## Purpose

The purpose of this study is to examine the possibilities and limitations of problem-solving as a basis for mathematics education in preschool class. The study investigates how children in preschool class use *non-guided documentation* when working with a probability task, and how they reflect on probability.

## Result

Overall, the study shows that it is possible to work with probability tasks in preschool class, and that many of the children were already familiar with the mathematical concepts used in the task. The children's non-guided documentation showed a diversity of strategies and contributed positively to their exploration of probability, both during the task and in the final discussions.

The analysis describes two overall strategies used by the children to document the results of the experiment: a *chronological strategy* in which each draw was noted in chronological order, enabling reconstruction of the entire experiment, and a *non-chronological strategy* in which it was not possible to reconstruct the result of the experiment. The study shows that 30 children used some form of chronological strategy in their documentation, although these strategies varied in their structure and illustration, whereas a total of 20 children used a non-chronological strategy.

The two overall strategies were further analysed on the basis of the sub-categories *words, icons, tally marks* and *other.* The study shows that only three out of 50 children used words or letters in their documentation, whereas 12 children used numbers in their documentation. Four children produced chronological documentation using both icons and numeric representation. For example, one child noted the result of the draw with two dots (icons) in colours corresponding to those of the glass balls, whereas the number of draws was noted using numbers. Thus, this documentation comprised two dimensions: the result of the draw and the number of draws. The remaining documentation only comprised one dimension: the result of the draw.

The authors find that the large differences between the children's documentation contribute to the children's reflection and their subsequent discussions in the group of children. While some of the children were able to give a mathematically related explanation to their predictions of the results of the experiment, others used more everyday explanations such as "I like red better than yellow" and "Red and yellow won, because you shook the bag and mixed the marbles". According to the authors, the children's different explanations and arguments suggest that the children's informal knowledge of probability influences their formal learning.

## Design

Data was collected from four Swedish preschool classes with a total of 50 children. The data material consists of notes and sound recordings of the children's reflections and interviews with the children before and after the intervention. In addition, the authors collected and analysed the notes/documentation made by the children during the probability task. The probability task, which was carried out by one of the authors of this article, consisted of the following: Two glass marbles were taken from a bag containing a total of four glass marbles (two red and two yellow), and each child was then asked to document/note down the result of a total of 20 draws. The children themselves decided how they wanted to document/note down the result. The children had to predict the colour combination (red-red, red-yellow, yellow-yellow) that would appear most often during the 20 draws. Finally, the children engaged in a joint discussion in which they were asked to look at each other's documentation and argue for and against the different types of documentation.

## References

Bommel, J. van, & Palmér, H. (2016). Young children exploring probability – with focus on their documentations. Nordic Studies in Mathematics Education 21(4), 95-114.

## Financed by

Not stated