GeoGebra in Teaching Linear Algebra

摘要

This contribution will present a study that focuses on the potential of using the GeoGebra software in a linear algebra course for pre-service teachers. This particular freeware enhances dynamic geometrical representations of both simple and more complex algebraic operations. Consequently, it seems suitable for the teaching and learning of linear algebra. The experiment was conducted during a practice session that complemented lectures in linear algebra. This semester-long course is compulsory to second-year students in the undergraduate program for future teachers of mathematics. The primary aim of implementing GeoGebra in the course was to offer students further representation of algebraic operations, supporting their abstract thinking. The secondary aim was to introduce the future secondary school teachers to the didactical advantages of the software. The main research question inquired whether using a set of pre? designed applets would lead to a better understanding of selected algebraic operations. The answers were based on two kinds of evidence: the objective outcomes that students produced in solving selected problems and the subjective response to this extra support (i.e. whether the students see the new representation as helpful). The experiment involved two different cohorts; the group consisted of a total of 34 students, who had attended various lectures on linear algebra prior to the practical seminars. During the seminar session they saw geometrical representations in dynamic applets designed in GeoGebra. The influence of this tool was studied with instruments of both qualitative and quantitative analysis. The method followed a quasi-experimental model of pre- and post-tests: a questionnaire was used at the beginning of the experiment to determine whether students could represent linear functions, systems of linear equations (in terms of the number of solutions) geometrically. When testing the ability to geometrically represent matrices, adding and multiplying matrices and determinants, students were asked to geometrically represent simple examples. Operational thinking necessary for matrix addition was prompted by an unfinished sentence. The students indicated on a numerical Likert-like scale what importance they gave to geometrical representation and dynamic geometry in helping them to understand algebraic topics. A similar questionnaire was used as a post-test at the end of the session. The questionnaire had been piloted on a small group of students and then adapted accordingly. The data was analyzed using relevant statistical methods. Although the number of students does not allow me to generalize the results, the group found the use of the program successful. Not only did the software help them deepen their knowledge but the students appreciated the didactic potential of this tool along with its versatility. In class the students freely expressed their enthusiasm for the geometrical representations: that they liked them and that they enhanced their understanding of the concepts in further complexities. The statistical results of the test confirmed this notion. A paired two-tailed t-test (a= 0.01) also showed a positive change in the students' expectations of the use of geometrical representations in class. These findings further inspired me to implement the relevant applets into an e-learning course.