Elementary and middle grade students' constructions of typicality

Aisling M. Leavy, James Middleton

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This study addresses the measures chosen by students when selecting or constructing indices to properties of distributions of data. A series of individual teaching experiments were conducted to provide insight into the development of five 4th to 8th grade students' conceptualizations of distribution over the course of 8 weeks of instruction. During the course of the teaching experiment (emergent) statistical tasks and analogous teacher activities were created and refined in an effort to support the development of understanding. In the process of development, attempts were made by students to coordinate center and variability when constructing measures to index properties of distributions. The results indicate that consideration of representativeness was a major factor that motivated modification of approaches to constructing indices of distributions, and subsequent coordination of indices of variation and center. In particular, the defining features of student's self-constructed " typical" values and notions of spread were examined, resulting in a model of development constituting eight " categories" ranging from the construction of values that did not reflect properties of the data (Category 1) to measures employing conceptual use of the mean in combination with other indices of center and spread (Category 8).

Original languageEnglish (US)
Pages (from-to)235-254
Number of pages20
JournalJournal of Mathematical Behavior
Issue number3
StatePublished - Sep 2011


  • Data and statistics
  • Elementary students
  • Mathematical thinking
  • Middle grade students
  • Statistical reasoning
  • Typicality

ASJC Scopus subject areas

  • Education
  • Applied Mathematics
  • Mathematics (miscellaneous)


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