Mathematical inquiry involving hands-on activities has received increasing attention in mathematics education. Besides various customized physical teaching aids, subject-specific information technology, such as Dynamic Geometry System (DGS), finds extensive use in mathematical inquiry activities. However, effects of DGS and physical manipulatives…

Providing all students with equitable treatment and access has been a cornerstone of mathematics education reform (Association of Mathematics Teacher Educators, 2015; National Council of Teachers of Mathematics, 2014). Studies in mathematics classrooms show that using hands-on and interactive materials (i.e., "manipulatives") support…

This timely book provides support for secondary mathematics teachers learning how to enact high-quality, equitable math instruction with dynamic, mathematics-specific technologies. Using practical advice from their own work as well as from interviews with 23 exceptional technology-using math teachers, the authors develop a vision of teaching with…

This study was an investigation of the use of manipulative materials in the mathematics classroom. The researcher guided students to create paper triangles, which were then used as a manipulative to calculate the sum of the interior angles of a triangle. On pre- and post-measures of quantitative data, although the data indicated a positive…

Eliciting and using student thinking (NCTM 2014) is a foundational pedagogical skill that informs the decisions teachers make during instruction. It informs the questions teachers pose, the focus of small-group and whole-class discussions, and even the small adjustments teachers make during a well-planned lesson. To use student thinking to…

Although teachers are expected to teach with technology, they often are not prepared or supported to do so (Albion, Tondeur, Forkosh-Baruch, & Peeraer, 2015), a critical issue in mathematics education (Wilson, 2008). The study described in this article investigated why and how secondary mathematics teachers implemented virtual manipulative…

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…

The goal of this design-based research study was the creation and evaluation of a mini-unit intended to foster perceptually grounded understandings of the concept of slope in middle-school students. Central to this unit was an innovative device designed to create a productive pedagogical space between student intuition for steepness and formal…

Students' attitudes and motivations toward mathematics decrease as they intensively confront cognitive information along the process of mathematics teaching in general. One of the most important reasons for this is the lack of activities for affective and psychomotor domains in the mathematics teaching process. One way to overcome this problem is…

Perceptually rich concrete manipulatives benefit mathematics learning. Because students should be challenged to consider connections between two-dimensional (2D) and three-dimensional (3D) perspectives of conics (NCTM 2000), this article describes hands-on teaching techniques that promote this type of student reasoning. This article aims to (1)…

We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…

Introduction: Knowing how to gather information from graphics and to use that information to solve mathematics problems is an important skill. Prior research indicates that many students with visual impairments face considerable challenges when attempting to locate information in math graphics. Little is known about how teachers of students with…

Mathematics instruction for students with intellectual disabilities and autism is important. However, it is imperative for researchers and practitioners to focus on the maintenance of mathematical concepts and not just acquisition for these students. Through a single-case multiple probe across participants study, researchers explored an…

Over the last two decades, the significance of academic achievement for students with disabilities in K-12 education has increased. To meet the needs of this population, educators turned to innovative strategies and technologies for instructional support in the classroom. For students with a learning disability, the need for such solutions is…