In many prekindergarten classes, children begin the day by singing a song as part of their opening routine. In reflecting on opening routines in public prekindergarten classrooms across Michigan, the authors have been struck by how often small changes in teachers' routines or materials could enrich the mathematical engagement of children. The goal…

Kyle, a kindergartner from a low-income family, is shown a set of three black dots on a white mat. His teacher then hides the dots with a small box lid and lays down an additional set of two dots. She pushes the two dots under the cover, one at a time. Kyle must now choose the number of dots "hiding" under the box from a set of four…

Counting all and counting on are distinct counting strategies that can be used to compute such quantities as the total number of objects in two sets (Wright, Martland, and Stafford 2010). Given five objects and three more objects, for example, children who use counting all to determine quantity will count both collections; that is, they count…

Math games can be powerful tools in helping students achieve automaticity in basic addition and related subtraction facts if both teachers and students use them purposefully. According to the National Council of Teachers of Mathematics (NCTM 2000), developing a solid mathematical foundation is essential for every child in prekindergarten through…

Connecting mathematical thinking to the natural world can be as simple as looking up to the sky. Volunteer bird watchers around the world help scientists gather data about bird populations. Counting flying birds might inspire new estimation methods, such as counting the number of birds per unit of time and then timing the whole flock's flight. In…

Elementary school teachers are responsible for constructing the foundation of number sense in youngsters, and so it is recommended that teacher-training programs include an emphasis on number sense to ensure the development of dynamic, productive computation and estimation skills in students. To better prepare preservice elementary school teachers…

Since 2001, the authors have been working with groups of teachers to investigate students' early algebraic thinking--learning representations, connections, and generalizations in the elementary school grades. They began paying attention to students' explicit remarks about regularities in the number system or what students imply by their…

This reprint from the June 1912 issue of "Mathematics Teacher" gives readers a sense of the timelessness of some of the issues relating to teaching for computational fluency.

This article describes one teacher's journey to improve her teaching of mathematics by conducting classroom-based inquiry to meet the specific mathematical needs in her second grade classroom. Her process to develop and improve computational fluency through research-based methods is detailed. (Contains 9 figures.)

Diezmann presents a series of classroom number-sense activities that encourage young students to use and refine their estimation, prediction, and observation skills. The activities explore the relationships between the number of objects in an opaque container and (1) its fullness and (2) the size of the objects in the container. Informal,…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article explores how counting collections of objects helps elementary-age children develop number sense and number relations. The authors provide evidence that counting collections offers multiple entry points for children at different places on the counting trajectory. It is suggested that the teacher's role is one of noticing, questioning,…

Discusses a content-integration program in which Spanish is introduced while mathematics and other subjects are reinforced, creating a winning combination for students, teachers, and preservice teachers alike. (Author/NB)

Students in the classroom should be provided with engaging activities for improving their computational fluency, making effective use of time, and as a medium of self-motivation. Games such as Contig, the 24 Game, and Number Jumbler are useful for practicing basic facts and computational fluency of mathematics.

This article challenges the traditional model for teaching computation in the primary grades. It describes a model in which students are encouraged to invent and use alternative computation procedures.