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A Learning Progression for Variability

Fife, James H.; James, Kofi; Peters, Stephanie
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Distribution, Learning Progression, Mathematics Education, Reasoning (Psychology), Random Sampling, Statistics, Variability (Psychometrics), Task Design, Student Responses


The concept of variability is central to statistics. In this research report, we review mathematics education research on variability and, based on that review and on feedback from an expert panel, propose a learning progression (LP) for variability. The structure of the proposed LP consists of 5 levels of sophistication in understanding variability, ranging from the learning that occurs prior to Grade 6 through an expert understanding of variability. Following our analysis of the variability research, the full LP is presented along with example tasks designed to elicit evidence of understanding at each of the proposed levels. The LP described in this report constitutes a new theoretical structure that must be independently validated vis-à-vis empirical recovery of the proposed levels by analyzing student responses to tasks designed to target different levels of the progression.

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