Is There any Impact of Teaching Vector Spaces From Real Problems? The Case of First Year Engineering Students

In some linear algebra courses at the university level in engineering majors, the vector spaces are presented to students in an abstract way with scarce connections with other subjects and real problems. The goal of this study was to examine the effectiveness, regarding content knowledge and motivation, of a didactic proposal based on a problem based learning and the necessity principle, PBL-NP, modelling real engineering problems through homogeneous systems of linear equations, to introduce the concept of vector space. A quasiexperiment (post-test) was designed with a convenience sample composed of two groups: the experimental group, EG, amounting 33 students who were taught using the PBL -NP, and the control group, CG, composed by 79 students, taught by following an abstract approach. Inferential statistics was used to compare the learning outcomes between groups, by using as contrast variable an external test. The results show that the students in the EG group felt more relaxed and put less effort than CG students, while both groups gather the abstract concepts in a similar extent. Also the percentage who passed the course is higher in the EG compared with CG. Although both groups value positively the subject, a percentage of students in the CG group add some comments referred to the lack of practice related with real problems in the algebra courses taught with the abstract approach.