AN EXPLORATION OF YOUNG STUDENTS' ABILITY TO GENERALISE FUNCTION TASKS

The Early Years Generalising Project involves Australian students, Years 1–4 (age 5–9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focussing on the identification, prediction and justification of function rules. It reports on students attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks. The Early Years Generalising Project (EYGP) 1 is a series of cross-sectional studies of cohorts of students from Year 1 to Year 4 (age 5 to 9) that aims to build theories regarding young students’ ability to grasp and express generalisations, the two components of the act of generalisation in terms of Radford, 2006). Each cross-sectional study covers a particular context and form of generalisation (e.g., growing patterns and pattern rules, equivalence and equation principles, operations and arithmetic processes and structures). Each study has two stages: (a) exploration—an initial stage where a small sample of students (n=5) from each Year level participate in one-on-one clinical interviews; and (b) validation—a final stage where, as a result of these interviews, conjectures were posed and tested in one-on-one semi-structured interviews conducted with a further cohort of 20 students from each Year level, selected to represent a wide range of academic abilities and cultures. This paper presents a single aspect of the project; an exploration of how Year 3 and 4 students (age 7 to 9) express and justify generalisations for the context of input-output changes using function machines and the form function rules. It covers two year levels of the initial stage of the cross-sectional study on function machines.