Students need to create mental models for different types of addition and subtraction situations in order to develop a broad and viable understanding of these operations. Although most students succeed when changing or combining sets, situations that demand a quantitative comparison of sets seem considerably more difficult in the first school…

As a key concept in early mathematics curriculum, number sense is crucial for children's learning of other mathematics concepts. An earlier curriculum with a strong focus on number sense development presumably helps children perform better in mathematics later on. Chinese students outperformed their United States (U.S.) peers on number sense at…

California is one of 4 states that have accelerated addition and subtraction basic-facts memorization. This article reports on teacher practices, first-grade achievement of the standard, and a broader conception of basic-facts competence. Even among students from the highest performing schools, fewer than 11% made progress toward the memorization…

To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…

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…