The Effect of Learners’ Knowledge of the Divisibility Rules on their Gaze Behaviour

Abstract

The Department of Basic Education in South Africa has identified factorisation as a problem area in Mathematics teaching. Learners in earlier grades are exposed to mathematical tasks, involving concepts, such as factors of integers, fractions, equivalent fractions and prime numbers, that are easier to solve when the divisibility rules are applied. An experiment was designed to investigate the effect of learners’ knowledge and their application of the divisibility rules on their gaze behaviour. Seventy-eight learners in Grades 4–7 participated in an eye-tracking study where questions on divisibility were presented on a computer screen. Learners were expected to indicate whether a five-digit dividend was divisible by a divisor and provide reasons for their answers. Gaze behaviour (expressed as the percentage of total fixation time that was spent on each digit), along with learners’ verbal responses were used to determine whether a given divisibility rule was applied correctly. The findings show that learners apply different strategies to inspect the dividend when they know the divisibility rules and apply them correctly as opposed to when they do not know the rules and/or apply them incorrectly. It is argued that, since knowledge of the divisibility rules is a reliable predictor for gaze behaviour, gaze behaviour can in turn be used to assist teachers to identify a lack of knowledge and/or the incorrect application of the divisibility rules. Teachers can then cautiously intervene with revision to assist learners whose gaze behaviour indicates that they need assistance.

Keywords:

• Divisibility rules
• eye-tracking
• gaze behaviour

ORCID

Pieter Potgieter http://orcid.org/0000-0002-2944-7485

Pieter Blignaut http://orcid.org/0000-0002-2800-0868