HYPOTHETICAL LEARNING TRAJECTORY ON INFORMAL HYPOTHESIS TESTING IN A PROBABILITY CONTEXT

Abstract

A design experiment where students in Grade 5 (11–12 years old) play the Color Run game constitutes the context for investigating how students can be introduced to informal hypothesis testing. The result outlines a three-step hypothetical learning trajectory on informal hypothesis testing. In the first step, students came to favor sample space reasoning over idiosyncratic reasoning when the sample space was changed between color runs. In the second and third steps, students used degrees of variation in the distribution of the mode across samples to infer whether an unknown sample space was uniform. Students’ reasoning disclosed the logic: the larger the variation, the greater the reason for rejecting a uniform sample space.