Using Eye-Tracking to Assess the Application of Divisibility Rules when Dividing a Multi-Digit Dividend by a Single Digit Divisor

Abstract

The Department of Basic Education in South Africa has identified certain problem areas in Mathematics of which the factorisation of numbers was specifically identified as a problem area for Grade 9 learners. The building blocks for factorisation should already have been established in Grades 4, 5 and 6. Knowing the divisibility rules, will assist learners to simplify mathematical calculations such as factorisation of numbers, manipulating fractions and determining if a given number is a prime number. When a learner has to indicate, by only giving the answer, if a dividend is divisible by a certain single digit divisor, the teacher has no insight in the learner’s reasoning. If the answer is correct, the teacher does not know if the learner guessed the answer or applied the divisibility rule correctly or incorrectly. A pre-post experiment design was used to investigate the effect of revision on the difference in gaze behaviour of learners before and after revision of divisibility rules. The gaze behaviour was analysed before they respond to a question on divisibility. It is suggested that if teachers have access to learners’ answers, motivations and gaze behaviour, they can identify if learners (i) guessed the answers, (ii) applied the divisibility rules correctly, (iii) applied the divisibility rules correctly but made mental calculation errors, or (iv) applied the divisibility rules wrongly.