This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' 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…

Background: The concept of rational numbers is one of the learner's first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct. Aim: This study…

Fractions are troublesome for many children, especially students with learning difficulties and disabilities in mathematics. To address this serious educational concern, this article recommends the use of number lines to build fraction sense. Math activities that center on the number line build fraction concepts as early as third grade. A number…

The goal of this study was to describe fraction-calculation errors among fourth-grade students and to determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low-, average-, or high-achieving). We…

The goal of the present study was to describe fraction-calculation errors among 4th-grade students and determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low- vs. average- vs. high-achieving). We…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…

The data used for the qualitative analysis reported here were generated as part of a larger study to understand and characterize teacher practice related to engaging students in algorithmic thinking associated with the fraction operations of addition, subtraction, multiplication and division. This paper presents ways in which teachers used…

Research Ideas for the Classroom is a three-volume series of research interpretations for early childhood, middle grades, and high school mathematics classrooms. Each volume looks at research from the perspective of the learner, the content, and the teacher, and chapters are co-authored by a researcher and a teacher. Chapter titles in the early…

Provides a bibliography of children's literature exploring mathematical concepts: classification; place value and numeration systems; counting, addition, and subtraction; multiplication and division; fractions; estimation; big numbers; geometry; measurement; and games and puzzles. Highlights one book for each concept, suggests class activities,…

The teacher's guide for unit four of a Spanish science/math strand for second graders contains instructional and assessment activities for kits 13-16. Each designed for a two- to three-week teaching period, the kits' activities are geared toward guiding the child to discover correct answers through methods provided and, by putting materials in his…

Built around a theme of communities in the nation, this teacher's guide for unit eight of a science/math strand for Spanish-speaking children in grade three contains both learning and assessment activities. This unit addresses what the elements are, how needs and wants are satisfied, how change occurs, and what the results of change are. The guide…