How can teachers engage students in learning essential mathematics? The National Council of Teachers of Mathematics recommends using "contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations" (NCTM 2006, p. 11). Understanding the Process Standards (NCTM 2000) enables teachers…

When the author asked her preservice elementary teachers what "order of operations" is and why it is important for children to learn, they recited "PEMDAS" or "Please Excuse My Dear Aunt Sally" but typically became silent when questioned about the importance of the order of operations. Reys and Fennell once suggested that the mathematics component…

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…

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…

In the move from elementary to middle school mathematics, students encounter major changes in instructional materials and approaches, work expectations, school structure, and general level of difficulty in material. Research shows that, in general, students suffer significant declines in academic achievement in the transition from elementary…

Analyzing student work can help teachers improve the teaching and learning of mathematics. Fortunately, the four authors have experienced professional development that supports teachers' professional growth and provides tools to begin the challenge of analyzing student work. However, as they began to assume leadership roles in their schools and…

Instructional settings are developed for conceptual understanding of measurement for the fourth-grade students to engage limited English proficient (LEP) students in effectively communicating about mathematics. When naturally enticed to compare solutions, the students were motivated to explain their mathematical thinking and understand the…

This article discusses the use of a problem-based instructional task in an elementary classroom. After estimating the number of blades of grass on a football field, students write letters to explain the results of their research.

This article describes ways in which technology-supported mathematical investigation can engage students with substantive mathematics. It focuses particularly on the ways in which the NCTM Process and Content Standards for the elementary grades can be supported by the use of interactive software such as The Geometer's Sketchpad. (Contains 6…

A Professional Development Schools partnership between the University of Maryland and other elementary schools in the district worked together to explore, discuss and reflect on the challenges of helping students to write about mathematics. Finding ways to help students effectively communicate their mathematical thinking is a challenge for…

Children begin to develop mathematical thinking before they enter school. Art, baking, playing with blocks, counting numbers, games, puzzles, singing, playing with pretend money, water play all these early mathematical experiences help the children to learn in the elementary school years.

Explains how to use the Chinese numeration system to enhance student understanding of place value. Includes sample activities. (Author/NB)

Discusses ways in which teachers can use the appealing study of quilts as a tool for teaching mathematics concepts and connecting multicultural history, literacy, and art. (Author/NB)

Presents the Perfect-Square Geometry Partners problem to teach students about patterns. (Author/NB)

Five primary-grade students identified as learning-disabled benefited from instruction that focused on making sense of mathematics word problems. Examples of student work demonstrate the students' ability to solve a variety of problem types and justify their solutions. (Author/NB)