Developing initial notions of variability when learning about box plots

Abstract

Variability is often underrepresented in (early) statistics classroom. We distinguish two different conceptualizations of variability: Variability as deviation from a center and variability as distance between boundaries. We argue that instruction on the boxplot is predestined to acquire the latter understanding. Conversely, this understanding is part of a comprehensive conceptual knowledge about boxplots. If this understanding is lacking, this leads to a systematic error in the interpretation of boxplots. We developed a digital learning environment assuming that enhanced variability-focused cognitive activities during learning indicate the acquisition of the necessary conceptual knowledge. We conducted an intervention study (N = 195) and using a structural equation model, we found–in line with our hypothesis–that a problem type in which variability, rather than central tendency, was predominantly relevant to the solution leads to higher gain in conceptual knowledge on the boxplot mediated by enhanced variability-focused cognitive activities.