This study investigates how collaborative, collective mathematical reasoning emerges when students jointly solve problems regarding fair sharing. Three 6-year-old children worked collaboratively in a group with a problem related to fair sharing, and their teacher was present. The data, captured in video recordings, was analysed using two frameworks: collective mathematical reasoning, and the theory of joint problem space. The results show that different things, such as physical artefacts aimed at sharing resources, challenges related to the task, and the students’ conceptions of mathematics, affect the students’ possibilities to engage in collaborative collective mathematical reasoning. 

The aim of this paper is to explore students mathematical and ethical reasoning in fair sharing tasks. In our study, 8-year-old students were asked to share eight biscuits between three soft toys, where one of the toys is hungry and sad. Two analytical frameworks were used, one for mathematical reasoning and one for ethical reasoning. The results show that sharing tasks can generate several solutions in which students use different mathematical arguments combined with ethical arguments. Another result is that the different arguments often interplay with, or depend on, each other, meaning that mathematical reasoning and ethical reasoning are intertwined.

L'objectif de cet article est d'explorer le raisonnement mathématique et éthique des élèves dans les tâches de partage équitable. Dans notre étude, il a été demandé à des élèves de 8 ans de partager huit biscuits entre trois peluches, l'une des peluches étant affamée et triste. Deux cadres analytiques ont été utilisés, l'un pour le raisonnement mathématique et l'autre pour le raisonnement éthique. Les résultats montrent que les tâches de partage peuvent générer plusieurs solutions dans lesquelles les élèves utilisent différents arguments mathématiques combinés à des arguments éthiques. Un autre résultat est que les différents arguments interagissent souvent entre eux ou dépendent les uns des autres, ce qui signifie que le raisonnement mathématique et le raisonnement éthique sont étroitement liés.

In this chapter, we challenge the view of mathematical modelling as a neutral practice and argue that ethical reasoning is an important part of the process. Using six cases, each describing different sharing scenarios, we analysed children’s mathematical reasoning and ethical reasoning. The cases were designed to cover a variety of aspects of mathematics and allow different types of ethics to be used. The results show that ethical reasoning plays a crucial part in task-solving, both when the children advocated for division or when they decided on sharing in unequal-sized parts.

Sharing and division are two concepts that have overlapping properties, and both are connected to the interpretation of fairness. In the present study, we study preschool children’s work with a case where eight biscuits were shared between soft toys. The focus is onthe different arguments that the children express. The results show that children use both ethical arguments and mathematical arguments in their solutions. Some of the arguments can be categorised as ‘Fair sharing related to number of pieces only’ or ‘Fair sharing employing ad hoc attempts at equal size’. The arguments that were coded as sharing not associated with mathematical sense of fairness were either classified as ethical reasoning or play. In the discussion, we raise the need of the combination of ethical reasoning and mathematical arguments if we want to create situations for children to develop critical thinking.