Exploring Year 13 students’ probabilistic reasoning from an eikosogram

Abstract

Education research on probability frequently raises concerns about the lack of effective teaching and learning strategies that truly depict the significance of probability in relationship to real life situations. Current strategies implemented are considered trivial and do not reflect the full potential of probability as a tool. Historically, probability was late in being introduced to the mathematics curriculum because of its conceptual complexity. In an attempt to improve the quality of the content and teaching strategies for probability, the University of Auckland Statistics Department recently designed some computerised modelling tools for probability, one of which was the eikosogram. The eikosogram is a tool that displays frequencies and proportions, both values and regional sizes, of categorical variables. The prototype eikosogram tool was trialled with university students in a research study. Hence this research sought to trial a modified version of the prototype eikosogram tool with secondary students and to explore their probabilistic reasoning. A small exploratory research study was conducted using a design-based research method over a period of three weeks. A sequence of tasks was developed and implemented with eight Year 13 students from a calculus class in a low decile school. Students worked in pairs through four one-hour sessions. The tasks consisted of a pre-task, a main task and a post-interview. The main task, which was allocated two sessions, involved students interacting with the eikosogram, first under the guided instruction of the researcher, and then exploring data on their own. A framework from the study on university students was used to analyse the data collected from the main task. The analysis resulted in a proposed new definition of graphicacy for an eikosogram and major changes to the framework. Hence, new additional data exploration components were added to the comprehension components of the framework to produce a new framework for graphicacy for the eikosogram. Three main themes emerged from the research related to: (1) the statistical and contextual knowledge of students; (2) the transitioning of students to explore data independently; and (3) the graphicacy behaviours of students for the eikosogram. The implications arising from these themes suggest that teachers must give more teaching attention to concepts underpinning probabilistic situations such as proportional reasoning skills, contextual and statistical knowledge, as well as concepts related to reasoning with categorical variable.