No abstract

The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126 observations of 4-5-yearolds solving a simple subtraction task, is to discuss different ways of using fingers, with some of the ways appearing more, and others less, powerful. The analysis suggests there is much more complexity to children's finger-related strategies than prior research has indicated. Empirical findings in our study point to the decisive effects of different ways of using fingers, and in particular for either keeping track of counted units or for presenting a structured awareness of number. Three ways of using fingers emerge in the analysis, which are discussed in relation to their rate of success in solving the subtraction task and with attention to why the differences matter for the success rate. Through this discussion we suggest that the complexity of how fingers are used must be considered.

Taking as its point of departure the discussion about the disconnection between research and practice, this article presents learning study as a research approach to overcoming this gap. Learning study has commonalities with design research and lesson study, but is a teacher‐researcher collaboration where both have a common object of research. Thus, it is research with teachers, rather than on teachers and focuses on constructing knowledge concerning objects of learning as well as teaching‐learning relationships. The focus of the research collaboration is professional problems related to the object of learning that teachers encounter in their everyday practice. The process is guided by a theory of learning and pedagogy—the variation theory. The knowledge product of learning study is a theoretical description of what must be learned in order to develop a specific capability. Examples of knowledge contributions from learning study are given and it is suggested that such knowledge can be considered to be public knowledge that can be shared, used and developed by other teachers in other contexts. Furthermore, it is suggested that there are specific features of learning study that make it a research approach that may strengthen connections between research and practice.