Students' Appreciation of Expectation and Variation as a Foundation for Statistical Understanding

This study presents the results of a partial credit Rasch analysis of in-depth interview data exploring statistical understanding of 73 school students in 6 contextual settings. The use of Rasch analysis allowed the exploration of a single underlying variable across contexts, which included probability sampling, representation of temperature change, beginning inference, independent events, the relationship of sample and population, and description of variation. Interpretation of the demands of increasing code levels for the resulting variable revealed an increasing appreciation of and interaction between the ideas of variation and expectation. Student progression in understanding is illustrated with kidmaps, and educational implications are considered.