This chapter focuses on how children’s everyday knowledge when entering school is different from subject matter knowledge and argues that children’s emotional imagination and motive orientation is a foundation for their acquisition of subject matter knowledge. We discuss how imagination supports children’s generalizations of experience, so that it becomes possible for them to move between the general and the concrete in analyzing and using knowledge about the world. We also argue for a dialectical relationship between the culturally developed content the children’s encounters in their interactions in the world and the formation of mind. Within the cultural-historical approach to learning and development Davydov was the first to clarify how concepts, within a subject matter system, that are related through the historical development of its content may become the foundation for children learning in school. Supporting the development of theoretical thinking among school pupils serves both to develop thinking with subject matter knowledge, and support children’s person formation.

Developmental teaching has a long history starting with Vygotsky’s ideas of teaching reaching into the zone of proximal development, an accomplishment that only are possible with the help of qualified teachers. Developmental teaching is oriented both to children’s acquisition of competence and to their formation as persons acquiring theoretical thinking and motive orientation. Central ideas in developmental teaching are that general knowledge in the form of core relations should come before specific and concrete knowledge, and that children through agentic but also teacher-guided exploration should be able to acknowledge these conceptual relations. These ideas have been extended with Hedegaard’s ideas of the double move in teaching and learning. In this process, teaching is a double and moving back to qualify children’s… knowledge to subject matter knowledge and back to quality children’s concept formation. This is illustrated in a project focusing on the subjects of biology, human geography and history working with oppositions, using children’s everyday knowledge and questions to create their activities and motivation for exploration. The Radical-Local approach extends the double move with inclusion of aspects of children’s community as a process of movement from the local to the general and the general to the local. The chapter also addresses assessment challenges through presenting a questionnaire addressing the child’s social situation of development, to capture the child’s perspective on their participation in school practices.

Ernst Mach’s appeal to the ‘economy of science’ has sometimes been interpreted as an overarching principle of minimisation, promoting the increasing simplification of scientific knowledge via principles that increase calculating power without adding substantively to the knowledge embedded in empirical facts. There is a growing literature arguing for a more robust understanding of Mach’s ‘economy of science’. Machian ‘economy’ appeals to the continuity between scientific experiences and concepts, but also to the increasing complexity of scientific concepts, building on connections between what Mach called world-elements or sensation-elements. Mach’s account emphasises not only continuities between experiences that allow for simplification, but also areas of divergence that promote the branching of scientific concepts and methods. I emphasise the roles of abstraction, pragmatism, and history in Mach’s economy of science and argue that these elements allowed Mach to investigate the productive tension between creative and conservative moments in the history of science.