4.2.1 Funded ($102,000): National Science Foundation (NSF) Post-doctoral Fellowship in Science, Mathematics, Engineering, and Technology Education (at ASU), 1999-2001.
4.2.2 Funded ($50,000): National Science Foundation (NSF) Pilot study on mathematics cognition and affect in non-routine problem situations, 2002.
4.2.3 Funded ($6,500): Faculty Research Publication Board Summer Research Fellowship, 2003.
4.2.4 Not funded ($750,000): NSF Early Career Award Program, CAREER: An investigation of college student and instructor agency in building mathematical self-efficacy, 2002.
Not funded ($750,000): NSF Early Career Award Program, CAREER: An investigation of college student and instructor agency in building mathematical self-efficacy, 2003.
Project Summary for CAREER proposal (2003).
Mathematical self-efficacy is the perception of what one can do with the mathematical skills one possesses.
Objectives. Two significant challenges face collegiate science, technology, engineering, and mathematics (STEM) education: (1) to increase mathematics understanding for all students and (2) to enhance the teaching efficacy of new college faculty. The project meets these challenges through basic, applied, and curricular research. Informed by work in cognitive science and psychology, the basic research advances theoretical models for analyzing and fostering intentionality and self-efficacy in college mathematics classrooms. The applied research addresses how to translate theory into effective practice. The curriculum development objective is the creation of video-vignettes of college mathematics learning and teaching along with discussion prompts, and teaching notes for their use in GTA training.
Methods. A Research Community of full-time faculty, graduate student Teaching Assistants (GTAs), post-docs, Advisory Panel members, and the Evaluation Team are organized into three Working Groups (WGs). WG1 is focused on basic research and theory development. WG2 is centered on applied research and practice development. Teacher-collaborators (GTAs and professors) conduct mathematics courses in a classroom equipped with digital video cameras. Video data are then observed, reviewed, and analyzed with naturalistic inquiry methods. Additional work by WG1 and WG2 includes survey, focus groups working collectively to solve mathematics problems, task-based interviews of undergraduates in novel mathematical problem situations, and of GTAs in novel teaching situations. WG3 produces an indexed, menu-driven, digital video disk (DVD) of visual case studies and textual training materials. The video-case materials are piloted, revised, field-tested, revised again, and then distributed to colleges and universities nationally through a publication agreement with the Conference Board of the Mathematical Sciences. The project's action-research cycles9 will inform the content and arrangement of resources in the book-DVD package. A web-based collection of Portfolios is used for data management and regular Research Community review of action-research cycles, draft presentations, and publications.
Intellectual Merit. The field of rigorous research on self-efficacy in collegiate mathematics populations, especially among GTAs, is virtually untilled. The relative youth of research in mathematics education as a field, particularly of research in collegiate mathematics education, means most new work has depended on a synthesis of cognitive science, psychology, and educational theory with a dash of inventiveness thrown into the mix. It is this very lack of history, and theoretical allegiances, that has kept inquisitiveness and diversity of approaches at a maximum. The project is based on a mix of qualitative interview and action-research with the triangulation afforded by coordinated and carefully validated quantitative efforts. This design builds on current trends in collegiate mathematics education research. It will also provide the foundation for further research and inform development of bridges from research to practice.
Broader Impacts. An improvement in novel problem solving ability yields a major benefit in the nations' workplaces, where college graduates who are stuck in the routine, means-ends mode, of problem-solving often cannot bring their academic knowledge to bear. Additional benefits occur for prospective school and college teachers who themselves will be expected to teach nonroutine problem-solving and proof. GTA-collaborators are prepared by the project to become national leaders in collegiate mathematics education. Moreover, because self-efficacy is relatively culturally independent, instruments developed in this project can be used by researchers working to enhance mathematical self-efficacy among diverse student populations. Finally, one of the most significant products of this five year CAREER project, is the video-case book and DVD for GTA preparation. The opportunity to view, re-view, and reflect on teaching situations is an effective pedagogic tool for future faculty. This tool will be broadly disseminated through field-testing and publication.