Childrenʹs reasoning by mathematical induction: normative facts, not just causal facts

My argument for an empirical and normative model of childrenʹs development applicable to reasoning in mathematics is in three parts. Part I is a review of the evidence from a recent study of the development of young childrenʹs (aged 5–7 years) reasoning by mathematical induction. Part II outlines an interpretation in terms of an inclusive unit of analysis, which is the act of judgement combining causal facts and normative facts. Norms are manifest as rules, obligatory commands, and technical directives about “what has to be done” and “what has to be”. Normativity has been marginalised, even omitted, from most other accounts of childrenʹs development and education. Causal regularity is not the same as normative regulation. The final part is a review of five educational implications, covering reasoning by induction in the mathematics curriculum for children, diagnostic assessment of both adults’ norms and childrenʹs norms in childrenʹs reasoning, formative assessment through normative regulation, and critical methods in investigating childrenʹs norms. Underlying all the three parts are key principles of Piagetʹs constructivism about norms at work in human minds in action.