Mathematical knowledge and skills as longitudinal predictors of fraction learning among sixth-grade students.

Abstract

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. Educational Impact and Implications StatementThis study provides evidence that a range of mathematical knowledge and skills is relevant for fraction learning in different roles. Based on the present results, acquiring prerequisites for fraction learning begins early during school and should also be considered via indirect mechanisms. It is essential to ensure several prerequisites directly before introducing fractions in class, particularly more proximal prerequisites such as knowledge of multiplication and division, symbolic proportional reasoning skills, and informal fraction knowledge. If students have problems acquiring these prerequisites, focusing on more distal prerequisites, such as whole number line estimation and different spontaneous focusing tendencies in interventions to support students' fraction learning, might be helpful.

Beyond linearity: Using IRT‐scaled level models to describe the relation between prior proportional reasoning skills and fraction learning outcomes

“…The current work focuses on the latter of the two approaches, connecting to a part-whole understanding of fractions. In this sense, fraction learning builds hierarchically on several domain-specific predictors from the multiplicative field, such as proportional reasoning skills (Long, 2015;Schadl & Ufer, 2023).…”

“…Whereas the parts of juice and water were presented in one bar in the part-whole representation, separate bars were used for the part-part representation in this study. Recently, Schadl and Ufer (2023) observed symbolic proportional reasoning skills (cf., Table 1) to predict three facets of later fraction knowledge (knowledge of fraction subconstructs, fraction arithmetic skills, and fraction word problems; cf., section "Models of fraction knowledge and skills" above) when analyses controlled for different mathematics-specific skills (e.g., skills of multiplication and division with natural numbers). The present study intends to investigate these predictive relations beyond linearity.…”

“…Note that data have already been analyzed in further publications. Schadl and Ufer (2023) present linear predictive models based on more scales. Contrary to this, the present analyses investigate such bivariate prediction in detail and make explicit use of level models.…”

“…Knowledge of fraction subconstructs comprised knowledge of the subconstructs part-whole, ratio, operator, quotient, and measure. It was assessed with 27 items taken from Schadl and Ufer (2023). Items contained more or less prestructured situations (see Figure A1 for examples).…”

“…Fraction arithmetic referred to fraction operations (addition, subtraction, multiplication, and division) and the representations of numbers. The instrument included 35 symbolic items taken from Schadl and Ufer (2023). Items required reducing and expanding fractions, comparing at least two fractions, and performing arithmetic operations with fractions.…”