I developed the multi-institutional proposal with the help of support from the University of Northern Colorado grant development fund (see Item 4.4.1, below). My colleagues n California, Michigan, Georgia, Maryland, Texas, and I used BlackBoard, professional meetings, conference calls, and email, to develop the FIPSE proposal. Below, I offer a summary of the proposed work.
Built on a firm foundation of existing theory, research, and best practice, this three year project aims to improve college mathematics teaching and learning through the creation of video case tools for teacher-scholar development of mathematics Graduate Teaching Assistants (GTAs). The project's objectives will be realized through two Working Groups, an Advisory Panel, and an Evaluation Team engaging in an annual reflective cycle of development, field-testing, evaluation, and revision. The hub for video vignette and text materials development is the University of Northern Colorado. Field-test sites for video cases include Arizona State University, California State University at Long Beach, Howard University, Michigan State University, and the University of Oklahoma.
Broad national need. For approximately 8% of undergraduates, their only collegiate mathematics experience will be with a GTA as instructor; another 27% will be taught by a novice instructor who has fewer than three years teaching experience (NCES Profile of Undergraduates, 2002). The vast majority of these students, 85%, will be in mathematics "service" courses like algebra, liberal arts mathematics, and prospective K-8 teacher classes. Nationwide, the average pass-rate for such courses hovers around 60% (the other 40% of students either withdraw or fail). Improving the ability of new college teachers to teach these students promises to have broad national impact on collegiate mathematics learning.
The current state of GTA training. Local programs in place in the U.S. for preparing mathematics GTAs to teach are a mixed bag, typically consisting of up to six hours of training in the week before classes begin. Sometimes, a training manual of sorts is given to GTAs as a reference to read on their own. Nationally funded programs like Preparing Future Faculty and their local incarnations and variations (e.g., Project NeXT) also include some information on college teaching. A few universities even devote a semester or more to the training of GTAs, guided by programs like that in DeLong and Winter's (2001) Learning to teach and teaching to learn mathematics. Each of these approaches could benefit from the addition of contact with video-case vignettes of college mathematics teacher-student and student-student interactions.
Case studies. The FIPSE-funded Boston College Case Study Project (BCCS) was a breakthrough in curricular development for college mathematics faculty preparation. The project produced a book of 14 fictionalized written accounts of college mathematics teaching interactions published by the Conference Board for the Mathematical Sciences (CBMS) and the American Mathematical Society (AMS). Building on the BCCS Project, and the proven efficacy of text and video case use in K-12 teacher preparation, this proposal is to create a collection of video cases from actual classroom practice on an interactive DVD. The PI, in consultation with the Advisory Panel (AdvP), will choose video-case interactions for their power to illuminate or stimulate teacher-reflection. Accompanying materials will include notes on case use for GTA trainers, problem sets, writing and grading rubrics, and comments by and for GTAs along with an independent reflective learning guide to facilitate online or distance course use.
Funds will be budgeted for digital video software and for a technical consultant to help organize the DVD as part of the video development group: Working Group 1 (WG1). Textual materials will be developed, piloted, revised, and edited by Working Group 2 (WG2). The PI and field-testers will belong to both groups. Like the BCCS Project, use of visual cases could be added to existing programs. Unlike the Boston College materials, the cases in the DVD and text will capture actual practice. Also, the materials will be field-tested, revised, and evaluated by institutions with socio-economically and culturally diverse faculties and student bodies to ensure the broadest possible usefulness, including their use in preparing Master's students who are future community college mathematics faculty members.
Video case development. The mechanics of collecting video data from college classrooms is complex. One of the primary concerns is the protection of students (human subjects).
Ethical gathering of video data for national use. The PI has worked with the Institutional Review Board (IRB) on an Informed Consent document with two signature subsections. The first is for Type A (anonymous) use of video data. The second allows for national dissemination of video, Type L (liability release). Researcher experience on college campuses indicates that obtaining Type A consent from an entire class is feasible. Obtaining Type L consent from everyone in a class may be problematic. When whole-class Type L consent is obtained, direct use of video data will be possible. On the other hand, if an interaction involving participants with Type A consent is found to be a valuable component of the video-case materials, then the production alternative will be used.
The production alternative. Before a post-doc in mathematics education, before a Ph.D. in mathematics, and before a stint as a high school English teacher, the PI worked for six years in film and television, including cinema-veritŽ production. With the transcript of a Type A consent interaction, a teacher-collaborator as instructor, and college-student actors (who have given Type L consent and are paid a bit for their efforts), the PI has the experience and expertise necessary to orchestrate credible re-creation of video-case vignettes. The production alternative will only be used when real-interaction video is not available. Time and money for the production alternative for up to 10 cases have been included in the project plan and budget.
Field-testing. The prototype materials will be field tested as they are (re)developed (at least once/year) in Arizona, California, Colorado, Michigan, Oklahoma, and Washington DC. Pending local IRB approval at field sites, additional video data will be gathered at other institutions. Evaluation of field-testing efforts will be built into piloting protocols. For example, in order to gain web access to more than one of the video prototypes, field-testers will have to provide contact information, feedback, and responses to evaluation questions. Moreover, the budget includes funds for field-test site-visits by project personnel.
Capturing teaching interactions, of novice and experienced teacher-collaborators, is key to the project. Instructors will teach in classrooms equipped with multiple digital video cameras. Three mathematics faculty members at UNCO have agreed to video-taping class time and office hours; four professors at other institutions have expressed interest. Additionally, four to 12 GTA instructor-collaborators will be chosen when the grant period begins (there are already six volunteers). Development Portfolios, overseen by the PI, will be maintained on the project web site by and for each teacher-participant, WG1, WG2, and the Evaluation Team (E-Team).
Dissemination. Digital technology is sufficiently advanced that the video cases and textual material could be provided on the DVD and hot-linked together. However, Ed Dunne at the AMS has pressed the point that the AMS publishes BOOKS. Consequently, Ron Rosier at CBMS advised producing a text and a self-contained DVD to be distributed together. At the suggestion of both Ron and Ed, funds have been included in the budget for initial publication and dissemination of one copy per advanced-degree-granting institution in the country (3000 copies). The Mathematical Education of Teachers (MET) was disseminated in just this way in 2001. In less than four years, the MET book has become a central reference for college mathematics departments working to prepare K-12 teachers.
Following the example set by the BCCS project, workshops showcasing video vignettes and inviting feedback will be held at the AMS national meeting each January. At least two papers will be submitted to peer-reviewed journals: one on the development of pedagogical content knowledge among mathematics GTAs and one on project evaluation efforts.
Evaluation. The E-Team is coordinated by Cindy Kronauge (External Evaluator, Prime Solutions, Inc.), Robert Powers (Internal Evaluator, U. Northern Colorado), and Jenq-Jong Tsay (Internal Evaluator, U. of Texas, Pan American). Implementation evaluation informed the design of the project and produced draft evaluation plans based on five [stakeholder] guiding questions:
To address (1), the E-Team will rely on student focus group interviews and evaluations of instructors who have participated in field-testing of video case materials. Student evaluations of teaching will be compared with those in sections taught by instructors outside the project. An institution's existing evaluation instruments will be used with the possible addition of four E-Team designed focus questions. For (2), learner outcomes on common final exams (in whole or part) at prototype testing sites will be compared to non-participating groups or pre-intervention data. To address (3), the E-Team will track progress towards publication and sales by surveying field-testers, January AMS workshop attendees, and CBMS. To tackle (4), in addition to evaluation of learner outcomes and field-test feedback, the E-Team will interview GTAs, their mentors, and undergraduate learners. This qualitative evaluation data and its analysis will support formative evaluation, informing video-case and text development, as well as providing summative evaluation. Finally, to address (5), evaluators will use the broad view from field-test data and the deep information available from GTA participant and mentor/trainer interviews and the Development Portfolios of GTA and other faculty teacher-collaborators.
4.1.2 Funded ($6,000): Center for Learning and Teaching in the West (CLT-W) Summer Research Support, Beyond gap gazing: Dynamical modeling of educational systems, 2005.
4.1.3 Funded ($10,000): CLT-W Summer Faculty Research Support, Walking the tightrope: Learning to validate mathematical proofs, 2004.