Abstract
Recently, owing to their desire to cultivate pupils' ability to learn and think for themselves, educational researchers and practitioners emphasize inquiry-based learning. Toward inquiry-based learning relying on proof and proving, this paper deliberates a normative meaning of mathematical inquiry from a Lakatosian fallibilist perspective, and discusses educational values of mathematical inquiry. Firstly, this paper examines three aspects of mathematical inquiry and their sub-aspects, through analyzing Lakatos' chief book Proofs and Refutations (Lakatos, 1976) in detail. By synthesis of these aspects, this paper then conceptualizes the meaning of mathematical inquiry as "conjecturing statements through investigation of properties or relations of mathematical objects, proving them, and then refining the statements and proofs through refuting them, with the aim to reducing their uncertainty". Subsequently, this paper discusses educational values of the mathematical inquiry from three standpoints; change of pupils' views of mathematics, and their learning on methods for productive mathematical activities; change of pupils' views of proof and proving; learning of proof and proving from primary school level.
