The objective of this case study was to identify the role of finger gestures in learning mathematics informally during play, especially in sociocultural settings. A mathematical activity involving addition was qualitatively analyzed at a Japanese preschool. We explored how the process of subjectification and objectification contributed to a…

Girls are less likely than boys to pursue a degree or career in a mathematics-based field. Girls tend to have higher grades and similar test scores when compared with boys. However, girls' affective beliefs, including confidence, fall behind those of their male counterparts. The purpose of this study was to understand how girls perceive the…

Working with language-independent logic structures can help students develop both inductive and deductive reasoning skills. The Japanese publisher Nikoli (with resources available both in print and online) produces a treasure trove of language-independent logic puzzles. The Nikoli print resources are mostly in Japanese, creating the extra…

This article encourages approaches that develop children's understandings of data representations. In particular, when children develope flexibility in their approaches to data representation and understanding, the same data can be represented in different ways. Flexible and adaptive use of representations is part of mathematics competence which…

This article describes the authors' three-component instructional sequence--a before-class activity, a during-class activity, and an after-class activity--which supports students in becoming self-regulated proof learners by actively developing class-based criteria for proof. All four authors implemented this sequence in their classrooms, and the…

Educational games provide a fun introduction to new material and a review of mathematical algorithms. Specifically, games can be designed to assist students in developing mathematical skills as an incidental consequence of the game-playing process. The programs presented in this article are adaptations of board games or television shows that…

The change in size from a smaller shape to a larger similar shape (or vice versa) is created through continuous proportional stretching or shrinking in every direction. Students cannot solve similarity tasks simply by iterating or partitioning a composed unit, strategies typically used on numerical proportional tasks. The transition to thinking…

When a child understands number relationships, he or she comprehends the meaning of numbers by developing multiple, flexible ways of representing them. The importance of developing number relationships in the early years has been highlighted because it helps children build a good foundation for developing a more sophisticated understanding of…

A perpetual dilemma of schooling is how to help students develop skills needed for everyday life, including the work world. Quantitative literacy, also called numeracy, involves an ability to apply essential mathematics skills to authentic or near-authentic tasks. Carefully planned classroom activities can help students develop these important…

As the last bell rings, students scurry to their respective classrooms, doors begin to close, and the class period begins. Imagine that you are in the hallway of the school and you look into an advanced mathematics class, into an Algebra I, Part I, mathematics class (a course designed for students who have not found success in mathematics). What…

This article presents and uses the notion of configuration of activity, which extends the Norbert Elias's original concept of social configuration based on the study and analysis of individual and collective activity. Although this concept embraces all types of social activities, in the present study the authors used it to describe and analyse…

This article presents an educational exercise in which statistical process control charts are constructed and used to identify the Steroids Era in American professional baseball. During this period (roughly 1993 until the present), numerous baseball players were alleged or proven to have used banned, performance-enhancing drugs. Also observed…

Since the dawn of civilization, pictorial representations and symbols have been used to communicate simple statistics. Efficient and effective, they are still used today in the form of pictures and graphs to record and present data. Who can tie their shoes? How many calories are in your favorite food? Make data and graphs relevant and interesting…

This article describes the extension of a simple activity into an exploration of multiple NCTM (National Council of Teachers of Mathematics) Standards. It includes the solution process undertaken by a combination fifth-sixth-grade class. In teaching students to attain Standards, all classroom activities should purposefully address one or more…

Use of spreadsheets in a beginning algebra course was investigated mainly with regard to their potential to promote generalization of patterns. Less is known about their use in promoting understanding and learning of transformational activities. The overall purpose of this paper is to consider the conceptual aspects of learning a transformational…