Revisiting the Definition of a Virtual Manipulative

In 2002, Moyer, Bolyard and Spikell defined a virtual manipulative as an “an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge” (p. 373). The purpose of this chapter is to revisit, clarify and update the definition of a virtual manipulative. After clarifying what a virtual manipulative is and what it is not, we propose an updated definition for virtual manipulative: an interactive, technology-enabled visual representation of a dynamic mathematical object, including all of the programmable features that allow it to be manipulated, that presents opportunities for constructing mathematical knowledge. The chapter describes the characteristics of five of the most common virtual manipulative environments in use in education: single-representation, multi-representation, tutorial, gaming and simulation

A Review of the Literature on Mathematics and Science Teacher Quality

A large body of literature exists that examines teacher quality characteristics and the relationship of indicators of those characteristics to teacher effectiveness. This existing research literature broadly views teacher quality research without illuminating specific areas of teacher quality, such as mathematics and science. In an effort to focus the literature base for researchers and policymakers more narrowly, this review specifically examines teacher quality as it relates to mathematics and science teaching and learning. The review highlights key policy and practitioner perspectives, provides a focused synthesis on current research findings on mathematics and science teacher quality, and suggests areas of research that are limited in the literature

Virtual Manipulatives Used by K-8 Teachers for Mathematics Instruction: Considering Mathematical, Cognitive, and Pedagogical Fidelity

This study examined teachers’ uses of virtual manipulatives across grades K-8 after participating in a professional development institute in which manipulatives and technology were the major resources used throughout all of the activities. Researchers analyzed 95 lesson summaries in which classroom teachers described their uses of virtual manipulatives during school mathematics instruction. The findings indicated that the content in a majority of the lessons focused on two National Council of Teachers of Mathematics (2000a) standards: Number & Operations and Geometry. Virtual geoboards, pattern blocks, base-10 blocks, and tangrams were the applets used most often by teachers. The ways teachers used the virtual manipulatives most frequently focused on investigation and skill solidification. It was common for teachers to use the virtual manipulatives alone or to use physical manipulatives first, followed by virtual manipulatives. One important finding of this study was that teachers used the virtual manipulatives during the main portion of their lessons when students were learning mathematics content. These results represent an initial exploration of teachers’ current use of virtual manipulatives in K-8 classrooms

Taking Professional Development From 2D to 3D: Design-Based Learning, 2D Modeling, and 3D Fabrication for Authentic Standards-Aligned Lesson Plans

There is currently significant interest in 3D fabrication in middle school classrooms. At its best 3D printing can be utilized in authentic design projects that integrate math, science, and technology, which facilitate deep learning by students. In essence, students are able to tinker in a virtual world using 3D design software and then tinker in the real world using printed parts. We describe a professional development activity we designed to enable middle school teachers who had taken part in a three-year Math Science Partnership program to authentically integrate 3D printing into design-based lessons. We include some examples of successful design-based lesson plans

The Assessment of Mathematics and Science Teacher Quality

The purpose of this study was to examine the types of instruments being used to document mathematics and science teacher quality characteristics in 48 nationally funded mathematics and science education awards. Each of the 48 projects operationalized teacher quality and determined how to assess it. The main research questions examined the instruments awardees used to gather data on mathematics and science teacher quality, and the main characteristics of teachers examined by awardees. Results showed that awardees most frequently used surveys or questionnaires to assess characteristics of mathematics and science teacher quality. The most common teacher characteristics examined by awardees\u27 included teacher behaviors, practices, and beliefs, followed by the assessment of subject and pedagogical knowledge, and the documentation of mathematics and science teachers\u27 certification. A few new instruments were under development and in use to assess characteristics of teacher quality. Detailed information on the development and psychometric properties of the instruments used for these examinations was not available from the reports. Because awardees were at different stages in their funded activities and data collection efforts were ongoing at the time of this analysis, this study offers a preliminary and formative review of the use of assessments to document mathematics and science teacher quality characteristics among these awards

Classify and Capture: Using Venn Diagrams and Tangrams to Develop Abilities in Mathematical Reasoning and Proof

This article describes a game of classifying objects according to their attributes using a three-set Venn diagram, then analyzing the classification of the objects to determine their accuracy. Students attempt to capture opponents\u27 game pieces (tangrams) by making mathematical arguments that identify misplaced pieces

Investigations in Algebra with Virtual Manipulatives

No abstract available

What are Virtual Manipulatives?

This article establishes a definition for virtual manipulatives, provides examples of virtual manipulative Web sites, and discusses their potential uses for teaching mathematics in K-12 classrooms

Second Graders’ Mathematical Practices for Solving Fraction Tasks

Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children’s mathematical practices through an exploratory examination of the practices of a group of second-grade students engaged in several mathematical tasks focused on rational number concepts. Twenty-five second-grade students completed three fraction tasks in structured clinical interviews. The interviews and student work were analyzed using an interpretational analysis to examine the data for constructs, themes, and patterns that were useful in explaining children’s mathematical practices. The results reveal that children used a variety of mathematical practices during the interviews to respond to the mathematical problems presented. Children’s mathematical practices were both a product that they used to solve the mathematical situations, and a process that was developing during the interactions of the interview. The findings lead to new insights about how mathematical practices develop and what promotes their development

Representations of Teacher Quality, Quantity, and Diversity in a National Mathematics and Science Program

A brief narrative description of the journal article, document, or resource. Growing awareness of the importance of teacher quality in mathematics and science has stimulated a variety of national reports and funded initiatives for the purpose of improving teaching and learning in K-12 schools. This study examined the work of awardees in one federally-funded program that included a focus on increasing the number, quality, and diversity of mathematics and science teachers. Secondary data sources were used to understand representations of mathematics and science teacher quality, quantity, and diversity reported by awardees, and to identify interventions awardees implemented to influence teacher quality, quantity, and diversity. Results indicated a primary focus on the development of teacher characteristics such as subject knowledge, pedagogical knowledge, and instructional practices. Seven common interventions were implemented across the program to influence the quality of individual teachers and the quantity and diversity of the teacher population. Three prevalent themes in the secondary documents included: a) awardees\u27 knowledge of and implementation of research-based professional development practices; b) a shift in emphasis to include specialized subject knowledge preparation for elementary teachers, in addition to the traditional emphasis on subject knowledge for middle and high school teachers; and c) involvement of STEM faculty and Teacher Leaders in various collaborative relationships, in activities at all levels (K-12) and in both mathematics and science. Intervention efforts to influence teacher quantity and diversity were in their initial stages and limited in scope. These findings are discussed with reference to the impact of the program on the quality, quantity, and diversity of mathematics and science teachers. (Contains 2 tables and 1 figure.