Researchers and developers at the University of Chicago are conducting an exploratory project to design, develop, and test a virtual learning community (VLC) to enhance the ability of first- and fourth-grade teachers to provide mathematics education. The project deploys cyberlearning technologies to allow teachers to interact with one another and with experts across the U.S. The goal is to produce a prototype of a VLC for first- and fourth-grade Everyday Mathematics teachers that integrates three primary elements: (a) learning objects rooted in practice, such as lesson video, (b) community-building tools offered by the internet, and (c) focused content that drives teachers' professional learning in mathematics.

This VLC is developed during two engineering cycles in which the project team engages teachers as central partners. The quality and utility of the resultant VLC is tested against the anticipated outcomes of (a) sustained participation by teachers in the VLC and (b) changes in teachers' "professional vision" in mathematics education. Sustained participation is tracked using web analytics and user logs. Changes in professional vision are measured by on-line assessment tools used by approximately 150 teachers.

The VLC develops learning objects; community-building tools; and focused content. The VLC will be launched during the third year of the project by way of the Everyday Mathematics website, which has over 6000 visitors per day, and the University of Chicago School Mathematics Project newsletter, which has a circulation of 40,000. The potential audience is quite large since Everyday Mathematics is used in 185,000 classrooms.

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.

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The primary goal of the project is to investigate the scalability of the Problem-Solving Cycle (PSC) model of mathematics professional development (PD) and accompanying facilitation materials—that is, whether the PSC can be implemented with integrity by multiple facilitators in multiple settings. In the proposed study we will provide ongoing support to a group of middle school mathematics instructional leaders (ILs) so that they can develop the skills to successfully implement the PSC with the mathematics teachers in their schools. The specific nature of this support is expected to change over the duration of the project, and to gradually decrease as the ILs develop the ability to implement the PSC on their own. Our research will address the following questions:

1. What preparation is provided to ILs prior to their implementation of the PSC? What support is provided during implementation? How does this support change with successive iterations of the PSC?
2. How do ILs implement the PSC? How does implementation vary across ILs and over time? What factors account for the variation?
3. What is the impact of preparation for, and implementation of, the PSC on ILs?
4. What is the impact of participation in the PSC on middle school mathematics teachers?
5. What is the impact on the mathematics achievement of students whose teachers participate in the PSC?

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Our research and development work focuses on one aspect of mathematics professional development, when teachers are engaged in solving, discussing, and sharing mathematical work. Although mathematics professional development may include other activities, we specifically focus on how leaders learn to attend to doing mathematics with teachers because it is a primary time during PD that teachers may be developing deeper understandings of mathematics. To support their learning about cultivating rich teacher learning environments, leaders explored two frameworks: sociomathematical norms (norms for mathematical reasoning) and a set of practices for orchestrating productive mathematical discussions. The staff of RMLL created and facilitated seminars as learning opportunities for leaders, studied what and how leaders learned about facilitation, and investigated how leaders facilitated PD in their schools and districts.

As our research project has evolved, we have revised our frameworks for supporting leader development to include a focus on identifying the purposes for doing mathematics with teachers.  We have used Deborah Ball and her colleagues' work at the University of Michigan to draw a distinction between common content knowledge that teachers hold in common with other professional using mathematics and specialized content knowledge that teachers need to know because of their unique role in   We engage in mathematics with teachers in professional development to help them develop not just common content knowledge but specialized knowledge as well. To develop specialized mathematical knowledge, teachers need to engage in explanations that make taken-for-granted ideas in mathematics explicit. Norms for explanation and representational use are vital. These norms are fostered through the orchestration of discussions. In redesigning seminars according to these ideas, we aim to have leaders select and design tasks that engage teachers more comprehensively with the mathematical knowledge they need to teach. Leaders need to know how to specify purposes for doing mathematics in ways that develop teachers’ SCK and identify tasks and discussion prompts that immerse teachers in SCK. They need to know how to pursue this purpose when orchestrating discussions and support the development of sociomathematical norms in ways that unpack teachers’ highly symbolic or incomplete reasoning. In short, we augmented our initial emphasis on sociomathematical norms with this new emphasis on SCK. supporting learners in the classroom.

We are completing analyses of the experiences of leaders in our revised seminars to understand what they gained from our revised frameworks in planning for and enacting professional development.

The American Museum of Natural History and Michigan State University propose a research and development project focused on DR-K12 challenge #2 and the hypothesis that learners must have access to the real work of scientists if they are to learn both about the nature of science and to do inquiry themselves. The overarching questions that drive this project are: How can informal science education institutions best design resources to support teachers, school administrators, and families in the teaching and learning of students to conduct scientific investigations and better understand the nature of science? How are these resources then used, and to what extent and in what ways do they contribute to participants’ learning? How are those resources then used for student learning? Answering these questions will involve the use of existing and new resources, enhancement of existing relationships, and a commitment to systematically collect evidence. Urban Advantage (UA) is a middle school science initiative involving informal science education institutions that provides professional development for teachers and hands-on learning for students to learn how to conduct scientific investigations. This project will (1) refine the UA model by including opportunities to engage in field studies and the use of authentic data sets to investigate the zebra mussel invasion of the Hudson River ecosystem; (2) extend the resources available to help parents, administrators, and teachers understand the nature of scientific work; and (3) integrate a research agenda into UA. Teaching cases will serve as resources to help teachers, students, administrators, and families understand scientific inquiry through research on freshwater ecosystems, and—with that increased understanding—support student learning. Surveys, observations, and assessments will be used to document and understand the effects of professional development on teachers, students, administrators, and parents. The study will analyze longitudinal, multivariate data in order to identify associations between professional development opportunities for teachers, administrators, and parents, their use of resources to support their own learning and that of students, middle school teachers’ instructional practices, and measures of student learning.