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

Understanding studentsʹ 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 studentsʹ 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 studentsʹ latent abilities in 3 primary concepts of fractions: equal sharing, units, and equivalent fractions. Studentsʹ 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.