This paper reports an overview of contemporary research on early childhood mathematics teaching and learning presented at recent mathematics education research conferences and papers included in the special issue (2020–4) of ZDM Mathematics Education. The research covers the broad spectrum of educational research focusing on different content and methods in teaching and learning mathematics among the youngest children in the educational systems. Particular focus in this paper is directed to what lessons can be drawn from teaching interventions in early childhood, what facilitates children’s mathematical learning and development, and what mathematical key concepts can be observed in children. Together, these themes offer a coherent view of the complexity of researching mathematical teaching and learning in early childhood, but the research also brings this field forward by adding new knowledge that extends our understanding of aspects of mathematics education and research in this area, in the dynamic context of early childhood. This knowledge is important for future research and for the development of educational practices.

The focus of this article is on mathematics teaching in a play-based and goal-oriented practice, such as preschool, and on how different lines of actions may impact children’s learning opportunities. Video recordings of authentic play activities involving children and nine teachers from different preschools were analyzed qualitatively to answer the following research questions: (1) What lines of action do teachers use when they teach mathematics in play? and (2) What implications may different ways of teaching have for children’s learning opportunities? The analysis revealed four different categories: confirming direction of interest; providing strategies; situating known concepts; and challenging concept meaning. As these differ regarding both the mathematics content focused on and the kind of knowledge emphasized, they have implications for children’s learning opportunities.

Revised guidelines for Swedish early childhood education that emphasize mathematics content and competencies in more detail than before raise the question of the status of pedagogical mathematical awareness among Swedish early childhood teachers. The purpose of this study is to give an overview of teachers’ current pedagogical mathematical awareness. A questionnaire was distributed to 147 teachers, asking them to respond to their habits of working with mathematics. The survey is based on theoretical conjectures of teacher professionality (pedagogical content knowledge), integrated with the idea of developmental pedagogy. Results from the questionnaire show that teachers account for mathematics as learning content but limitations are discerned concerning teachers’ awareness of spatial aspects of mathematics and problematization of mathematical content in goal-oriented manners. The results also point out areas for further stimulation in teacher training.

In this empirical study, we investigate an early childhood education activity in mathematics on the concept of ‘pattern’. The children participating in the study attend an intermediate form of schooling in Sweden called ‘the preschool class for six-year-olds’, intended to facilitate their transition from preschool to school. Following a prolonged activity over 45 minutes, we analyse for what the children are supported in discerning and what they give as evidence of having discerned in and about patterns. The theoretical point of departure is variation theory, conceptualising learning as increased discernment. The results show that in terms of the important Vygotskian distinction between ‘pseudo concepts’ and ‘concepts (proper)’, the children's discernment and what they are supported in discerning are of the former kind. Pseudo concepts are discussed as integral to the institutional form of the preschool class and premised to be important to the child's further conceptual development.

In this paper, we present a way of describing variation in young children’s learning of elementary arithmetic within the number range 1–10. Our aim is to reveal what is to be learnt and how it might be learnt by means of discerning particular aspects of numbers. The Variation theory of learning informs the analysis of 2184 observations of 4- to 7-year-olds solving arithmetic tasks, placing the focus on what constitutes the ways of experiencing numbers that were observed among these children. The aspects found to be necessary to discern in order to develop powerful arithmetic skills were as follows: modes of number representations, ordinality, cardinality, and part-whole relation (the latter has four subcategories: differentiating parts and whole, decomposing numbers, commutativity, and inverse relationship between addition and subtraction). In the paper, we discuss particularly how the discernment of the aspects opens up for more powerful ways of perceiving numbers. Our way of describing arithmetic skills, in terms of discerned aspects of numbers, makes it possible to explain why children cannot use certain strategies and how they learn to solve tasks they could not previously solve, which has significant implications for the teaching of elementary arithmetic.

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.