An analysis of students’ initial statistical understandings: developing a conjectured learning trajectory

Abstract This paper reports the analysis of performance assessment tasks administered in a seventh-grade classroom. The purpose of the assessments was to obtain data on students’ current statistical understandings that would then inform future instructional design decisions in a classroom teaching experiment that focused on statistical data analysis. The tasks were designed to provide information about students’ current understandings of creating data, organizing data, and assessing the center and “spreadoutness” of data. In considering the analysis, we found that the students typically viewed the mean as a procedure that was to be used to summarize a group of numbers regardless of the task situation. Data analysis for these students meant “doing something with the numbers.” Based on this analysis, a goal that emerged as significant for the classroom teaching experiment was to support a shift in students’ reasoning towards data analysis as inquiry rather than procedure. The influence of the students’ prior experiences of doing mathematics in school was also apparent when they developed graphs. They were primarily concerned with school-taught graphical conventions rather than with what the graphs signified. In the course of the analysis we distinguished between additive and multiplicative reasoning about data. This distinction is significant given that the transition from additive to multiplicative reasoning constitutes the overriding goal of statistics instruction at the middle-school level.