The presentation of the concept of variable in textbooks: A comparative analysis

Main Article Content

José Luis Díaz Gómez

Abstract

The concept of variable is fundamental in learning algebra and other areas of mathematics, but its understanding remains a significant challenge for students at various educational levels. This article analyzes how the concept of variable is presented in 100 elementary, middle school, high school, and college textbooks, with the objective of identifying patterns, inconsistencies, and opportunities for improvement. The results show that most of the texts approach it as a general number or an unknown, while more advanced approaches, such as the variable as a functional relationship, are less frequent. It is concluded that it is necessary to integrate broader and contextualized definitions to improve students' conceptual understanding.

Article Details

How to Cite
Díaz Gómez, J. L. (2025). The presentation of the concept of variable in textbooks: A comparative analysis. El cálculo Y Su enseñanza, 20(2), 1–18. Retrieved from http://recacym.org/index.php/recacym/article/view/226
Section
Guest Articles

References

Auvil, D., y Poluga, Ch. (1984). Elementary Algebra. Addison Wesley Publishing Company.

Barnett, R. (1960). Algebra: Principles and Applications. McGraw-Hill.

Barnett, R. (1960). Elementary Algebra. Schaum’s.

Barnett, R. (1984). Intermediate Algebra. McGraw-Hill.

Blitzer, R. (2010). College Algebra. Pearson.

Chevallard, Y. (1985). La transposición didáctica. Revue Internationale de Didactique, 2(1), 5-21.

Clement, J. (2000) Analysis of clinical interviews: Foundations and model viability. In Lesh, R. and Kelly, A., Handbook of research methodologies for science and mathematics education (pp. 341-385). Hillsdale, NJ: Lawrence Erlbaum.

Demana, F., Waits, B., Foley, G., Kennedy, D. y Blitzer R. (2009) Matemáticas Universitarias Introductorias con Nivelador Mymathlab. Pearson Educación.

Díaz, J, y Morales, L. (2005). El concepto de variable en los libros de texto. Publicación de la XV Semana Regional de Investigación y Docencia en Matemáticas.

Dogbey, James K., (2010). Concepts of Variable in Middle-Grades Mathematics Textbooks during Four Eras of Mathematics Education in the United States. Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/1615

Freeman, D. J., & Porter, A. C. (1989). Do textbooks dictate the content of mathematics instruction in elementary schools? American Educational Research Journal, 26(3), 403-421.

García, B., y Llinares C. (1995). El concepto de función a través de los textos escolares: reflexión sobre una evolución. Qurriculum, No 10-11, pp. 103-115.

Glencoe. (1999). Matemáticas: Aplicaciones y Conexiones. Glencoe/McGraw-Hill.

Gobran A. (1990). Algebra Elemental. Grupo Editorial Iberoamericana.

González A., y Sierra, M. (2004). Metodología de análisis de libros de texto de matemáticas: los puntos críticos en la enseñanza secundaria en España deurante el siglo XX. Enseñanza de las ciencias: revista de investigación y experiencias didácticas, 22(3), 389-408. https://doi.org/10.5565/REV/ENSCIENCIAS.3872

Herrera, E, Cuesta, B, y Escalante, J. (2016). El concepto de variable: un análisis con estudiantes de bachillerato. Educación Matemática, 28(3).

Howson, G. (1995). Mathematics Textbooks: A comparative Study of Grade 8 texts. Vancouver: Pacific Educational Press.

Kieran, C. (1981). Concepts associated with equality symbols. Educational Studies in Mathematics, 12(3), 317-326.

Kieran, C. (1980). Constructing meaning for non trivial equations. Paper presented at the AERA conference, Boston.

Kilhamn, C., Bråting, K., Helenius, O., y Mason, J. (2022). Variables in early algebra: exploring didactic potentials in programming activities. ZDM – Mathematics Education, 54. 1273–1288. https://doi.org/10.1007/s11858-022-01384-0

Kuchemann, D. (1987). Leaming and Teaching Ratio: A Look at some Current Textbooks. En P. Ernest (Ed.) Teaching and Learning Mathematics. Part 2. Perspectives 34. School of Education. University of Exeter.

Lang, S. (1990). Basic Mathematics. Springer-Verlag.

Larson, R., y Hostetler, R. (1985). College Algebra. D.C. Heath and Co.

Lavin, A. (2022). Variability in Variables: An Analysis of Variable Use in A Middle School Mathematics Textbook. Undergraduate Honors Theses. 220. https://scholarsarchive.byu.edu/studentpub_uht/220

Lovaglia, F. M. (1972). Álgebra. Harla.

Love, E. y Pimm, D. (1996). This is so: A text on texts. In International handbook of mathematics edited by Alan Bishop, Ken Clements, Christine Keitel-Kreidt, Jeremy Kilpatrick and Colette Laborde, 371-409. Boston: Kluwer.

Masani, P., Patel, R. y Patil, D. (1968). Cálculo Diferencial e Integral. Publicaciones Cultural S.A.

Matz, M. (1975). Towards a process model for high school algebra errors. Cognitive Psychology, 6(3), 317-339.

Morales, L., Díaz, J. (2008). Un estudio del concepto de variable en los libros de texto. Acta Latinoamericana de Matemática Educativa, 21(1), 201-211.

Murray R. (1969). Álgebra Superior. Schaum´s, McGraw Hill.

NCTM (1979). Gráficas y Relaciones y Funciones. National Council of Teachers of Mathematics.

Okeeffe, L. (2013). A Framework for Textbook Analysis. Int. Rev. Cont. Lear. Res. 2, No. 1, 1-13 (2013)

Otte, M. (1986). What is a Text? En Christiansen, B., Howson, A.G. y Otte, M. (eds.). Perspectives on Mathematics Education, pp. 173-204. Dordrecht: Reidel.

Pang, J., Cho, S. y Kim, J. (2017). An Analysis of Variable Concept in the Elementary Mathematics Textbooks and Workbooks. The Mathematical Education, 56(1), 81–100. https://doi.org/10.7468/MATHEDU.2017.56.1.81

Peterson, J. (1985). Algebra and its Applications. Pearson.

Purcell, E., y Varberg, D. (1998). Cálculo. Prentice Hall.

Reys, R., Lindquist, M, y Lambdin, D. Smith, N. (2014). Helping Children Learn Mathematics. John Wiley & Sons.

Rivers, J., (1990), Contextual Analysis of Problems in Algebra 1 Textbooks, University of South Carolina, Presented at the annual meeting of the American Educational Research Association, April, Boston, Massachusetts

Schmidt, W., Houang, R., y Cogan, L. (2001). A Coherent Curriculum: The Case of Mathematics. Journal of Direct Instruction, 4(1), 13–28.

Steward, J., Redlin, L, y Watson, S. (2013). Precálculo. Matemáticas para el cálculo. Cengage Learning.

Stewart, J. (1994). Calculus. Brooks/Cole Publishing.

Sullivan, M. (2008). Algebra and Trigonometry. Pearson.

Tan, S., (2018). Matemáticas Aplicadas. A los negocios, las ciencias sociales y de la vida. Cengage Learning.

Thompson, R. (1976). Intermediate Algebra. Prindle, Weber & Schmidt, Inc.

Trigueros, M. & Ursini, S. (2000). La conceptualización de la variable en la enseñanza media. Educación Matemática. 12(2).

Valverde, G. and L. Bianchi and R. Wolfe and W. Schmidt and R. Houang, (2002), According to the Book: Using TIMSS to Investigate the Translation of Policy into Practice through the World of Textbooks, London: Kluwer Academic Publishers

Van Dormolen, J. (1986). Textual Analysis. In: Christiansen, B., Howson, A.G., Otte, M. (eds) Perspectives on Mathematics Education. Mathematics Education Library, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4504-3_4

Zill. D. (1987). Cáculo. Grupo Editorial Iberoamérica.

Zill, D., y Dewar, M. (2008). Precálculo, con avances de cálculo. MacGrawHill. Cuarta edición.