This project aims to develop a software diagnostic tool for integrating diagnostic interviews, group administered assessments, and student data in real-time so that teachers can enter and view student status information. This project would concentrate on rational number learning in grades 3-8. The design is based on a model of learning trajectories developed from existing research studies.

The diagnostic system to be developed for teachers would be used in assessing their students' knowledge and would identify difficulties in understanding five key clusters of concepts and skills in rational number reasoning. It would also investigate the diagnostic system's effects on student and teacher learning in relation to state standards, assessments, and curricular programs. The five areas include understanding: (1) multiplicative and division space; (2) fractions, ratio, proportion and rates; (3) rectangular area and volume; (4) decimals and percents; and (5) similarity and scaling.

The diagnostic measures will include diagnostic interviews collecting data using a handheld computer, two types of group-administered assessments of student progress, one set along learning trajectories for each of the five sub-constructs and one composite measurement per grade. The diagnostic system will produce computer-based progress maps, summarizing individual student and class performance and linking to state assessments.

The Video Mosaic Collaborative features  videos of student mathematics reasoning,  tools and services to encourage learning, research and practices fostering the development of student reasoning.  The VMC is a collection and service portal intended to support three primary audiences—teacher educators and their pre-service and in-service students, practicing teachers, and researchers.  The Video Mosaic Collaborative features a 22-year longitudinal study of students’ mathematical reasoning skills as they are developed from elementary through high school grades.  The VMC has been carefully designed to leverage the insights and strategies that can be mined in this extensive and unique video collection featuring observations, interventions and interviews with students solving mathematics problems in the classroom and in informal learning settings.  A careful metadata strategy was designed by the library and education research partners in collaboration to capture elements for searching that include forms of reasoning and heuristics, math strand, math problem, NCTM standards, grade level and type of educational environment.  Students and researchers are identified and can be individually tracked through the collection.  Transcripts, student work and dissertations resulting from the videos are linked in metadata.  Tools, such as the VMCAnalytic, a video annotation and analysis tool, are provided to enable registered participants to reuse the videos for instruction, study and research by creating personal clips and combining clips to accomplish research goals such as demonstrating changes in reasoning for an individual student studying probability over several video sessions.  Unlike other video annotation tool, the VMC analytic creates  XML-based independent resources that can be kept private in the researcher’s workspace but that can also be shared.  Shared analytics will be mined for keywords, which will retrieve the video(s) being analyzed, thus adding user tagging to the metadata for the videos.  The analytic resources created are not independently searched and displayed but will display as part of the context for the videos in the collection, along with student work, dissertations, and ultimately published articles, etc., all of which form the critical context of research and study surrounding each video.

Different search strategies, guidance in using videos and opportunities to consult or collaborate with others will be provided for each primary audience of the VMC.  The latest iteration of the portal, with collections and services available for immediate use, will be presented and demonstrated at the DRK12 Principal Investigators’ meeting poster session.  Visitors to the poster will be encouraged to search the portal and to create a small analytic, in a hands-on, interactive one on one demonstration.  We believe that the VMC makes a unique and significant contribution to the efforts of teacher educators, practicing teachers and researchers to discover insights and develop innovative strategies to support the development of student reasoning in mathematics education.

Intensified Algebra I, a comprehensive program used in an extended-time algebra class, helps students who are one to two years behind in mathematics become successful in algebra. It is a research and development initiative of the Charles A. Dana Center at The University of Texas at Austin, the Learning Sciences Research Institute at the University of Illinois at Chicago, and Agile Mind, that transforms the teaching of algebra to students who struggle in mathematics. Central to the program is the idea that struggling students need a powerful combination of a challenging curriculum, cohesive, targeted supports, and additional well-structured classroom time. Intensified Algebra I seeks to addresses the need for a robust Algebra I curriculum with embedded, efficient review and repair of foundational mathematical skills and concepts. It aims to address multiple dimensions of learning mathematics, including social, affective, linguistic, and cognitive. Intensified Algebra I uses an asset-based approach that builds on students’ strengths and helps students to develop academic skills and identities by engaging them in the learning experience. The program is designed to help struggling students succeed in catching up to their peers, equipping them to be successful in Algebra I and their future mathematics and science courses.