MATHCONSTRUCTION · Constructing Mathematical Knowledge beyond Core Intuitions

Humans and other animals possess dedicated systems of core knowledge to represent numeric and geometric information. In the case of number at least, these representations are abstract (independent of the format of the stimuli represented), they are present early in life, and they can be used to compute the outcome of simple arithmetic problems. Such intuitive knowledge is thought to guide the acquisition of elaborate concepts of numbers and geometry. However, core systems of representations for numbers and geometry fall short of providing the representational power to support even the most fundamental mathematical concepts: Integers, and Euclidean geometry. In this research project, we are seeking to understand the process of knowledge construction by which children acquire adult-like numeric and geometric concepts, focusing on two case studies: exact numbers, and plane angles. Our approach is multidisciplinary, bringing together researchers from the fields of developmental psychology, cognitive neuroimaging, and linguistics. For both number and geometry, we will first start by characterizing core intuitions in behavioural studies involving infants and children. Second, we will look at the factors influencing the acquisition of more elaborate concepts based these core intuitions. In order to separate the factors of age, education, and environment, we will conduct studies with occidental children, as well as children and adults from the Amazon. Third, we ultimately aim at studying the neural bases of conceptual changes in childhood, and in this perspective we are planning brain imagining experiments in adults. Once we have a thorough description of the neural codes for number and geometry in adults, we will be in position to ask which aspects of the code have undergone change during childhood, as new knowledge was being constructed.