Abstract

This thesis analyzes students' theoretical thinking in a technology-assisted environment. The impact of such environment on students' thinking was studied on the sample of written solutions in a final examination in a Linear Algebra with Maple course. For analyzing students' solution a model of theoretical thinking proposed by Sierpinska in the context of her research on students' difficulties in linear algebra was used as a tool. The motivation for undertaking this study was grounded in my belief that the use of technology in the teaching and learning of mathematics may turn students away from theoretical thinking towards a more action-oriented practical way of thinking. My study neither confirmed nor refuted this belief, but allowed me to refine my understanding of the nature of the influence technology may have on students' learning. It appears that whether the student's use of technology is effective or not depends also on the features of his/ her thinking (which may have been developed in previous study of mathematics). Students in my sample who approached the problems with a theoretical mind also knew how to make use of the computer in an effective way. On the other hand, students who demonstrated poor theoretical behavior could not control the software so as to arrive at a correct and complete solution. For these students, the computer acted as an obstacle (called an "instrument-generated" obstacle here) that hindered the accomplishment of the task. This study acknowledges the existence of certain phenomena that may arise in the process of working with the computer. Some of the findings reinforce or illustrate in the specific context of linear algebra various phenomena that mathematics educators had previously discovered in other mathematical subjects taught with other technology