Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

This guide was created as a resource to help families better understand "Measures of Academic Progress"® (MAP®), and their child's results. The guide provides answers to a variety of questions such as: "What is MAP?"; "What does MAP measure?"; "How do schools and teachers use MAP scores?"; "Can MAP tell…

This Framework builds upon the foundation of the 2010 Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework published since 1995. The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in implementing the 2010 standards in their…

The National Assessment of Educational Progress (NAEP) is the only continuing and nationally representative measure of trends in academic achievement of U.S. elementary and secondary school students in various subjects. For more than four decades, NAEP assessments have been conducted periodically in reading, mathematics, science, writing, U.S.…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

"Probability is a difficult concept to teach, because children and adults find it counterintuitive." This is impetus to consider the detailed planning of a set of lessons with a "mixed", in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is…

Using sequences of coin flips as a model of serial independent events, we asked schoolchildren in grades 1 through 5 to estimate the likelihood of the next flip. Most children in each grade expected short patterns to continue.

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…

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…

It is important to use rich problem-solving tasks to develop students' understanding of important mathematical ideas (NCTM 2000). Rich tasks are complex, nonalgorithmic, and nonroutine, requiring reasoning, problem solving, and communication of thinking. Evidence has shown that using rich tasks in student-centered classrooms is especially…

The technical complexities and sheer size of international large-scale assessment (LSA) databases often cause hesitation on the part of the applied researcher interested in analyzing them. Further, inappropriate choice or application of statistical methods is a common problem in applied research using these databases. This article serves as a…

More than 10 percent of the students in our nation's public schools are English language learners, and this number grows each year. Many of these students are falling behind in math. "Supporting English Language Learners in Math Class, Grades 3-5" outlines the challenges ELL students face when learning math and provides a wealth of specific…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

Integrating mathematics across the curriculum offers students the opportunity to link ideas in a natural, impactive way. In this article, the author shares some interactive math activities that she used in a fourth-grade class on "Cinco de Mayo," a holiday honoring Mexican independence. These fun activities not only allowed connections to be made…