Developing students' reasoning about samples and sampling in the context of informal inferences

The expanding use of data in modern society for prediction and decision-making makes it a priority for mathematics instruction to help students build sound foundations of inferential reasoning at a young age. This study contributes to the emerging research literature on the early development of informal inferential reasoning through the conduct of a two-phase exploratory study carried out in an urban upper elementary school (Grades 4 to 6) in Cyprus. In Phase I, Grade 6 (11-year-old) students' initial understandings of samples and sampling were examined through an open-ended written assessment (n = 69), and follow-up interviews (n = 5). In Phase II, a teaching experiment guided by a hypothetical learning trajectory (HLT) was implemented in a Grade 6 classroom (n = 19). The HLT aimed to support the emergence of children's reasoning about sampling issues through the provision of an inquiry-based learning environment designed to offer ample opportunities for informal, data-based inferences. Findings indicate that the efforts of the teaching experiment to integrate the existing body of research into a HLT that starts with children's initial understandings supported students in moving towards more nuanced forms of reasoning about sampling.