This research aims to determine second-year university students' understanding in interpreting and representing fractions. A set of fraction tests was given to students through two direct learning interventions. An unstructured interview was used as an instrument to obtain explanations and confirmations from the purposive participants. A total of…

Background: While it has been widely demonstrated that children's and adolescents' understanding of rational number plays an important role in their mathematics achievement, we have limited knowledge about the cognitive correlates of this understanding. Aims: The current study aimed at examining whether children's non-symbolic ratio processing and…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

A formative pilot study of a fractions intervention was conducted to address the intervention's potential for improving fifth-grade struggling students' knowledge of fractions, and to identify any logistical or instructional design issues, before scaling up for a randomized control trial. In the first section, we provide details of the formative…

In this article, we present some mathematical tasks designed to support pre-service teachers (PSTs) in obtaining a broader, more connected understanding of decimal numbers and quantities. We describe classroom scenarios from a content course in which PSTs experienced these cognitively demanding decimal tasks, enacted in ways that maintain high…

Many elementary and junior high school students do not become proficient with common and decimal fractions because they have established few connections between the form they learn in the classroom and understandings they already have. (Author/GC)