We analyzed the development of 4th-grade students’ understanding of the transition from experimental relative frequencies of outcomes to theoretical probabilities with a focus on the foundational statistical concepts of variation and expectation. We report students’ initial and changing expectations of the outcomes of tossing one and two coins, how they related the relative frequency from their physical and computer simulated trials to the theoretical probability, and how they created and interpreted theoretical probability models. Findings include students’ progression from an initial apparent equiprobability bias in predicting outcomes of tossing two coins through to representing the outcomes of increasing the number of trials. After observing the decreasing variation from the theoretical probability as the sample size increased, students developed a deeper understanding of the relationship between relative frequency of outcomes and theoretical probability as well as their respective associations with variation and expectation. Students’ final models indicated increasing levels of probabilistic understanding.

Item Type:	Refereed Article
Keywords:	expectation, probability models, relative frequency, statistical literacy, theoretical probability, variation, modelling probability, Grade 4
Research Division:	Education
Research Group:	Curriculum and pedagogy
Research Field:	Mathematics and numeracy curriculum and pedagogy
Objective Division:	Education and Training
Objective Group:	Teaching and curriculum
Objective Field:	Pedagogy
UTAS Author:	Watson, J (Professor Jane Watson)
ID Code:	105747
Year Published:	2016
Funding Support:	Australian Research Council (DP120100158)
Web of Science® Times Cited:	16
Deposited By:	Education
Deposited On:	2016-01-13
Last Modified:	2017-11-10
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