Shifts in students’ predictive reasoning from data tables in years 3 and 4

In this exploratory descriptive study, changes in one cohort’s responses to an authentic statistical investigation at the commencement of years 3 and 4 were analysed. Forty-four students made predictions by interpreting a data table of historical monthly temperatures, represented these data and explained their reasoning. An Awareness of Mathematical Pattern and Structure (AMPS) framework was extended to analyse students’ responses at five increasing levels of predictive reasoning. More developed predictive reasoning was observed in year 4 than for year 3, as well as large individual differences in both years. Most year 4 students (87%) made predictions within the historical range, relative to half the same cohort in year 3 (54%). More year 4 students (79%) made predictions based on extraction, clustering and aggregation of these data than those in year 3 (51%). Year 4 students noticed patterns such as seasonal trends and variability in these data and observed measures of central tendency. By year 4, 57% of students’ representations demonstrated transnumeration using extracted data from the table, including pictorial, column and line graphs. However, most students’ representations and explanations of these data lagged behind their predictions at both year levels.