Reasoning about Shape as a Pattern in Variability

This paper examines ways in which coherent reasoning about key concepts such as variability, sampling, data, and distribution can be developed as part of statistics education. Instructional activities that could support such reasoning were developed through design research conducted with students in grades 7 and 8. Results are reported from a teaching experiment with grade 8 students that employed two instructional activities in order to learn more about their conceptual development. A “growing a sample” activity had students think about what happens to the graph when bigger samples are taken, followed by an activity requiring reasoning about shape of data. The results suggest that the instructional activities enable conceptual growth. Last, implications for teaching, assessment and research are discussed.