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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.

This chapter focuses on learning activity that was suggested by El’konin and Davydov as a framework for teachers to design opportunities for students to emerge collective mathematical reasoning. The data for the chapter were taken from a 3-year longitudinal research project in which learning activity was used to design teaching, tasks and learning models in a multicultural and multilingual Swedish primary school. As a result of using this framework, a situation was highlighted whereby the learning models specific to learning activity had been constructed by second-language students aged 6 and 7 years as they emerged collective mathematical reasoning that focused on comparing two different quantities. The contribution to previous research concerning how learning models can be used in such student groups for collective reasoning about relationships between quantities is twofold; that is, (1) the use of the learning models can help students and teachers to return to the problem they have jointly identified in the collective reasoning and (2) the use of the learning models can help students who struggle with different linguistic dilemmas to jointly reflect on both their own and others’ arguments.

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 argument soften 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 paper, we focus on the expansion of a task developed in one educational context in another educational context. The working process was conducted as a collaboration within a research team consisting of researchers and teachers. The aim of this paper is to describe how a task designed for students to work in base four, was collaboratively expanded into a task that deals with both base four and base ten. The overarching idea is the importance of early exposure to the structural aspects of the positional system and to advocate for exploring different bases to enhance learning. The theoretical framework of the project is based on learning activity, inspired by the El’konin and Davydov mathematics curriculum. The paper includes an analysis of the task staged in a Swedish classroom, highlighting collaborative design work, task features, and outcomes. The results indicate challenges and insights in students’ understanding of base ten as one of many possible base numbers.

This paper identifies and discusses children’s mathematical reasoning in preschool and preschool class when they work with a fair sharing case. The case came from a selection of cases designed to promote collective mathematical as well as ethical reasoning. Data comes from six children’s work when sharing four paper biscuits between three soft toys, first when the children were five years old and then, a year later, when they were six years old. The results show that their reasoning, both when they were five and six, used mathematical and ethical arguments. In preschool class, the students were able to use each other’s arguments in collective reasoning to identify, predict, and verify their reasoning. The students began to measure the fraction parts of a remainder but could not evaluate the conclusion with respect to what is aspects for division; equal numbers and equal size. The results also signal that teacher’s input, of posing evaluating questions, appears to stimulate the reasoning.

The article examines didactic choices in teaching where mathematics and sustainable development meet. The purpose of the teaching was to encou­rage preschool children to reason collectively about distribution problems. It was the children's reasoning about possible solutions that was in focus, not a correct answer. The preschool teacher's role was to create opportunities for agency: enable childrens own contributions to knowledge, pit different conflic­ting perspectives on sustainable solutions against each other and discuss the solutions. Based on the didactic modeling method, researchers and preschool teachers discussed the teaching based on different expertise. Documenta­tion created during these meetings was analysed, in order to investigate if the didactic what and how questions could help the preschool teachers create agency in teaching. The result shows how reflection on the didactic issues crea­ted opportunities for agency in relation to organization of time and environ­ment, of pairing children for collective work and language development work.

I artikeln undersöks didaktiska val i undervisning där matematik och hållbar utveckling möts. Undervisningens syfte var att uppmuntra förskolebarn att kollektivt resonera kring fördelningsproblem. Det var barnens resonemang om möjliga lösningar som låg i fokus, inte ett rätt svar. Förskollärarens roll var att skapa möjligheter för agens: att barnen kunde göra egna bidrag i kunska­pandet, där barnen kunde ställa olika konflikterande perspektiv om hållbara lösningar mot varandra och diskutera lösningarna. Utifrån metoden didaktisk modellering förde forskare och förskolläre diskussioner om undervisningen utifrån olika expertis. Dokumentationen som skapades under dessa möten analyserades, för att pröva om en didaktisk modell som hanterar de didaktisk vad- och hur-frågorna kunde hjälpa förskollärarna att skapa agens i undervis­ningen. Resultatet visar hur reflektion kring de didaktiska frågorna kan skapa möjligheter för agens i undervisningen. Didaktiska lösningar handlade om organisation av tid och miljö, om svårigheter att para ihop barn för kollektivt arbete samt språkutvecklande arbete.

The El’konin-Davydov Curriculum (EDC), developed and tested in the 1960s and 1980s in Russia, proposes an interesting and effective method of developing students’ understanding of the general structure of the base system independent of a particular base. However, the tasks and teaching strategies developed in a cultural setting (Russia) cannot be mechanically transferred to another cultural setting (Sweden). To benefit from EDC, we try to adapt the tasks to a Swedish culture while respecting and preserving the theoretical basis. Therefore, in a workshop, we have discussed some of the tasks from the EDC in order to, without missing the theoretical basis, help young Swedish students to understand the general principles behind the base system.

Le programme El'konin-Davydov (EDC), développé et testé dans les années 1960 et 1980 en Russie, propose une méthode intéressante et efficace pour développer chez les élèves la compréhension de la structure générale du système de base, indépendamment d'une base particulière. Cependant, les tâches et les stratégies d'enseignement développées dans un contexte culturel (Russie) ne peuventpas être transférées mécaniquement dans un autre contexte culturel (Suède). Pour bénéficier de l'ECD, nous essayons d'adapter les tâches à la culture suédoise tout en respectant et en préservant la base théorique. C'est pourquoi, dans le cadre d'un atelier, nous avons discuté de certaines tâches de l'ECD afin d'aider les jeunes étudiants suédois à comprendre les principes généraux qui sous-tendent le système de base, sans pour autant perdre de vue la base théorique.