLA

Blanco, Lorenzo J. et al. "Difficulties in Learning Inequalities in Students of the First Year of Pre-University Education in Spain". Eurasia Journal of Mathematics, Science and Technology Education, vol. 3, no. 3, 2007, pp. 221-229. https://doi.org/10.12973/ejmste/75401