EJMT Abstract

In mathematics education research, the focus has generally been on a single factor or on a few partial factors at a time. Researchers have neglected the relationship between conceptual and procedural knowledge and how progressive technology alters this relation. The relationship between systematic planning of teaching and the reality of often chaotic learning situations has not been properly explored. There is no pragmatic theory of collaborative socio-constructivist student-centered learning, especially with regard to the use of technology. The studies in this article were conducted in order to consider the effects of a minimalist instruction philosophy within a quasi-systematic model for mathematical concept building. The cognitive and affective development of high school students was studied within a collaborative, technology-based, socio-constructivist, self-guided environments, using a CAS calculator without traditional teaching or homework. Another research objective was to study the professional development of prospective teachers involved in the project. The studies utilized both quantitative and qualitative methods, including quasi-experimental pretest-posttest design and grounded theory.

The findings suggest that optimal ‘student-centered learning’ emphasizes students’ freedom to choose learning objectives and working methods in problem-based socio-constructivist technology-based environments, in which open questions about both mathematics and technology are solved in collaboration between students or student teams. Even though students proceeded more or less chaotically, it was found that learning to link conceptual and procedural knowledge can be organized succesfully within a quasi-systematic framework. This paradigm allows integrate study modules of teacher education in new way. The term ‘student-centered’ should be redefined to minimize the role of the teacher as decision-maker with regard both to learning objectives and working methods. As this paradigm reflects how students work, communicate, and utilize technology outside the classroom, the focus should be shifted from well-tailored classroom lessons to students’ free time activities. To use a motor racing analogy, the teacher becomes a team manager and the school serves as a pit stop. However, prospective teachers seem to be hesitant if this approach could replace the conventional teaching in school.