Understanding of cardinality is at the core of the number concept, but children find it challenging to grasp the meaning of numerosity (Fluck et al., 2005). Moreover, the ontological and epistemological nature of the cardinal concept seems to be in dispute, and more research on children’s early development of the number concept in natural settings is needed (Reikeras et al., 2012).
This design study on early learning in mathematics concerns the relation between nonverbal and verbal representations of magnitudes and the formation of the number concept of 3-5 year olds in full bodily-spatial interaction. The overarching objective is to investigate how the cardinal concept of numbers is perceived, conceptualized and measured in an embodied design outdoors in the vicinity of the kindergarten. The design aims to support 3-5 years olds ability to embody quantifiable spatial structures and dialectically use number words and number-metaphors to communicate and reflect upon embodied experiences, and environmental and designed affordances. Intervention will be conducted in kindergarten for testing, refinement and modification of the design, and for producing verbal- and non-verbal data-material for a multi-case analysis. The study is abductive and applies both explorative and explanatory approaches to the investigated phenomena, and combines theory building and theory testing. To achieve theory triangulation, models of core knowledge systems, conceptual metaphor theory and embodied cognition will be used as main theoretical stands. Moreover, the notion conceptual mapping will serve as a structuring framework for the analyses of the relation between cognitive structures and observable non-verbal and verbal representations of numerosity. We will also use and elaborate on the knower-level theory of how children represent numbers as develop by Lee and Sarnecka (2010), which is based on the Give-N-task for assessing understanding of cardinality (Schaeffer et al., 1974).
The research question elaborated in sub-questions and articles
The overarching research question is as follows: “How is the cardinal concept of numbers perceived and conceptualized by 3-5 years old children in body-spatial interaction, and how can their competences in the cardinal concept be measured?”
This research question has been elaborated into articles.
1) Subset-knowers’ cross-domain mapping of numerosity in path navigation
2) Pre-schoolers’ ability to synchronise multiple representations of numerosity in embodiment of a counting-on-strategy
3) Analysing 3- and 4- year olds strategies in a ‘Part-Part-Whole’-task from a numeracy perspective
The objective is to contribute to a more comprehensive understanding of early learning of numbers in embodied interaction outdoors.