Informal strategies reflecting the representation of a situation described in an arithmetic word problem mediate students' solving processes. When the informal strategies are inefficient, teaching students to make way for more efficient ways to find the solution is an important educational issue in mathematics. The current paper presents a…

Six widely used US Grade 1 curricula do not adequately address the following three developmental prerequisites identified by a proposed learning trajectory for the meaningful learning of the subtraction-as-addition strategy (e.g., for 13-8 think "what + 8 = 13?"): (a) reverse operations (adding 8 is undone by subtracting 8); (b) common…

During the author's everyday math discussions with her class, young children talk about mathematical ideas, theories, and concepts within a predictable structure. These discussions include many concepts from--and beyond--the first-grade math curriculum, and their depth and complexity build throughout the school year. Concepts and skills include…

Rather than feeling overwhelmed at the thought of integrating the new Common Core State Standards for Mathematics (CCSSI 2010) into their teaching practice, teachers might view this as an opportunity to deeply embed mathematics into the K-grade 2 curriculum in the same way that literacy has long been rooted into early learning environments.…

This article showcases the benefits of the alliance the authors have established during the past two years with the Barnes Foundation to add more mathematics activities to their repertoire and to integrate more art into their mathematics lessons. Recently, they decided to focus on activities at the K-grade 2 level that could be used as an on-site…

"Focus in Grade 2: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 2 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…

The first goal of this Project is the development of elementary school mathematics curricula sensitive to indigenous mathematical thought and experience. A necessary prerequisite for the achievement of this goal is to recapture and honor the mathematics developed and practiced in the Micronesian communities. This is the Project's second goal. The…

This article reports that two programs for teaching mathematics in the early grades--Math Expressions and Saxon Math--emerged as winners in early findings released last week from a large-scale federal experiment that pits four popular, and philosophically distinct, math curricula against one another. But the results don't promise to end the…

This article describes one teacher's efforts at creating a differentiated mathematics program in her multi-age first- and second-grade classroom. The author describes challenges encountered and successes met in this process, as well as the structures she uses to meet a variety of student abilities, including open-ended problem-solving tasks,…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

In this Appendix, we provide details about the data used for the current study, the curricula used in the classrooms from which data were collected, and the current study's methodological approach. (Contains 14 tables and 5 footnotes.)[For full report, see ED544189.]

"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…

Responsiveness to intervention (RTI) is an innovative approach to the identification of learning disabilities (LD). The central assumption is that RTI can differentiate between two explanations for low achievement: poor instruction versus disability. If the child responds poorly to validated instruction, then the assessment eliminates…

This article describes Everyday Mathematics, a new math education curriculum targeted to kindergarten, first grade, and second grade students in Holland. It will be introduced to third and fourth grades in 2008. The curriculum helps prepare pupils for standardized tests; allows for students to work at their own rate; involves parents in helping…

Cross-cultural studies on mathematical cognition and education have suggested that curriculum and teaching have contributed to U.S. versus Asian differences in student performance; however, previous discussions of curriculum and teaching practices have been very general and have not focused on a detailed analysis of how mathematics concepts are…