Exploring Group-Wise Conceptual Deficiencies of Fractions for Fifth and Sixth Graders in Taiwan

Abstract

Abstract Understanding students' conceptual deficiencies of fractions is an essential step toward effective teaching. The authors proposed a novel 2-component multidimensional item response theory (MIRT) model to analyze students' conceptual deficiencies of fractions in a group-wise fashion. They identified 5 latent classes for the 5th and 6th graders in Taiwan on the basis of latent class analysis with 2,612 students involved. With the 2-component MIRT model, the authors estimated students' latent abilities in 3 primary concepts of fractions: equal sharing, units, and equivalent fractions. Students' latent abilities in the fraction concepts characterized each latent class. The authors found the units concept to be a common conceptual deficiency of all students, revealing an important flaw in current teachings of fraction concepts in Taiwan. Keywords: equal sharing conceptequivalent fractions conceptfractionslatent class analysismultidimensional item response theoryunits concept