In this article we report on a study of children’s attention to numerical content in picture books. Specific research questions are 1) how the content in a designed picture book directs children’s attention to numbers, and 2) what kind of numerical reasoning the book reading entails. To answer these questions, we conducted an educational design research study in two cycles, with a specially designed picture book and two ways of reading: first without any prompting from the reading teacher, and second with teacher-child interaction. Nineteen preschool children (aged 3–5 years) and three teachers participated in video-observed individual reading sessions. The observations of the reading activities were analyzed with focus on the children’s attention to numbers as well as on their numerical reasoning during the book talks. Based on the observations, we suggest that preschool children do direct their attention to aspects of numbers, but that the design of the pictures and the framing of the reading sessions influence which numerical aspects are discerned. Furthermore, teachers’ support in transforming empirical clues into mathematical representations and comparisons seems critical for more advanced reasoning about numbers to occur.

In this article, we direct attention to what becomes critical in teaching activities for toddlers (1–3-year-olds) to learn the meaning of numbers. One activity we thoroughly explore is interactive book reading, based on previous research indicating positive learning outcomes from this type of mathematical activity, as it has shown to simultaneously embrace the child’s perspective and encourage interaction and ‘number talk.’ A specially designed picture book presenting small quantities was developed, and variation theory principles were embedded in both the book design and the teaching acts. Through qualitative analyses, we aim to identify what is critical in the interactive book reading sessions for toddlers to discern essential aspects of numbers, with a specific focus on the conditions for making modes of representations into resources for learning. Preschool teachers frequently read the book to 27 toddlers over the course of a year. Video documentation of their reading sessions was analyzed, and exposed the significance of addressing the child’s perspective when choosing what representation to emphasize and in what ways connections within and between representations can be made. Thus, the study contributes knowledge on the teaching of numbers with toddlers, and problematizes as well as extends the potential of interactive book reading as a quality-enhancing educational tool.

This article reports on an educational design research study exploring the potential of combining entrepreneurship and mathematics – two of the key competencies stressed as important in a society of lifelong learning. The aim of the study was to explore what happens when entrepreneurship is integrated into mathematics lessons. Eight Swedish primary schools were involved in the iterative design wherein researchers and teachers together planned, implemented, and evaluated lessons. The results indicate that combining entrepreneurial and mathematical competencies may produce a win-win situation. Entrepreneurial competencies can be of value when students are learning mathematics, and at the same time mathematics teaching can be organised so that students develop both mathematical and entrepreneurial competencies.

This paper focuses on problem solving and problem posing in mathematics education with 6-year-olds. After working on a problem-solving activity, the young students were asked to pose a similar task to a friend. This article explores how the students interpret the notion of similar. To be able to pose a problem-solving task themselves the students had to change perspective, from searching for information to providing information, and from searching for a solution to searching for a question. Also, to create a similar task the students had to reflect on the original problem-solving task. Thus, their posed tasks shed light on their interpretation of what the original problem-solving task was really about. The results show that the large majority of the students included some three-dimensional aspects from the original problem-solving task in their posed tasks. However, the questions they posed varied in terms of whether or not they included mathematical elements.

In mathematics education, digital tools have been used to enhance young children’s understanding of specific subject matter. In such implementations, the digital tool can replace, amplify or transform ‘ordinary’ mathematics teaching. In an initial study, systematization and duplication were identified as critical when young children were to solve a combinatorial task. Therefore, a digital version of the task was developed and combined with a non-digital version, to introduce the use of dual artefacts. The digital version of the task enabled the children to visually explore systematization as well as the principle of completion. After using this digital version of the task, the children’s written records became more systematic and included fewer duplications. We conclude that the digital version of the task reinforced young children’s understanding of the combinatorial task and that the use of dual artefacts enhanced children’s understanding of what a combinatorial problem encompasses.

The results presented in this article are taken from a case study of novice primary school mathematics teachers’ professional identity development from the perspective of the teachers themselves. The empirical material was collected through self-recordings, observations and interviews. The results show how the professional identity development of these novice teachers becomes a pursuit in line with their image of a primary school teacher. To develop a sense of themselves as primary school teachers they need to establish their own criteria - individual (including graduation and personal knowledge) and social (the ability to work in one school, have colleagues and have a class of their own for which they do the planning and teaching). These criteria are shown to be both a precondition for and a part of professional identity development. The novice teachers’ image of what it means to be a primary school teacher directs their actions and becomes the goal of their professional identity development. Because of its high impact, student and novice teachers’ image of primary school teachers ought to be made visible in both teacher education and teacher induction.