Linköping Studies in Education and Psychology Dissertations
No. 51

Skolmatematiken - kultur eller myt?
Mot en bestämning av matematikens didaktiska identitet.

Anita Sandahl

Akademisk avhandling

som med vederbörligt tillstånd av filosofiska fakulteten vid Linköpings universitet för avläggande av filosofie doktorsexamen kommer att offentligt försvaras på institutionen för pedagogik och psykologi, Eklundska salen, lördagen den 24 maj, 1997, kl. 14.00

Abstract

Mathematics is a sociocultural phenomenon. In educational contexts, no account has been taken of this; instead, learning has focused on the formal language.

In this study, pupils' and students' conceptions of the school subject Mathematics are analysed. The ability to describe what takes place in teaching contexts is of importance in didactic research. This regards especially people's conceptions of how they learn and what the content is. In this thesis, a description is given of people's conceptions of a specific content and how a new aid, the pocket calculator, affects the teaching of mathematics.

Qualitative research makes it possible to describe, interpret and understand different phenomena. With the methods used in qualitative research, reflection in the analysis must take place from different perspectives in a lengthy process. An increasingly accepted conception is that the triangulation of methods reinforces validity. Validity is also reinforced in the thesis by virtue of the fact that students and teachers were able to participate in the process over several years.

The first two empirical studies, deal with conceptions of mathematics in school. The studies were carried out over a period of seven years and in which 7,000 pupils and 900 trainee teachers were involved, deal with conceptions of mathematics in school. Although the descriptions originate from different points in time, they describe more or less the same mathematics teaching.

In the third and fourth studies, pupils' conceptions of the pocket calculator are studied. The difference between these two studies is that in the third study, the pupils had access to pocket calculators in school after several years of studying mathematics. In the last study, the pupils used pocket calculators from the beginning. This affects the role of the teacher and the methods teachers use in teaching contexts.

I felt that it was important to uncover the pupils' conceptions of mathematics since these conceptions are a significant factor in their learning. Also significant are students' conceptions prior to their option of mathematics or language. The results show that the teaching of mathematics in school has not succeeded in demonstrating the usefulness of the subject or showing connections between different mathematical skills. The technical skills were not linked to each other in any context. Since pupils and students constantly returned to the view that mathematics was about numbers and doing arithmetic, it would be interesting to see whether doing arithmetic could be made easier by using a technical aid, the pocket calculator, and whether it could focus mathematics on something else. I was also interested in teachers' conceptions of the pocket calculator as an aid.

The results showed that the training of skills ought to be given a new content. Skills in interpreting, handling a situation and being able to handle numbers are part of this change.

Indexed: pocket calculator, ethnomathematics, mathematics, education, qualitative methods, school mathematics, socioculture.

Department of Education and Psychology
Linköping University, S-581 83 Linköping, Sweden
Linköping 1997

ISRN LiU-IPP-STU--51-SE ISBN 91-7871-945-3 ISSN 1102-7517