The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

In theory, both virtual manipulatives and explicit instruction are viable options to support students with disabilities as they learn mathematics. This study explored the effect of a treatment package--an app-based virtual manipulative (Cuisenaire® Rods) in conjunction with explicit instruction--on students' acquisition and generalization of…

This paper examines the process of instrumental genesis through which students develop their proficiency in making use of movable points and slider bars--two tools that dynamic mathematics software provides for working with variable coordinates and parameters in the field of functions. The paper analyses students' responses to task sequences…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem-solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

A fundamental component of mathematical learning is spatial visualization. To improve their spatial visualization skills, students should be given opportunities to work with two- and three-dimensional objects. The authors describe two activities that use tetrahedra nested within cubes to help improve students' visualization of two- and…

This research aims to explore the role of physical representations in young children's numerical learning then identify the benefits of using a graphical interface in order to understand the potential for developing interactive technologies in this domain. Three studies are reported that examined the effect of using physical representations…

The chapters in this book were written by teachers to share strategies they have found effective in the mathematics classroom. Most describe a teaching idea or activity in sufficient detail for other teachers in elementary, middle, and secondary schools to be able to use it. The chapters concern: manipulative materials, developing a mathematics…