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…

Providing effective mathematics instruction to learners with disabilities is challenging enough in a classroom. Providing the same level of high quality instruction can be more difficult in an online environment. This article describes an effective use of virtual tools for mathematics that can both engage students and provide the supports they…

The emerging field of mathematics educational neuroscience provides researchers with new approaches to understanding mathematical development, as well mathematics itself. This paper focuses on the role of the hand in constructing mathematics through activity. We rely on Piaget's distinction of three kinds of activity: sensorimotor activity,…

One of the biggest challenges for primary school children is moving beyond the use of counting in calculation. The purpose of this study was to investigate how Zambian Grade 1 to Grade 4 children at primary school see a group of 10 as an effective pattern and structure with the given concrete material. The study consisted of three phases…

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based…

Empirical evidence indicates that students are not learning geometry with relational understanding of the concepts. Studies have shown that digital technologies can support students in mathematics. The purpose of this study was to find which technologies and technological affordances are specific to learners of geometry. This paper presents the…

The purpose of this study was to contribute to the research on mathematics app use by very young children, and specifically mathematics apps for touch-screen mobile devices that contain virtual manipulatives. The study used a convergent parallel mixed methods design, in which quantitative and qualitative data were collected in parallel, analyzed…

Introduction: The study presented here investigated the ways in which students who read braille were able to complete geometric tasks and how they constructed mental representations of the shapes of objects. Methods: Data were collected in an educational experiment conducted as a geometry course for students who read braille. A case study approach…

How do concrete objects that cue real-world knowledge affect students' performance on mathematics word problems? In Experiment 1, fourth- and sixth-grade students (N = 229) solved word problems involving money. Students in the experimental condition were given bills and coins to help them solve the problems, and students in the control condition…

Presents two primary-level peer tutoring field studies and suggests ways to implement peer tutoring in a classroom. Lesson planning, students' journal writing, manipulative activities, and students' responses are discussed. Among the benefits of peer tutoring are enhanced self-esteem, enhanced sense of responsibility, improvement of skills,…

Use of manipulatives is neither a sufficient nor a necessary condition for meaningful learning. Provides some incidents in support of the argument. Lists 14 references. (YP)

Three third graders with a history of low achievement in math were first given verbal (abstract) instruction in solving word problems. Students were then introduced to manipulatives instruction using Cuisenaire rods to set up word problems. Students exhibited immediate and sustained improvement on subsequent probes administered without…

This ERIC digest examines recent research about the use of manipulatives to teach mathematics. "Manipulatives" refers to objects that can be touched and moved by students to introduce or reinforce a mathematical concept. The digest also speculates on some of the challenges affecting future use of manipulatives. Since the 19th century,…

This article discusses the challenge mathematics educators face in deciding what and how mathematics is to be taught, and offers some suggestions for teachers of young children based on Piaget's developmental theory of mathematics. Piaget's cognitive stages are briefly described and the concrete stage, which spans the age range included in early…

The Animation Tutor[TM] is a curriculum project that uses software to supplement instruction in courses such as intermediate algebra. Its purpose is to ground mathematical reasoning in concrete experiences through the use of interactive animation and the virtual manipulation of objects. This article summarizes how the project has progressed from…