From sample to population: A hypothetical learning trajectory for informal statistical inference

Abstract

This paper presents the results of a teaching experiment to enhance 9th-grade students’ understanding of informal statistical inference (ISI). The teaching experiment was conducted to evaluate and revise a hypothetical learning trajectory (HLT) as a step towards an empirically and theoretically based HLT-design for ISI. The challenge was to invite young students, inexperienced with sampling, to making statistical inferences without knowledge of formal probability theory. In this trajectory, the students proceeded from a first experience with sampling physical objects, through an understanding of sampling variation and resampling, to reasoning with sampling distribution. The results of the intervention suggest that young students can informally interpret sample data with corresponding uncertainty. Engaging in concrete sampling, in simulations and in deepening whole-class discussions seem essential parts of this HLT-design.