Viseu, F., P. Mendes, and H. Rocha *The notion of function by basic education preservice teachers*. ATEE Winter Conference ‘Science and mathematics education in the 21st century. Brussels: ATEE and CIEd, 2019.

AbstractThe current curricular guidelines for mathematics education in Portugal emphasize the relevance of working with different representations of functions to promote understanding. Given this relevance, we seek understanding about the notion of function held by 37 basic education pre-service teachers in their first year of a master’s course. Data were collected through a task focusing on identifying functions in situations based on different representations. The content analysis technique was then adopted in the search for an understanding of the justifications given by the participants. The results achieved suggest it is easier for the pre-service teachers to identify examples that are not functions than examples that are functions. There is also a tendency for greater accuracy in the identification of examples expressed by tables than by algebraic expressions. The justifications presented show a notion of function as a relation between values of two non-empty sets, but without guaranteeing that this relation is single-valued.

Viseu, F., and H. Rocha. "

Interdisciplinary technological approaches from a mathematics education point of view."

*Science and mathematics education for 21st century citizens: challenges and ways forward*. Eds. L. Leite, E. Oldham, A. Afonso, F. Viseu, L. Dourado, and H. Martinho. Nova Science Publishers, 2020.

AbstractMathematics has a strong presence in the school curriculum, often justified by its usefulness in social life, in the world of work and by its connections with other sciences. This interdisciplinary connection, in particular when it requires constructing and refining mathematical models and discussing their applications to solve problems of other sciences, can assist students to understand why mathematics is so important in school. In the development of interdisciplinary activities, the characteristics of the tasks emerge as an important aspect. The emphasis is on the use of technological materials and the way they can support the development of concepts, provide different representations and support deeper understandings, and offer a multifaceted support to collect data and simulate experiences. Based on these assumptions, the aim of this chapter is to present, analyse and discuss tasks that promote interdisciplinary technological approaches from a mathematical point of view. In this chapter we assume interdisciplinarity as a complex construct, and in order to clarify its meaning we will discuss several types of conceptions, from multidisciplinary, to interdisciplinary, and to transdisciplinary. We will then address related concepts, such as modelling and STEM, highlighting similarities and differences between them, to reach an understanding of interdisciplinarity. In the process of the interdiciplinary approach, digital technologies arise as a central element. Based on a set of tasks on mathematics and on different sciences, we discuss what can change on an interdisciplinary approach to the teaching and learning of mathematical content and on the articulation between subjects.