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Using Routines as an Instructional Tool for Developing Students' Conceptions of Proof

This project will develop and systematically investigate a teaching model to assist teachers in developing ideas about proof in grades 2-5. The teaching model provides both a tool for learning on the part of elementary teachers and a model of practice from which they can learn as they implement it.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1019482
Funding Period: 
Wed, 09/01/2010 to Fri, 08/31/2012
Project Evaluator: 
Megan Franke
Full Description: 

Developers and researchers at TERC, the Education Development Center, and Mount Holyoke College are participating in the development and systematic investigation of a teaching model to assist teachers in developing ideas about proof in grades 2-5. The teaching model provides both a tool for learning on the part of elementary teachers and a model of practice from which they can learn as they implement it.

The project is a teaching experiment in which the model is iteratively implemented and refined, first with teachers experienced in incorporating ideas about proof into their classroom instruction (Phase 1), then with teachers who are relatively inexperienced, both in their own understanding of proof and in their knowledge of how their students can learn about proof (Phase 2). Research questions focus on developing the components of the model, the learning of teachers as they implement the model, and the learning of students as they engage in the instruction that is guided by the model, with particular attention to students with varied histories of achievement in grade-level work on number and operations.

The expected outcome is a teaching model that can be tested on a larger scale as well as instruments for assessing student learning and teacher understanding of proof. The model includes printed material with descriptions of the routines and instructional sequences, guidelines for implementing each component, and a teaching framework as well as written and video case examples.

Virtual Learning Communities: An Online Professional Development Resource for STEM Teachers

This project will design, develop, and test a virtual learning community (VLC) to enhance the ability of first- and fourth-grade teachers to provide mathematics education. 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.

Project Email: 
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1020083
Funding Period: 
Thu, 07/15/2010 to Sun, 06/30/2013
Project Evaluator: 
none
Full Description: 

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.

CAREER: Supporting Students' Proof Practices Through Quantitative Reasoning in Algebra

The aim of this project is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Award Number: 
1743356
Funding Period: 
Mon, 03/15/2010 to Fri, 06/30/2017
Full Description: 

The aim of this CAREER project led by Amy Ellis at the University of Wisconsin is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Work of the project will produce: (a) insights into ways of unifying two previously disconnected lines of research on quantitative reasoning and proof; (b) models describing realistic ways to support development of students' proof competencies through quantitative reasoning; (c) improvement in students' understanding of algebra through engagement in proof practices based on quantitative reasoning; (d) insights into middle-school students' thinking as they negotiate the transition from elementary to more advanced mathematics; and (e) increased understanding of teachers' knowledge about proof and their classroom practices aimed at helping students progress towards understanding and skill in proof.

This project was previously funded under award #0952415.

Introducing Dynamic Number as a Transformative Technology for Number and Early Algebra

This project operationalizes research in number, operation, and early algebra. It builds on the paradigm of Dynamic Geometry (the interactive and continuous manipulation of geometric shapes and constructions) with a new technological paradigm, Dynamic Number, centered on the direct manipulation of numerical representations and constructions. Using The Geometer’s Sketchpad as a starting point, KCP Technologies is developing new software tools to deepen students’ conceptions of number and early algebra in grades 2–8.

Project Email: 
Lead Organization(s): 
Award Number: 
0918733
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Project Evaluator: 
John Olive

Iterative Model Building (IMB): A Program for Training Quality Teachers and Measuring Teacher Quality

This project aims to improve professional development programs for pre-service teachers (PSTs) as a way to improve student learning in mathematics and science. PSTs engage in a series of teaching cycles, and then engage in lesson study groups to develop, teach, and analyze a whole-class lesson. The cycle is completed by reexamining students' knowledge in teaching experiments with pairs of students. These teaching cycles are called Iterative Model Building (IMB).

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0732143
Funding Period: 
Wed, 08/15/2007 to Tue, 07/31/2012
Project Evaluator: 
Center for Evaluation and Education Policy

NanoTeach: Professional Development in Nanoscale Science

This project is exploring the introduction of a nanoscience curriculum into high schools. It is creating and studying a professional development model based on two products, the NanoTeach Teacher's Guide and the NanoTeach Facilitator's Guide. The NanoTeach Teacher's guide is being designed for self study by teachers (low treatment group) and for use in a facilitated development model (high treatment group). The NanoTeach Facilitator's Guide outlines the professional development experiences and provides guidance for facilitators.

Award Number: 
0822128
Funding Period: 
Mon, 09/15/2008 to Wed, 08/31/2011
Project Evaluator: 
Aspen Associates and Dr. Doug Huffman
Full Description: 

NanoTeach: Professional Development in Nanoscale Science 

NanoTeach is a full research and development project that addresses two challenges:

1.      Contextual Challenge: How can the learning of significant STEM content be achieved to ensure public literacy and workforce readiness? by moving nanoscale science and technology (NS&T) into high school science courses; and

2.      Frontier Challenge: What will support STEM teachers’ practice and development in an era of cyber-enabled learning? by testing an innovative, synchronous online video technology (Versatile Classroom) for use in professional development with cutting edge NS&T content.

 

Mid-continent Research for Education and Learning along with ASPEN Associates, Stanford Nanofabrication Facility, and the National Nanotechnology Infrastructure Network (NNIN) propose to develop NanoTeach. The project will develop and test professional development that combines an instructional design framework with nanoscale science content using multiple delivery methods for high school science teachers. The project has two research questions:

 

RQ #1    Does the NanoTeach facilitated professional development improve teachers’ ability to integrate NS&T content into their classes in a way that promotes effective science teaching?

RQ #2    To what extent is the approach utilized in the NanoTeach project a viable approach to the development of professional development materials and experiences that support integration of nanoscale science in high school science?

 

Methods: The research design includes a formal pilot test and field test with random assignment treatment and control groups. The NanoTeach Teacher’s Guide will be designed for self-study (control group) and for use in a facilitated (80 hours plus significant follow-up) professional development model (treatment group). The results of the pilot test will inform revisions to NanoTeach prior to the field test. The research design and evaluation include ongoing structured data collection and reporting to support the development team in formal reflection about the viability of the design process and the quality of the resulting products.

 

Intellectual Merit: NanoTeach builds on the significant investments that the NSF has made in NS&T and on the existing findings and resources generated from these projects, including NanoLeap, NanoSense, and the NanoEd Resource Portal at the National Center for Teaching and Learning in Nanoscale Science and Engineering (NCLT). NanoTeach will test both self-guided and facilitated professional development and advance the field by studying how a carefully designed framework can help teachers learn NS&T content and integrate this content into existing curricula in a way that is essential to meeting their local curricular goals. While bringing current, cutting edge science into K-12 classrooms, NanoTeach also tests a cyber enabled learning tool (Versatile Classroom) to deliver high quality video in real time as part of distance-learning professional development for teachers.

 

Broader Impact: NanoTeach will significantly contribute to the pool of teachers trained in NS&T, reaching over 200 teachers directly and preparing them not only to teach NS&T but also to become ambassadors and mentors for teaching NS&T in high school classrooms. The project targets teachers from in and around large urban centers who teach traditionally under-represented groups and helps them form a learning community that includes NS&T scientists, researchers, and educators, as well as K-12 teachers. Following the study, the NanoTeach professional development model will be widely disseminated through the cadre of participating teachers and the project partners’ national networks, including NSTA, NCLT, and NNIN. The successful demonstration of the Versatile Classroom as a vehicle for professional development will engage teachers in lifelong learning and improve their practice in a timely and inexpensive manner.

Mathematics Discourse in Secondary Classrooms (M-DISC): A Case-Based Professional Development Curriculum

This project is developing, designing, and testing materials for professional development leaders (e.g., teacher educators, district mathematics specialists, secondary mathematic department chairs) to use in their work with secondary mathematics teachers. The aim is to help those teachers analyze the discourse patterns of their own classrooms and improve their skills in creating discourse patterns that emphasize high-level mathematical explanation, justification, and argumentation.

Award Number: 
0918117
Funding Period: 
Sat, 08/01/2009 to Thu, 07/31/2014
Project Evaluator: 
Horizon

Diagnostic E-learning Trajectories Approach (DELTA) Applied to Rational Number Reasoning for Grades 3-8

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.

Project Email: 
Award Number: 
0733272
Funding Period: 
Sat, 09/01/2007 to Tue, 08/31/2010
Project Evaluator: 
William Penuel (SRI)
Full Description: 

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.

Multimodal Science: Supporting Elementary Science Education through Graphic-enhanced Communication

This project enhances elementary students' engagement in and learning of science through visual communication skills using student-generated graphics in science notebooks. The products include two professional development modules for each grade level 2–5 that explicitly teach specific forms of graphical representation used in science, how these representations complement written and numeric information, and how teachers can promote the thoughtful reflection and discussion of these representations in small-group and whole-class settings.

Partner Organization(s): 
Award Number: 
0733217
Funding Period: 
Tue, 01/01/2008 to Wed, 06/30/2010
Project Evaluator: 
....
Full Description: 

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Cyber-enabled Design Research to Enhance Teachers' Critical Thinking Using a Major Video Collection on Children's Mathematical Reasoning (Collaborative Research: Maher)

This project is working to create a cyber infrastructure that supports development and documentation of additional interventions for teacher professional development using the video collection, as well as other videos that might be added in the future by teacher educators or researchers, including those working in other STEM domains.

Lead Organization(s): 
Award Number: 
0822204
Funding Period: 
Mon, 09/15/2008 to Fri, 08/31/2012
Full Description: 

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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