Mathematical Knowledge and Skills as Longitudinal Predictors of Fraction Learning Among Sixth-Grade Students

It is well known that fraction knowledge is relevant for later success in mathematics. However, many students still face difficulties when dealing with fractions. Predictors of fraction knowledge have been widely examined. Systematizing mathematical predictors, whether their predictive contributions are direct or indirectly mediated via other mathematical knowledge and skills, could reveal how mathematics teachers could support students' fraction learning. The present longitudinal study investigates these roles for six mathematical prerequisites of fraction knowledge that differ in their connection to the multiplicative field. N = 363 students' skills regarding six prerequisites were measured at the beginning of Grade 6. For three of these prerequisites ("distal prerequisites," e.g., whole number line estimation), possible indirect effects via one or more of the other three prerequisites ("proximal prerequisites," e.g., symbolic proportional reasoning skills) can be argued. After the systematic introduction of fractions in class, students worked on tests for three central facets of fraction knowledge (knowledge of fraction subconstructs, fraction arithmetic skills, and fraction word problem-solving). All prerequisites predicted later fraction knowledge but in different roles. The three proximal prerequisites directly predicted all facets of fraction knowledge, even when controlling for all other prerequisites. As assumed, the distal prerequisites indirectly predicted all facets of fraction knowledge, with the three proximal prerequisites as mediators. The results extend previous findings on the effects of indirect predictors on fraction learning and highlight their role in building up necessary direct predictors before fraction teaching.