O ensino e a aprendizagem de conceitos de álgebra linear no ensino superior politécnico: The teaching and learning of linear algebra concepts in polytechnic higher education

Linear algebra is a source of difficulties for many students, a problem that is aggravated by the fact that this area integrates the curriculum of several higher education courses. On the other hand, the few research carried out in Portugal in this field highlights the need to carry out further studies, which can support the decisions regarding its teaching and learning. Thus, based on these concerns, the study sought to answer the following research questions: 1. What are the mistakes made and difficulties experienced by students in learning linear algebra contents?; 2. What are the characteristics of linear algebra teaching in polytechnic higher education according to teachers?; 3. What is the influence of a teaching centred on the exploration of students’ errors and difficulties and on the use of software on students’ learning in linear algebra? In order to answer the aforementioned questions, a research has been developed in two interlinked parts and, methodologically, quantitative and qualitative methods were used. The first part of the study was developed in two phases: in the first one the errors and difficulties of 310 students of several engineering degree courses when solving questions about matrices and determinants and systems of linear equations were identified, and in the second an online questionnaire was applied to public polytechnic higher education teachers with the purpose of characterizing their linear algebra teaching. In the second part of the study, a teaching intervention involving 28 students from a Chemical and Biological Engineering class was carried out, in which an attempt was made to implement a student-centred teaching and to promote learning based on errors. Microsoft Mathematics software was also used as support. Data collection focused essentially on recording lessons, the student's productions and by applying a questionnaire and interviewing each one of them to get their opinion about the intervention performed by the teacher. The obtained results allowed to verify that students have several difficulties in the resolution of issues related to matrices and determinants and systems of linear equations, having concluded that some of them have origin in propaedeutic contents to linear algebra. Regarding the teaching of linear algebra, as it had been perceived by the teachers, it was concluded that it is still strongly supported in traditional methodologies, privileging the expository method and with a brief expressive use of technologies. Lastly, the strategies followed in the teaching intervention contributed for students to participate more actively in the classes and, in the opinion of most students, it also allowed to identify their mistakes, to be aware of their difficulties and to clarify some concepts/procedures. Microsoft Mathematics, besides the motivational effect, also had an important role in the detection and correction of mistakes. However, the lack of commitment and study is still, in the opinion of the students, a hindrance to their…