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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.

Mathematical knowledge has developed from human activities through thousands of years and is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans' everyday life, an environment where people reach agreement regarding principles in mathematics. Through interaction with worldly phenomena and people, children will strive to understand their surrounding world, gaining experience that they can then in turn use to understand future situations. The environment in which a child grows up, thereby plays an important role in what that child experiences and what opportunities for learning that child has. This article aims at describing what opportunities there are for toddlers to experience and learn basic aspects of mathematics, such as mathematical concepts and the relation between parts and whole, in interaction with other people and the surrounding world. In order to fulfil this aim, an analysis has been done of critical conditions of learning that may be discerned in toddlers' daily activities. Four authentic examples are described and discussed in this article. Results from the qualitatively analyzed videographic study of toddlers' experiences of mathematics in day-care show that variation, simultaneity and reasonableness seem to be critical conditions of learning, as well as the opportunity to focus on important aspects in a phenomenon. Adults working with toddlers therefore play a very important role in setting perimeters for toddlers' experiences and opportunities to explore mathematical phenomena. RÉSUMÉLa connaissance mathématique s'est développée à partir des activités humaines au cours de milliers d'années ; elle est liée au monde et aux cultures dans lesquels vivent les hommes et les femmes. Nous pouvons dire que les mathématiques sont ancrées dans la vie quotidienne des humains, dans un environnement où les gens se mettent d'accord sur des principes mathématiques. Les enfants s'efforceront de comprendre le monde qui les entoure à travers l'interaction avec les phénomènes du monde et avec les gens, acquérant ainsi l'expérience dont ils pourront, à leur tour, se servir pour comprendre les situations futures. L'environnement où un enfant grandit joue donc un rôle important dans les expériences de cet enfant et dans les possibilités d'apprentissage à sa disposition.Le présent article a pour but de décrire les occasions offertes à de petits enfants pour expérimenter et apprendre des aspects fondamentaux des mathématiques, comme par exemple des concepts mathématiques et le rapport entre les parties et le tout, en interaction avec d'autres personnes et avec le monde qui les entoure. Pour atteindre ce but, nous avons fait une analyse des conditions critiques de l'apprentissage perceptibles dans les activités quotidiennes de petits enfants. Cet article présente et discute quatre épisodes authentiques. Les résultats de l'étude vidéographique des expériences mathématiques de tout-petits en milieu de garderie, analysée qualitativement, montre que la variation, la s...

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