Refuting misconceptions: Computer tutors for fraction arithmetic

Abstract

Fractions, known to be difficult for both children and adults, are especially prone to misconceptions and erroneous strategy selection. The present study investigated whether a computer tutor improves fraction arithmetic performance in adults and if supplementing problem solving with erroneous examples is more beneficial than problem solving alone. Seventy-five undergraduates solved fraction arithmetic problems using a computer tutoring system we designed. In a between-subjects design, 39 participants worked with a problem-solving tutor that was supplemented with erroneous examples and 36 participants worked with a traditional problem-solving tutor. Both tutors provided hints and feedback. Overall, participants improved after the tutoring interventions, but there were no significant differences in gains made by the two conditions. For students with low prior knowledge about fraction arithmetic, the numerical gains were higher in the erroneous-example group than the problem-solving group, but this effect was not significant. Thus, computer tutors are useful tools for improving fraction knowledge. While erroneous examples may be particularly beneficial for students with low prior knowledge who may hold more misconceptions, more research is needed to make this conclusion.

The hierarchical relations among mathematical competencies: From fundamental numeracy to complex mathematical skills.

“…All fractions had single-digit numerators and denominators. Foil answers were created based on the misconceptions and errors noted in Di Lonardo Burr et al (2020): They were either the result of a common arithmetic mistake, the result of a common math misconception, or the result of applying the correct procedure for a different operation. Participants were encouraged to use paper and pencil to solve the problems.…”

Attending to what’s important: what heat maps may reveal about attention, inhibitory control, and fraction arithmetic performance

“…Given the inherent difficulty of developing competency in math and an understanding of fractions specifically, it is perhaps unsurprising that both children and adults make frequent errors when asked to solve fraction arithmetic problems (Siegler et al, 2011;Siegler and Pyke, 2013;Braithwaite and Siegler, 2018a;Di Lonardo Burr et al, 2020). Examining people's self-reported strategies for solving math problems (i.e., "strategy reports") can provide insight into the types of errors participants make.…”