To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

A computerized sequential event sampling decision-making task was administered to 187 5- to 10-year-olds and adults. Participants made a series of choices between alternatives that differed in win probability (Study 1) or win and loss probability (Study 2). Intuitive and more explicit measures were used. Study 1 revealed that, across ages,…

The paper discusses the interaction between intuitive biases of probabilistic thinking and mathematical knowledge. It would appear that students may answer numerical problems correctly but falter on simple descriptive solutions. Students appear to relinquish formal knowledge for simpler heuristics when attempting to describe the outcome of an…