How robust are learners’ misconceptions of fraction magnitude? An intervention study comparing the use of refutation and expository text

Abstract

Although a good rational number understanding is of crucial importance for learners’ general maths achievement, many learners have misconceptions about fractions. An often described misconception is that a fraction’s numerical magnitude increases when its denominator, numerator, or both increase. The present intervention study investigated how robust this misconception is, after learners have specifically been instructed on the incorrectness of their idea by means of a refutation text, as opposed to a condition where they received an expository text. Results of 76 fourth graders showed a (long-term) learning effect, but no larger learning gains in the group that received a refutation text compared to the group that received an expository text. Results further pointed to large individual differences in the learning gains. While there is a subgroup of learners that benefits from the refutation text, another subgroup was found that tend to overuse and misapply the information given in this text.