Fler bråk i matematikundervisningen: En aktionsforskningsstudie där lärare lär om progression

Nagy, C.
Licentiatuppsats. Göteborgs universitet.


The overall purpose of the study is to explore the teaching of fractions from preschool to ninth grade (age 1-16). Specifically, the study examines how a group of teachers (including one preschool teacher) work on developing and improving their teaching in a community of practice across grades.



The author identifies four main themes in the participants' discussions of teaching fractions: (1) interpreting children's understandings, (2) basing instruction on children's understandings, (3) clarifying fractions and (4) ensuring children's learning.

Overall, the analysis indicates that reflections on recordings of teaching enable the participants to analyse and interpret the children's understandings and to observe which kind of teaching enables learning. Cooperation between the participants across grades enables them to identify the children's understandings of fractions and to use these understandings in ensuring quality and progression in teaching. An important factor is that the participants in the community of practice are able to draw on each other's didactic knowledge.

The study shows that, across ages, the children have many of the same difficulties in understanding fractions. In preschool, these difficulties are the children's understanding of part and whole. The results clearly show that the children aim at "sharing equally", while "sharing unequally" is much harder for them to understand. This is evident when the children were asked to divide nine grapes into two piles. They put four grapes in each pile, and then indicated that the last grape did not fit in. The children seem to have more experience in "sharing equally", and the participants reflect on the fact that focus in preschool and at home is often on equal shares, among other things because of principles of fairness. In this way, the participants become aware of the necessity to provide children with experiences of unequal shares.

Overall, the results also indicate that small didactical changes might help improve teaching. This could involve using other words or changing the way a question is asked, expanding the teaching content or using a variation of materials to clarify and visualise fractions. In preschool, the children have difficulties understanding that a whole can have different appearances, for example two semicircles can be matched in other ways than in a perfect round circle. The participants reflect on the fact that visualising fractions using pictures from everyday life, for example pies or apples, can mean that the children focus too much on the everyday function and look of the object, and therefore come to the wrong mathematical conclusions. For example, if an apple is used to illustrate part and whole, the children could get the perception that the whole can only look one way (two half applies must form one whole apple). On this basis, the participants conclude that is it necessary to use many different materials to show the children that the appearance of the whole is not necessarily given on the basis of what the parts look like.


Three teachers (from one third grade, one fifth grade and one ninth grade) and a teacher from one preschool were invited to a temporary community of practice focusing on teaching fractions. Five research cycles were conducted over a period of three semesters. The first cycle was a pilot study. The next four cycles focused first on preschool, then on third grade, fifth grade and finally ninth grade. Each cycle consisted of planning meetings and reflection meetings in the community of practice. Before each planning meeting, a test of the children's understanding of fractions was carried out. During the planning meeting, the participants analysed the test results and planned two teaching sessions to be conducted by the teacher/preschool teacher in the given grade. The teaching sessions were videotaped and subsequently discussed at the following reflection meeting. The reflection meetings were also videotaped and formed the primary empirical basis for the analysis. The author used Wenger's dimensions of social learning as an analytical tool, and a thematic analysis was conducted.


Nagy, C. (2017). Fler bråk i matematikundervisningen: En aktionsforskningsstudie där lärare lär om progression. Licentiatuppsats. Göteborgs universitet.

Financed by

Ängelholms Municipality and Halmstad University contributed to making this study possible. The project is within the framework of a larger research and development project involving two universities and three municipalities.