Stephen Tucker presents a fractions game that addresses a range of fraction concepts including equivalence and computation. The REFractions game also improves students' fluency with representing, comparing and adding fractions.

Stephen Norton, Do Thi Phurong Thao and Mai The Duy provide an interesting insight into the teaching of fraction division in Vietnam. The article highlights one of the many teaching strategies available to teachers for building fraction concepts.

Similarity is a fundamental concept in the middle grades. In this study, we applied Vergnaud's theory of conceptual fields to answer the following questions: What concepts-in-action and theorems-in-action about similarity surfaced when students worked in a novel task that required them to enlarge a puzzle piece? How did students use geometric…

One of the most common household polyhedra is a cereal box. For over 100 years, American companies like Kellogg's™ have packaged cereal in containers shaped like rectangular prisms. Why is a rectangular prism the most commonly used solid for holding cereal? Would another design work equally or more efficient? This article describes an…

Ratio, rate, and proportion are central ideas in the Common Core State Standards (CCSS) for middle-grades mathematics (CCSSI 2010). These ideas closely connect to themes in earlier grades (pattern building, multiplicative reasoning, rational number concepts) and are the foundation for understanding linear functions as well as many high school…

The branch of biology that studies ecosystems, habitats, their developments, and the equilibrium of species is called conservation biology (Soule 1986). It is important to study this balance of species within an ecosystem, where species might live for a short period of time (such as mosquitoes, the main source of food for frogs) or live for…

This project highlights preschool teachers' views of toddlers' learning in mathematics. The Swedish national curriculum covers even the youngest children who are 1-3?years old. Interesting questions are thus: what should mathematics be for this age group and how should preschool teachers work with maths to achieve the curriculum objectives? Data…

In this article, authors Jordan T. Hede and Jonathan D. Bostic present a classroom activity that challenges upper elementary students' understanding of area beyond a memorized formula and explores the meaning behind students using A = l × w to solve rectangular area problems. This activity will deepen students' understanding of the area…

This article is a discussion drawing on a learning study with a teacher working with one- and two-year-olds. The focal interest is a scrutiny of the use of manipulative objects, emanating from observations of a teacher's and children's use of, and responses to the use of, different objects. The concept of size and the notions "large" and…

This article investigates some of the specific features involved in accommodating the idea of actual infinity as it appears in set theory. It focuses on the conceptions of two individuals with sophisticated mathematics background, as manifested in their engagement with variations of a well-known paradox: the ping-pong ball conundrum. The APOS…

This research analyses preservice teachers' knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed…

This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…

We analyze a classroom design experiment, conducted in a fourth grade classroom, that served to explore an instructional path in which the introduction of unit fractions and supporting proportional reasoning coincide. Central to this path is the use of means of support in which the objects that unit fractions quantify are not characterized as…

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

Students with mathematics learning disabilities have a weak understanding of mathematical concepts that underlie success in Algebra I, such as ratios and proportional reasoning. In this study, researchers used a multiple baseline across participants design to evaluate the effects of a intervention based on a instructional trajectory of how…