Introduction: In this paper, we present how seventh-grade students become aware of rational numbers during mathematics instruction through the social process of objectification when comparing two magnitudes. Methods: Theoretical elements of the Theory of Objectification and the Onto-Semiotic Approach to Mathematical Instruction and Cognition guide…

This article investigates the interplay of time words with how children position hands on an analog clock. Using a mathematics discourse framework (Sfard, 2008), we analyzed how students interpreted precise (e.g., 2:30) and relative (e.g., half past 11) times, finding that particular words are dynamically interwoven with activity. Interviews with…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…

"Fraction Face-Off!" is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to…

Mathematical and didactic knowledge presented in mathematics textbooks and other resources, like mathematics comics (MCs), needs to be evaluated from a lens of appropriate theoretical framework in mathematics education before it can be used as a medium for teaching and learning mathematics. Therefore, this study investigates mathematical and…

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…

Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create…

The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

Math outcomes for students with disabilities, in particular students with emotional disturbance (ED), are bleak, warranting intervention strategies that have research to support their utility. The purpose of this meta-analysis was to examine the literature of math interventions used with students with ED to improve math outcome variables. Our…

In this article, Derek Hurrell, points out that while it's easy to fall into the impression that the proficiency strand "Fluency" is all about knowing basic number facts in all its many and splendid ways. He add it is easy to overlook, that within Fluency there are requirements that are based in Algebra; Measurement and Geometry; and…

This compendium organizes information on the math and science projects sponsored by NCER and NCSER into two main sections: Mathematics and Science. Within each section, projects are sorted into chapters based on content area, grade level, and intended outcome. In determining the chapters, we considered the emerging college- and career-readiness…

The third of four quins intended to develop computational skills with non-negative rational numbers through applications to business and industry, this guidebook on minimum course content is designed for the student who has acquired basic computational skills with non-negative rational numbers. Topics include measurement and geometrical…

Measurement experiences can promote and illustrate number work in an intuitively satisfying way. Some current practices that are counterproductive for developing number sense and some alternative strategies that are more constructive are included in discussions of the approximate nature of measurement, realistic measurement, and work with rational…