Fraction Errors in a Digital Mathematics Environment: Latent Class and Transition Analysis

Student struggles with fractions are well documented, and due to fractions’ importance to later mathematics achievement, identification of the errors students make when solving fraction problems is an area of interest for both researchers and teachers. Within this study, we examine data on student fraction problem errors in pre- and post-quizzes in a digital mathematics environment. Students (N=1,431) were grouped by prevalence of error types using latent class analysis. Three different classes of error profiles were identified in the pre-quiz data. A latent transition analysis was then used to determine if class membership and class structure changed from pre- to post-quiz. In both pre- and post-quiz, there was a class of students who appeared to be guessing and a class of students who performed well. One class structure was consistent with the idea that early fraction learners rely heavily on whole number principles. Identification of co-occurrence of and changes to fraction errors has implications for curricular design and pedagogical decisions, especially in light of movements toward personalized learning systems.