EXPLORATION AND INDUCTION VERSUS CONFIRMATION AND DEDUCTION

摘要

Application of the scientific method involves two interacting kinds of reasoning: heuristic exploration and inference to arrive at hypotheses and deductive reasoning to confirm or refute them. Theoretical statistics draws on abstract mathematical reasoning, much of which lies beyond the capability of young students. Nevertheless, they can acquire a sophisticated understanding of statistical concepts by drawing on natural intuitions. There is an analogy in physics with its mathematical basis, which may be understood heuristically. In a similar way, many concepts in probability and statistics have physical analogues. Analogues such as the familiar ball and urn model connect to natural cognitive structures the brain has evolved to enable survival in a complex world. By drawing on these natural cognitive tools, teachers can have greater success both in developing intuitions and in facilitating the formation of abstract concepts.