A first-grade teacher has students use their hands and fingers to engage in and develop understanding of counting, to combine groups to facilitate counting by fives and tens, and to describe their findings using words and equations.

As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

Learning through meaningful problem solving is integral in any successful mathematics program (Carpenter et al. 1999). The National Council of Teachers of Mathematics (NCTM) promotes the use of problem solving as a means to deepen understanding of all content areas within mathematics (NCTM 2000). This article describes a first-grade lesson that…

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…

A two-year project was conducted, mainly with two goals, to make the students fluent in addition and subtraction and to have the students develop an understanding of computation that was strong enough to solve more than routine problems. The most common method for teaching children computation is teaching the standard procedures and then giving…