Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems…

The purpose of this article is to provide strategies for recognizing meaningful mathematics in common play contexts in early childhood classrooms and to offer suggestions for how teachers might intervene in these moments to help children attend to the mathematical ideas embedded in their play. In particular, the author's focus on the concepts…

In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

This article describes how in early mathematics learning, young children are often asked to recognize and describe visual patterns in their environment--perhaps on their clothing, a toy, or the carpet; around a picture frame; or in the playground equipment. Exploring patterns in the early years is seen as an important introduction to algebraic…

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…

Tasks that develop spatial and algebraic reasoning are crucial for learning and applying advanced mathematical ideas. In this article, the authors describe how two early childhood teachers used stories as the basis for a unit that supports spatial reasoning in kindergartners and first graders. Having mathematical experiences that go beyond…

Kolby is a four-year-old, identified on the autism spectrum as having sensitivity issues, attention challenges, and limited verbal language abilities. Next to Kolby sits Melanie, a reserved four-year-old with visual, fine-motor, and gross-motor challenges. Amy rounds out the group as one of the peer models in the inclusive classroom setting. Mrs.…

The widely adopted Common Core State Standards for Mathematics (CCSSM) are designed to deepen instruction of number sense and will demand that elementary school teachers have a strong understanding of number. These changes arrive at a time when it is still understood that teachers and the curriculum in the United States have not been fundamentally…

Measurement is a difficult concept for many children. Trend data from the National Association of Educational Progress (NAEP) indicate that student achievement with measurement is disappointing, given the amount of instructional time it receives in K-grade 5. In an attempt to address the problem of student achievement with measurement, the authors…

When a child understands number relationships, he or she comprehends the meaning of numbers by developing multiple, flexible ways of representing them. The importance of developing number relationships in the early years has been highlighted because it helps children build a good foundation for developing a more sophisticated understanding of…

Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages…

A child's demonstration of his conceptual understanding of number bodes well for his future success in school mathematics. As youngsters' thinking becomes more logical, they apply one-to-one correspondence relationships to quantification. Yet, reliable assessment of young children's mathematical ability is difficult because of social and emotional…

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…

The Maine Learning Results (MLR) expects the state's students in prekindergarten through grade 2 to describe two-dimensional shapes as well as use positional language. Requiring translations of two-dimensional shapes supports this expectation. Students in grades 3-4 are expected to "use transformations," while students in grade 5-8 are expected to…

How learning about learning trajectories has helped a teacher develop goals and objectives for her preschool children's mathematical knowledge, identify children's developmental levels in specific mathematical topics, and chart paths for instruction that will guide their learning of mathematics. Participating in research encouraged her to develop…