There is mixed evidence as to whether concrete manipulatives (e.g., toy animals) are better than abstract manipulatives (e.g., counters) for teaching mathematical concepts to children. Concreteness is defined as the amount of extraneous information a manipulative provides, and in this study we aimed to unpick which dimensions of concreteness…

Instructors ("N"?=?204) of elementary mathematics methods courses completed a survey assessing the extent to which they value cognitive research and incorporate it into their courses. Instructors' responses indicated that they view cognitive research to be fairly important for mathematics education, particularly studies of domain-specific topics,…

Proficiency with fractions serves as a foundation for later mathematics and is critical for learning algebra, which plays a role in college success and lifetime earnings. Yet children often struggle to learn fractions. Educators have argued that a conceptual understanding of fractions involves learning that a fraction represents a magnitude…

Using Central Conceptual Structure theory as an heuristic, learning sequences in the acquisition of number knowledge are described in three forms that bridge theory and practice: as a four-stage theoretical progression, as items on a developmental test created to test the theoretical progression, and as learning objectives in a curriculum designed…

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…

The central and peripheral visual fields are structurally segregated in the brain and are differentiated by their anatomical and functional characteristics. While the central field appears well suited for tasks such as visual search, the periphery is optimized for rapid processing over broad regions. People vary in their abilities to make use of…