Ferdinand Rivera

This project addresses three central challenges: 1) the tendency for students to not engage in real mathematical thinking as they use technologies; 2) the tendency for teachers to not enact pedagogically-effective approaches; and 3) the lack of adoption of effective technologies by teachers due to a variety of barriers. This project will use rich, exploratory, interactive simulations and associated instructional materials as a pathway for making rapid progress and focusing on advancing algebraic thinking in Grades 6-9.

The purpose of this project is to investigate issues in the design and implementation of effective virtual learning communities (VLCs) for teachers and to examine the relation between teachers' reflective engagement with VLCs and their students' mathematics learning outcomes. Findings from this project will be used to build and share effective ways to support teacher learning online.

Understanding Space Through Engineering Design investigates how engaging K-5 children from underrepresented populations in the design of packages, maps, and mechanisms supports the development of spatial reasoning and spatial mathematics. The prime conjecture is that engineering design makes spatial mathematics more tangible and purposeful, and that systematic support for spatial reasoning and mathematics, in turn, influences the nature of children's designs and their understanding of how those designs work.

This project will test new instructional approaches designed to help K-1 students comprehend place value. The project will emphasize the underlying relational structure of place value symbols, and target this structure with instructional materials and techniques drawn from the structure mapping literature. Its theory of action is that instruction which scaffolds structure mapping for place value will better prepare children to face the challenges of advanced operations, such as multi-digit calculation.

This project will test new instructional approaches designed to help K-1 students comprehend place value. The project will emphasize the underlying relational structure of place value symbols, and target this structure with instructional materials and techniques drawn from the structure mapping literature. Its theory of action is that instruction which scaffolds structure mapping for place value will better prepare children to face the challenges of advanced operations, such as multi-digit calculation.

The goal of this design and development project is to address the critical need for innovative resources that transform the mathematics learning environments of preschool children from under-resourced communities by creating a cross-context school-home intervention.