Eye love arithmetic: an inversion and associativity eye tracking study

Abstract

Arithmetic is important for developing the cognitive and problem-solving skills that are fundamental for higher levels of math. As such, it is important that individuals understand arithmetic concepts such as inversion and associativity, which can be reflected in how they solve three-term arithmetic problems. If an adult solves an inversion problem like 27 + 46 – 46 by cancelling the 46s, it suggests they understand inversion and have used an inversion shortcut. Similarly, when adults solve an associativity problem like 3 × 26 ÷ 13 by first computing 26 ÷ 13, they have used an associativity shortcut. To deconstruct why some individuals are better at using shortcuts, the current study used an eye tracker to generate heat maps and compare the visual attention of shortcut users to shortcut non-users. Participants (n =22) solved 32 three-term arithmetic problems while their eye fixations were tracked. Half of the problems were inversion, and the other half were associativity. Problems differed by operators (additive or multiplicative) and their format (conducive or non-conducive). Results support previous findings that adults are more accurate and use more shortcuts on inversion, additive, and conducive problems than associativity, multiplicative, and non-conducive problems. When comparing the eye movements of shortcut users to shortcut non-users, the heat maps indicate that participants focused on different areas. Further visual and statistical analyses are needed to compare the eye movements of shortcut users to shortcut non-users. Continuing to study the visual attention of shortcut users might explain why they perform well on these problems.