Abstract:

Despite curricular calls for the use of diverse representations in the teaching and learning of mathematics, the teaching of functions has been quite supported in algebraic representations, failing to ascribe educational value to more visual representations. Even considering the compulsory use of graphing calculators in secondary school mathematics in Portugal, students do not give the proper meaning to algebraic representations of functions (Rocha, 2015).

This study was developed within the context of the student teaching internship of the second author and it aimed at knowing the visual preferences of students in a 10th grade class (students aged around 15 years-old) and understanding how they use visual images when solving tasks involving functions. Two research questions guided the study:
(1) What are students’ visual preferences? and
(2) How do students resort to visual images when solving tasks about functions?

Under a qualitative and interpretative approach, the study was carried out in two phases. The first phase involved the implementation of an adaptation of the Mathematics Processing Instrument – MPI (Presmeg, 1986) to all participating students, in order to know their visual preferences. The second phase occurred after a pedagogical intervention targeting the topic of transformations of functions and emphasizing treatments and conversions of representations (Duval, 2006) of functions as vehicles to give meaning to the concepts involved in the teaching unit. Due to the COVID-19 pandemic restrictions, all classes in this pedagogical intervention were conducted at distance, via Google Meet, using different technological resources, such as graphing calculators and GeoGebra, which allow the transition from visual to algebraic representations and vice versa. This second phase of the study looked for a better perception of how students used visual images in solving tasks of diverse nature regarding the theme of functions. For this phase, data were collected through students’ written productions and audio recordings of semi-structured and task-based interviews.

The results of the MPI revealed that approximately half of the students were visual and half were non-visual thinkers. However, the results of the MPI did not prove to be totally decisive in students’ visual preferences in the theme of functions. In this presentation, we will focus on two students whose visual preferences are not reflected in their choices of representations to solve mathematical tasks involving functions. The results of the study call attention to the need of working with students an array of different representations, and of attending to students’ visual preferences but going beyond them, reinforcing the importance of conversions of mathematical representations.

References:
[1] Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103-131.
[2] Presmeg, N. C. (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42-46.
https://flm-journal.org/Articles/1917B083BE4534511A32616EED75A8.pdf
[3] Rocha, H. (2015). Múltiplas abordagens, múltiplas representações: um contributo para incrementar a relevância da representação algébrica. In L. Santos, [4] M. Vara Pires, R. A. Tomás Ferreira, A. Domingos, C. Martins, M. H. Martinho, I. Vale, N. Amado, S. Carreira, & T. Pimentel (Eds.), Atas do EIEM: Representações matemáticas (pp. 327–339). SPIEM.

Keywords:

Visualization, representations, functions, distance learning.