High-leverage practices are essential components of specially designed instruction required by the Individuals with Disabilities Education Improvement Act. High-leverage practices such as explicit instruction and use of instructional and assistive technology have research evidence demonstrating their effectiveness when teaching students with…

Background: The study on which this article is based investigated the Mathematics Knowledge for Teaching (MKfT) that a well experienced Grade 2 teacher utilized when teaching counting. Aim: In this paper we share excerpts from one of the lessons of this Grade 2 teacher, which we analyzed to illuminate the various domains of MKfT and their…

Students in the United States continue to struggle with fraction mastery despite the fact that understanding fractions is essential for further progress in mathematics (NAEP, 2008). This research project investigated the potential of using high-press mathematical discourse (Kazemi & Stipek, 2008) to investigate fourth graders' emerging…

What would the curriculum look like if it were developed from the perspective of measuring? Without formal tools, the Yup'ik Eskimos of Alaska used their body as a measuring device and employed ratios extensively in their daily practices. "Math in a Cultural Context" is developing curriculum materials based on Yup'ik Elders use of…

This paper describes the development and intended uses of the Early Grades Mathematics Assessment (EGMA), which measures essential early mathematical knowledge and skills that are foundational to more sophisticated mathematical abilities, predictive of later achievement, and teachable. Administering the EGMA can provide policy makers,…

Asian children, including Chinese children, perform better than their English-speaking peers in cross-national mathematics studies. This superior Asian performance is attributed to several factors including cultural beliefs, educational systems and practices, and the Chinese number naming system. Given the limited empirical evidence on pre-school…

Given the vital importance of using a scientific approach for curriculum development, the authors employed a design experiment methodology (Brown, 1992; Shavelson et al., 2003) to develop and evaluate, FUSION, a first grade mathematics intervention intended for students with or at-risk for mathematics disabilities. FUSION, funded through IES…

How this teacher develops composition of ten with second graders was dramatically reshaped by the 2006 release of NCTM's "Curriculum Focal Points." The release of "Curriculum Focal Points"--particularly the suggestion that number sense and computation be focal areas in the second-grade mathematics curriculum--resulted in positive changes in this…

The results of the cognitive research on numbers' representations can provide a sound theoretical framework to develop educational activities on representing numbers. A program of such activities for a nursery school was designed in order to enable the children to externalize and strengthen their internal representations about numerosity and link…

This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…

"Focus in Grade 1: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 1 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate…

A study investigating the linguistic structure of Oneida and Lakota number systems found that base-10 numeracy is communicated more explicitly in these languages than in English. Further research is needed to determine whether teaching Oneida and Lakota students in their Native languages would help them to develop better number sense. A sample…

This study describes a teacher preparation program in mathematics and science and explores what impact the reformed curricula and teaching methods instituted in the program have on prospective teachers' understanding of rational numbers and integers. The study pursues obtaining in-depth insights regarding prospective teachers' concept development.…

Learning about mathematics begins in the early years. Through their everyday activities, young children build important foundational knowledge and understanding of mathematics, especially when adults provide specific opportunities to learn and practice concepts and skills. Young children develop early on an informal understanding of important…

This guide represents the final experimental version of an extended pilot project which was conducted in the United States between 1973 and 1976. The manner of presentation and pedagogical ideas and tools are based on the works of Georges and Frederique Papy. They are recognized as having introduced colored arrow drawings ("papygrams")…