Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is students' tendency to apply the properties of natural numbers (inappropriately) when they are working with rational numbers (a phenomenon called "natural number bias"). Focusing on rational…

I examined the impact of a self-diagnosis activity on students' conceptual understanding and achievements in physics. This activity requires students to self-diagnose their solutions to problems that they have solved on their own--namely, to identify and explain their errors--and self-score them--that is, assign scores to their solutions--aided by…

Background: The ability to generate and flexibly change concepts is of great importance for the development of academic and adaptive skills. This paper analyses the conceptual reasoning ability of children with mild intellectual disability (MID) by their achievements on the Wisconsin Card Sorting Test (WCST). Method: The sample consisted of 95…

Although many students struggle with fractions, students with mathematical learning disabilities (MLDs) experience pervasive difficulties because of neurological differences in how they process numerical information. These students make errors that are qualitatively different than their typically achieving and low-achieving peers. This study…

The reports of research in this monograph reflect 18 years of observation of the behaviors of children learning to read in New Zealand schools. The first section of the monograph urges teachers to look more closely at language behaviors in their classrooms to see how children go about the tasks set before them. The second section reports on…