Manipulatives are considered a best practice for educating students with disabilities, but little research exists which examines virtual manipulatives as tool for supporting students in mathematics. This project investigated the use of a virtual manipulative through the National Library of Virtual Manipulatives--polynominoes (i.e., tiles)--as a…

Children's literature involving mathematics provides a common, natural context for the sharing of mathematics. To learn more about how preservice teachers included children's literature in their mathematics lessons, a study was conducted over two semesters during a required field experience component of an undergraduate teacher education program.…

Teaching physics concepts with the basic materials that are around us is one of the beauties of physics. Without expensive lab materials and long experiments, many physics concepts can be taught to students using simple tools. Demonstrations with these tools can be presented as discrepant events that surprise, amaze, or puzzle students. Greenslade…

Multi-touch tablets allow users to interact with computers through intuitive, natural gestures and direct manipulation of digital objects. One advantage of these devices is that they can offer a large, collaborative space where several users can work on a task at the same time. However the lack of privacy in these situations makes standard…

A well-known optimization problem is the Popcorn Box investigation, which involves a movie theater snack container. The problem has been tailored for classroom investigations by the Ontario Association for Mathematics Education. The exploration was designed for students in grades 9 through 12. A common strategy proposed for algebra students is to…

Teachers in early childhood and elementary classrooms (grades K-5) have been using ten-frames as an instructional tool to support students' mathematics skill development for many years. Use of the similar five-frame has been limited, however, despite its apparent potential as an instructional scaffold in the early elementary grades. Due to scant…

This case study analyzed the impact of a concrete manipulative program on the understanding of quadratic expressions for a high school student with a learning disability. The manipulatives were utilized as part of the Concrete-Representational-Abstract Integration (CRA-I) intervention in which participants engaged in tasks requiring them to…

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics [NCTM] 2000). However, the…

Three-dimensional (3D) nuclear charts were created using toy blocks, which represent the atomic masses per nucleon number and the total half-lives for each nucleus in the entire region of the nuclear mass. The bulk properties of the nuclei can be easily understood by using these charts. Subsequently, these charts were used in outreach activities…

To promote the implementation of manipulatives into mathematics instruction, this research project examined how the instructional practices of four Grade 9 applied mathematics teachers related to their beliefs about the use of manipulatives in teaching mathematics, its effects on students' learning, and enabling and disabling factors. Teacher…

Activity-based instructional strategies promote physical interaction with manipulatives to represent abstract concepts. As a means to improve student achievement in mathematics, educational researchers and practitioners often recommend instructional strategies that capitalize on the assumed benefits of manipulatives. Recent research has indicated…

This single-subject multiple-baseline across participants study was designed to investigate the effects of explicit instruction with manipulatives on the conceptual and procedural knowledge of addition and subtraction of like and unlike fractions of elementary school students with autism. This study included six 8- to 12-year-old students with…

The purpose of this article is to provide strategies for recognizing meaningful mathematics in common play contexts in early childhood classrooms and to offer suggestions for how teachers might intervene in these moments to help children attend to the mathematical ideas embedded in their play. In particular, the author's focus on the concepts of…

It is not surprising, as research has shown, that fractions are one of the most difficult of the elementary school math topics to teach and learn in ways that are meaningful. The authors reference a work by James Hiebert, "Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions" (1992), that mathematical concepts should…