Percepções dos/as professores/as sobre o ensino de cálculos matemáticos em engenharia: acolhendo estudantes com defasagem da educação básica

Abstract

The challenges encountered by students entering Engineering programs—particularly those related to the teaching and learning of Mathematical Calculations—continue to represent a significant challenge within the context of Brazilian education. Grounded in the theoretical frameworks of Paulo Freire (1996, 2005, 2013a) and Pierre Bourdieu (1997, 1998a, 1998b), this thesis explores teachers’ perceptions of their pedagogical practices, emphasizing the challenges that emerge from the learning gaps carried over from Basic Education. Additional theoretical contributions (Altet, 1994, 1996, 2000, 2005; Abdalla, 2006, 2011, 2015, 2017a, 2021, 2024; Tardif, 2014) have also informed this study, particularly in addressing discussions on the teaching and learning process, with an emphasis on the demands of teacher education and the development of approaches aimed at welcoming and including students in the educational environment. There are also contributions from authors who focus on mathematics education, taught in a contextualized and meaningful way, with a view to welcoming situations. Among them are: Skemp (1976), Skovsmose (2000), Borba and Penteado (2001), Silva (2001), Franco (2004), Alexander (2008), D’Ambrosio (2012), and Freeman et al. (2014), Bianchini, Lima and Gomes (2019). Methodologically, this research employs a qualitative approach, structured around three key data collection instruments: a questionnaire administered to 20 participants, individual interviews conducted with 15 teachers, and a Discussion Group comprising 9 teachers. Drawing on Bardin’s (1977) content analysis technique, two analytical dimensions were established, each corresponding to teachers’ perceptions regarding the teaching of Calculations within the context of Engineering education. The first dimension focuses on the challenges that must be addressed to effectively embrace students. It highlights the category “The Learning Process in Teaching Calculations,” which unfolds into three units of meaning: the educational gaps observed among incoming students, the anxiety associated with learning mathematics, and the necessity for teachers to engage in reflective practices aimed at fostering an inclusive and supportive learning environment. The second focuses on the perspectives to be achieved in the process of supporting students. It introduces the category “Pedagogical Practices Aimed at Embracing Engineering Students,” which is divided into three units of meaning: the needs and expectations related to teacher training, the contrast between traditional and innovative teaching methodologies, and the emergence of new perspectives for promoting inclusion and fostering a more welcoming educational environment for engineering students. The analyses reveal the necessity of reinforcing continuing teacher education and re-evaluating institutional policies to ensure more consistent and meaningful support for teaching practices. The findings indicate that, while welcoming and inclusive practices are evident in both the discourse and certain actions of the teachers, considerable limitations persist—particularly concerning the effectiveness of these practices when confronted with the wide diversity of student profiles and the structural fragilities present within educational institutions. They underscore the urgent need to broaden formative and diagnostic initiatives at the onset of undergraduate programs, and to invest: first, in teacher training as a continuous and institutionalized policy; second, in the didactic reorganization of teaching practices, aiming to establish dialogical and discursive routines that encourage participation, the sharing of experiences, and the strengthening of the students’ engagement and sense of belonging; third, in welcoming as a structured element of the learning process, providing dedicated times and spaces for reflecting on and problematizing learning through dialogue; and fourth, in improving institutional conditions that sustain pedagogical changes and innovations, thereby fostering collective and collaborative planning, promoting more welcoming and inclusive didactic and pedagogical contexts for students, and creating opportunities to integrate and disseminate successful practices already present within the institutions. Finally, this study aims to provide both theoretical and practical contributions to the enhancement of mathematics teaching, with the broader objective of helping to reduce learning inequalities within engineering programs.