Abstract:

Percentages are a mathematical topic widely used in everyday life ([1], [2]). Its diversity of uses involves a broad variety of meanings ([3]), which makes it a complex mathematical topic ([4], [5]). Furthemore, the percentage is a key piece in the mathematics Spanish curriculum, both at the primary and secondary levels.

On the other hand, the interest in textbooks and their use in mathematics education is a growing research field. On the basis that the teachers need knowledge to evaluate the characteristics of topics in the school textbooks, and decide about their relevance and didactic suitability, this paper shows a method to perform a didactic analysis of a lesson on percentages from a Primary Education textbook of sixth year. The aforementioned lesson is considered as an instructional process (possible or implemented) consisting of the sequence of didactic practices proposed by the author for the study of percentages.

In this context, this research has a twofold purpose:
1. Show a mathematics textbooks analysis technique proposed by the onto-semiotic approach to mathematical knowledge and instruction (OSA) ([6]). The analysis is oriented to identify elements that can be potentially conflicting from the point of view of the intended mathematical knowledge and the instructional process in which they are proposed. This information can be useful for the teacher who uses the textbook as a resource, in order to take into account such conflicts of learning.
2. Identify specific suitability criteria for the studied topic. Considering the textbook as an instructional process, it allows applying the OSA didactic analysis tools to evaluate the didactic suitability of said process, identify possible conflicts of meaning and potential improvements, resulting in an effective resource for the teacher.

The results reflect that in the sample of tasks, in which the percentages must be contextualized and applied, is not sufficiently representative. In addition, the analysis shows possible conflicts of meaning, as well as potential improvements that should be considered in the development of educational textbooks with the purpose to define and characterize quality aspects of the textbooks.

References:
[1] L. A. Steen, (eds.), Mathematics and democracy: The case for quantitative literacy. Washington, DC: National Council on Education and the Disciplines, 2001.
[2] M. Van den Heuvel-Panhuizen, “New forms of assessment, but don't forget the problems,” in Proceedings of the Seventeenth International Conference for the Psychology of Mathematics Education, 1993. University of Tsukuba, Japan, 1993. vol. 3, pp. 186-193, 1993.
[3] M., Parker, and G. Leinhardt, “Percent: a privileged proportion,” Review of Educational Research, vol. 65, no. 4, pp. 421-481, 1995.
[4] B. H. Ngu, A. Yeung, and S. Tobias, “Cognitive load in percentage change problems: unitary, pictorial, and equation approaches to instruction,” Instructional Science, vol. 42, no. 5, pp. 685-713, 2014.
[5] S. Prediger, and B. Pöhler, “The interplay of micro-and macro-scaffolding: An empirical reconstruction for the case of an intervention on percentages,” ZDM-Mathematics Education, vol. 47, no. 7, pp. 1179-1194, 2015.
[6] J. D. Godino, C. Batanero, and V. Font, “The onto-semiotic approach to research in mathematics education,” ZDM-Mathematics Education, vol. 39, no. 1-2, pp. 127-135, 2007.

Keywords:

Percentages, textbooks, onto-semiotic approach.