Upper primary students' errors in interpreting graphically-oriented mathematics assessment items

Often primary students are required to interpret or produce graphics (e.g., maps, number lines, graphs, tree diagrams) in mathematics assessment tasks. Thus, to become proficient in mathematics, students need to become graphicate as well as articulate, literate and numerate. This paper reports on one aspect of graphicacy, namely, students' ability to interpret graphically-oriented mathematics items. Such items include graphics and text and might include symbols. Our study focussed on the errors that students make in the interpretation of graphically-oriented items because knowledge of errors is an important aspect of pedagogical content knowledge. Based on the literature on spatial intelligence and graphical understanding, we hypothesised that (1) Upper primary students would make perceptual and conceptualisation errors in interpreting graphics, and that (2) Upper primary students would make fewer perceptual errors than conceptualisation errors. These hypotheses were tested with a data set of final year primary students' responses to 12 graphically-oriented interview items that were selected for theoretical diversity. Both hypotheses were supported. However, of particular note in our findings was that 66% of the students' total errors related to the interpretation of a graphic with the remaining errors associated with the text (30%) or calculation (4%). The graphical errors were predominantly related to conceptualisation (56%) rather than perception (10%). Examples of perceptual and conceptualisation errors are presented in the paper. Based on our findings, we draw attention to three pedagogical issues. First, given the proportion of graphical errors on mathematics items, fostering graphical understanding should be an integral component of any mathematics program. Second, upper primary students may need support to develop their spatial perception skills although these skills are typically associated with the lower to middle primary years. Finally,interpreting graphically-oriented items is a complex process which requires students to interpret multiple representations including graphics simultaneously.