The development of conceptual multiplication knowledge will assist students in making progress within current mathematics standards. Previous research has shown the concrete-representational-abstract (CRA) sequence to be successful in teaching multiplication with regrouping with an emphasis on conceptual understanding while developing fluency and…

"Patterning" is a cognitive intervention that is unknown to psychologists, but has nevertheless been taught for half a century in nearly all kindergartens and many preschools in English-speaking countries. Patterning is the understanding that a certain rule governs the sequence of items in a series. At the simplest level, if the series…

Open-ended learning environments (OELEs) allow students to freely interact with the content and to discover important principles and concepts of the learning domain on their own. However, only some students possess the necessary skills for efficient and effective exploration. Guidance in the form of targeted interventions or feedback therefore has…

Mathematics instruction -- and interventions to support mathematics teaching -- for students with intellectual disability is important yet underexamined. This study explored a graduated instructional sequence referred to as the virtual-representational (VR) as a mathematical intervention. Researchers taught four students with disabilities what…

Children who struggle in mathematics have a limited understanding of the foundational processes of mathematics. A lack of conceptual understanding causes students to fall behind as they progress through the core curriculum. Children at high risk for developing mathematics disabilities fail to gain numeracy knowledge. The purpose of this case study…

The New York State Education Department, in partnership with the New York City Department of Education, developed a "Striving Readers project" to address the literacy needs of early adolescent struggling readers in middle school. The goal of the project was to implement and examine the impact of a one-year comprehensive supplemental…

This article presents a story of James, an elementary student who was recently mainstreamed into a regular education classroom for science and now struggles to succeed in his new environment. It also describes how the New Tools reclaiming intervention puts him on the right track to making new friends. James is a ten-year-old African American…