We discuss an emerging program of research on a particular aspect of mathematics learning, students' learning through their own mathematical activity as they engage in particular mathematical tasks. Prior research in mathematics education has characterized learning trajectories of students by specifying a series of conceptual steps through which…

Toys in the classroom was the result of a National Science Foundation grant that brought two engineering graduate students to a middle school math class. The graduate students and teachers collaborated in an effort to enhance students' mathematical learning. An engineering context was theorized as a way to further develop students' understanding…

Communicating and collaborating online are becoming common requirements in education. The specialized notations and symbols necessary for some content areas where mathematical expressions are part of the conversation require that users select appropriate communication tools. The purpose of this article is to describe tools that can be used for…

The binomial distribution is used to predict the winner of the 49th International Shooting Sport Federation World Championship in double trap shooting held in 2006 in Zagreb, Croatia. The outcome of the competition was definitely unexpected.

Recognizing schemes, which are different from strategies, can help teachers understand their students' thinking about fractions. Using Steffe's advanced fraction schemes, the authors describe a progression of development that upper elementary and middle school students might follow in understanding fractions. Each scheme can be viewed as a…

Early math skills are the strongest predictors of later math achievement in school. This two-wave study addressed three research questions about the role of families in fostering these skills in preschool-aged children. First, how do families talk about math at home? Second, how do these conversations vary across families with different…

This paper reports on research from a network of high school and museum partnerships designed to explore techniques for integrating mathematics and physics learning experiences during the first year of high school. The foundation of the curriculum is a problem-based, museum-based, and hands-on approach to mathematics and physics. In this paper, we…

The purpose of this three-paper manuscript dissertation is to add value to the limited knowledge base of research surrounding the quality of teacher-child interactions in pre-k mathematics contexts. The first paper, based on an extensive review of literature, presents a theoretical basis for using five-frames to support children's development of…

This research study, carried out in South Africa and the United States of America, investigated issues that may hamper prospective primary school teachers from writing acceptable problem posing scenarios involving the addition of fractions. Pre-service teachers (n=44) were asked to compose real life problems involving the addition of two fractions…

Manipulatives have been used in many mathematics classrooms across many age groups with the aim of helping students to understand abstract concepts through concrete, kinesthetic, and visual experiences. In this paper, after we provide a background for the use of physical and virtual manipulatives in teaching and learning of mathematics, we will…

Outdoor education has received greater attention in the United Kingdom with the launch of the Learning Outside the Classroom Manifesto. However, teachers' lack of confidence and competence appear to be key factors underpinning the extent of outdoor learning provision in schools. This paper reports on a partnership project in which student teachers…

Engineering technology students can attain a meaningful mathematics learning if they are allowed to actively participate in hands-on activities. However, the current dissemination of knowledge in the classroom still focuses on teacher-centered paradigm of teaching. A study to explore lecturers' views regarding a newly developed integral calculus…

Say that a subset S of the plane is a "circle-center set" if S is not a subset of a line, and whenever we choose three non-collinear points from S, the center of the circle through those three points is also an element of S. A problem appearing on the Macalester College Problem of the Week website stated that a finite set of points in the plane,…

This article seeks to provide an insight into little known numerical methods for deriving meaning from ancient sacred texts to give an understanding of some of the symbolism contained in the wonderful artwork and sculptures of Venetian artist Tobia Rava. The author describes how he used Rava's artwork to inspire a multi-faceted mathematics…

Middle grades are a critical time for capturing the interest and imagination and developing the potential of mathematically promising students. This is a time for students to make sense of mathematics, build a solid foundation and enthusiasm, and set the course for the highest levels of mathematics in the future. This is a time to explore their…