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

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.