Abstract
In this paper we describe an experiment in a linear algebra course. The aim of the experiment was to promote the students' understanding of the studied concepts focusing on their definitions. It seems to be a given that students should understand concepts’ definitions before working substantially with them. Unfortunately, in many cases they do not. Influenced by their high school experience they concentrate in learning patterns for problem solving without deep understanding of the relevant concepts. In order to educate the students to appreciate the importance of understanding definitions, we changed the homework problems and the didactical contract with the students. We discuss the positive outcomes of these changes from theoretical and educational points of view. We chose to try our approach in a linear algebra course since it is probably the most abstract course for first semester students. We hope that our approach can be useful in teaching other undergraduate courses.
Highlights
Teachers of linear algebra know that the course is difficult for many students
The resulted difficulties are described in Dorier et al (2000): „...the main criticisms made by the students toward linear algebra concern the use of formalism, the overwhelming amount of new definitions and the lack of connection with what they already know in mathematics
The results show that the linear algebra course is very difficult for our students as well and that the homework assignments helped most of them to organize their studies systematically and to understand the theory
Summary
Teachers of linear algebra know that the course is difficult for many students. In the words of Stewart and Thomas (2007), students often find their first university linear algebra experience very challenging. Understanding of formal definitions is strongly connected to students' concept image. The resulted difficulties are described in Dorier et al (2000): „...the main criticisms made by the students toward linear algebra concern the use of formalism, the overwhelming amount of new definitions and the lack of connection with what they already know in mathematics.
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