When the focus of instruction is on learning to use mathematical tools--such as a ruler or a calculator--as a procedure, students tend not to incorporate their own mathematical reasoning. This unreflective use of tools hinders students' questioning of the reasonableness of their answers. This article describes how children expressed their…

Tape diagrams, also known as strip diagrams, bar models, fraction strips, or length models, are linear representations that can be used to effectively model quantitative relationships during problem solving. Tape diagrams are a powerful model recommended by the Common Core, but they are relatively new to teachers and students in the United States.…

This article describes how a teacher in Mexico City worked with two researchers on an instructional design project to help kindergartners become proficient in participating in whole-class mathematical conversations.

In Australia, the term "numeracy" is used to describe "the competence and disposition to use mathematics to meet the general demands of life at home, in paid work, and for participation in community and civic life" (Australian Association of Mathematics Teachers 1997, p. 15). The implemented mathematics curriculum is…

This article describes a series of two linear measurement activities designed to integrate the related content and processes of Common Core State Standards for Mathematics (CCSSM) into classroom practice using nonstandard units. In the article, nonstandard units refer to same-size, repeatable units (e.g., paper clips, feet) for a specified…

In this article, the authors begin with a description of an algebraic dance--the translation of composite linear growing patterns into choreographed movement--which was the last component of a research-based instructional unit that focused on fostering an understanding of linear functional rules through geometric growing patterns and…

The concrete, pictorial, and abstract methods of this lesson give students access to investigate, isolate, define, and use prime numbers. In this article, the authors describe an enrichment lesson that offers opportunities to investigate prime numbers in concrete, pictorial, and abstract ways. Originally introduced by Jerome Bruner in 1960, the…

Quite a bit of the arithmetic in elementary school contains elements of algebraic reasoning. After researching and testing a number of instructional strategies with Irish third graders, these authors found effective methods for cultivating a relational concept of equality in third-grade students. Understanding equality is fundamental to algebraic…

Parents as Literacy Supporters (PALS) is an interactive, culturally responsive, family literacy program that brings parents of kindergartners into the classroom as partners in their children's education. Co-developed by Jim Anderson of the University of British Columbia and Fiona Morrison, Director of Family Literacy and Early Learning at 2010…

The topic of fractions is an important concept in elementary school mathematics. The study of fractions not only enables students to perform computations but also provides a foundation for later work with rates, percents, slope, and other topics in secondary school mathematics. However, research has long reported that many students and even adults…

It is easy to fall into the trap of thinking that teaching mathematics should greatly differ from teaching language arts. Classroom teachers at Munich International School in Starnberg, Bavaria, Germany, did not pay much attention to what language means to learning and teaching mathematics--until their geometry students offered language surprises…

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 depicts the rewarding experience of creating mathematical environments for kindergarten and elementary students by focusing on one of the most important and often difficult-to-grasp concepts (fractions) through play methods incorporated into a math fair. The basic concept of a math fair is threefold: (1) to create preplanned,…

Mathematics consultants from the United States provide ongoing professional development founded on the National Council of Teachers of Mathematics' Principles and Standards for School Mathematics (2000). Consultants provide teachers with sustained, hands-on opportunities to expand their abilities to teach mathematics more effectively. Readers will…

Describes a typical fifth-grade mathematics lesson as taught in a Japanese elementary school, followed by a reflective commentary focused on problem solving, using manipulative aids, and multiple solutions. (ASK)