Fagleg sterke elevar sitt læringsutbytte av å arbeide med praktiske oppgåver i matematikk

The Norwegian Ministry of Education and Research has implemented several actions to increase the interest for mathematics within the school system. One of these has been to make the mathematics teaching more practically oriented. I have altered my own teaching practice because of this change, a development from what would be considered to be standard theoretical lectures towards more student activity through problem solving and exercises. Most of the activities the students have worked with are developed by me; based on ideas I have got from former and current teaching environments. Time spent on these activities has varied from single classes to several weeks, where the latter has required a finalized product to be handed in by the students for evaluation. These finalized products have showed that students that score well on standard tests have less theoretical insight and do not perform as well as it could be expected. This presented itself as a conflict of interested to me, since I experience that these as students are not challenged enough through standard lecturing procedures. I have therefore chosen to raise the question whether or not this is an efficient way to prepare the students for more challenging mathematics in their future education. Based on the experiences with this discrepancy between intentions and practice, I have in this project worked with the following research question; what learning outcome do theoretically strong students get from working with practice related mathematical exercises? Through group interviews with students and analysis of their work and pre and post-testing of each student I have approach the research question from different angles. The interviews have been conducted with students who have participated in practice based mathematics lectures for about three years. In the discussion of results the main focus is on theses interviews, as I find it important that the students themselves are allowed to reflect upon what they have learned through such a mathematics teaching priority. The pre and post-tests enabled me to compare how students who followed the standard theoretical lecturing process performed in comparison to those who followed the practice based lecture process. Analysis of the work handed in by the students has been used to support the findings in the interviews and tests. As a theoretical basis I have used Dewey and his theory on the reflexive thought, which I interpret as learning. I have also examined Vygotsky's theories about social learning and the expansion of the proximal zone of development. Motivation and willingness to learn are essential factors in all teaching environments, which is why I also have studied the coherency between motivation and learning. The competency goals stated in the Norwegian national curriculum have also been used in the discussion. My conclusion states that if one considers the competency goals alone, practical activities result in a lower learning outcome than traditional lecturing for theoretically strong students. However, if we consider the intention of mathematics in school, we see that the theoretically strong students learn from doing practical work and activities. They become capable of using mathematics as a tool, and their motivation for working with all kinds of mathematical problem is increased