Common Core State Standards for Mathematics (CCSSM) is different from the objectives that many teachers have previously experienced in their state frameworks. Although the mathematical topics of the two may be the same, the mathematical expectations within the Standards require a deeper understanding by teachers and students. In this article, the…

Exploring number systems of other cultures can be an enjoyable learning experience that enriches students' knowledge of numbers and number systems in important ways. It helps students deepen mental computation fluency, knowledge of place value, and equivalent representations for numbers. This article describes how the author designed her…

Quilt investigations, such as the Barn quilt problem in the December 2008/January 2009 issue of "Teaching Children Mathematics" and its solutions in last month's issue, can spark interdisciplinary pursuits for teachers and exciting connections for the full range of elementary school students. This month, North Dakota's centennial quilt…

"Classroom number talks," five- to fifteen-minute conversations around purposefully crafted computation problems, are a productive tool that can be incorporated into classroom instruction to combine the essential processes and habits of mind of doing math. During number talks, students are asked to communicate their thinking when presenting and…

Rigor is an important concept both in and out of school. To many teachers and teacher educators, rigor includes using national and state standards to inform curriculum; using best practices to guide instruction; testing and evaluating students to assess learning; and maintaining fidelity to academic disciplines. In this article, the authors…

In this article, the author shares how his fourth-grade students' creative thinking concerning a long-standing research problem stimulated changes in his instructional strategies. He begins by providing an example which illustrates that the standard tool of democracy, the plurality vote, suffers serious deficiencies: "The winner can be the…

A team of authors, including a fourth-grade teacher and his professor from a local graduate school, describe culminating elementary lessons with an index card recap and peer review. In an urban district that traditionally struggles with standardized testing, this activity prompts students to summarize and communicate the day's lesson and key ideas…

Problem solving, introduced in every grade and practiced throughout elementary school, is an essential foundation on which students build their understanding of mathematical ideas, operations, and relationships. This article discusses 1-2-3 Time, an instructional mode that promotes multimodal math learning in ways that engage and sustain students'…

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…

Teachers' professional identities are associated with an ongoing commitment to professional development and the explicit aim of improving practice in order to increase student learning. During the last century, professional development initiatives took many forms, including laboratory schools, lesson study, video clubs, and demonstration…

This article examines important geometric concepts embedded in the shape and design of natural and manufactured objects. The Whitins first describe fourth graders exploring why manhole covers are circles. Then the authors offer a range of activities to demonstrate how inquiring about shape in botany, geology, biology, and industry can effectively…

This article describes how teachers can use students' conversations to assess their mathematical understanding. The authors draw on their own classroom experiences to show what they learned about planning for future lessons based on discussions in their own classrooms.

This article describes how a survey designed to assess attitudes and dispositions about mathematics informed curricular decision making in a fourth-grade setting. (Contains 7 figures.)

This article describes how to incorporate problem-solving investigations in a fourth-grade classroom within a structured and rigid mathematics program.

This article reports on a sample of fourth graders' responses to the 2003 NAEP exam. Readers are invited to analyze the responses to assess students' concepts of fractions.