In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems…

Recent intervention research has demonstrated success in raising the achievement level of students who are struggling with mathematics. This practice guide, developed by the What Works Clearinghouse™ (WWC) in conjunction with an expert panel, distills this contemporary mathematics intervention research into six easily comprehensible and practical…

Recognizing and using mathematical structure are key components of mathematical reasoning. The authors believe that one productive way to support students' use of structure is by identifying opportunities to address structure in the context of what teachers are already doing, rather than developing additional tasks or new curriculum materials. The…

This article reports on a study in which researchers asked children to "make up as story and a picture about marbles for this number sentence: 3 x 5 = 15." Students in this study came from pre - dominantly low- to average-income families living in three distinct geographical areas within the United States. A similar division task was…

As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

The purpose of this article is to examine one possible extension of greatest common divisor (or highest common factor) from elementary number properties. The article may be of interest to teachers and students of the "Australian Curriculum: Mathematics," beginning with Years 7 and 8, as described in the content descriptions for Number…

This article presents a number of carefully selected activities for the mathematics classroom in the early grades. The motivation for their selection is the development of concepts rather than the learning of the procedural skills of arithmetic. As the teacher is faced with a great heterogeneity of children starting school, the concrete learning…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

Interactive whiteboards are somewhat unimpressive at first and look like the whiteboards that already hang on the walls of many classrooms. However, integrating interactive whiteboard technology in a unit on adding and subtracting integers enhances student engagement and understanding. In this article, the author describes how she used an…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

The number Pi (approximately 3.14159) is defined to be the ratio C/d of the circumference (C) to the diameter (d) of any given circle. In particular, Pi measures the circumference of a circle of diameter d = 1. Historically, the Greek mathematician Archimedes found good approximations for Pi by inscribing and circumscribing many-sided polygons…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained in decades of mathematics teaching and research,…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Sandards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained in decades of mathematics teaching and research,…