Educational Studies in Mathematics

, Volume 88, Issue 3, pp 385–404 | Cite as

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.


Samples and sampling Sampling method Statistical reasoning Informal inferential reasoning Informal statistical inference Hypothetical learning trajectory 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Maria Meletiou-Mavrotheris
    • 1
  • Efi Paparistodemou
    • 2
  1. 1.European University CyprusNicosiaCyprus
  2. 2.Cyprus Pedagogical InstituteNicosiaCyprus

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