Teaching Abstract Algebra for Understanding


The Teaching Abstract Algebra for Understanding (TAAFU) project was sponsored by NSF (DUE CCLI #0737299).

Sean Larsen (Principal Investigator)
John Caughman of Portland State University (Co-Principal Investigator)
Mark Yannotta of Clackamas Community College (Co-Principal Investigator))


Other Project Personnel:

Graduate Research Assistants: Joanna Bartlo & Estrella Johnson

UnderGraduate Research Assistants: Amy Brandenburg, Faith Rutherford, Cliff Smith, Travis Scholl

Instructor Support Website Development Support: Travis Scholl

The grant period was July 2008 - December 2011

NSF Abstract (2008): Mathematical sciences (21) This project is developing instructor materials to support the implementation of innovative course materials for abstract algebra developed through a series of research and development (R&D) efforts. The course materials engage students actively in understanding fundamental concepts of group theory, balancing reinvention phases (in which students develop concepts based on their intuition, informal strategies, and prior knowledge) and deductive phases (in which students prove important results based on formal definitions and previously established results). The earlier R&D efforts confirm that a sequence of successive uses of these two phases helps students connect an intuitive understanding of concepts to the formal theory. The curriculum has been piloted successfully at the PI's institution in a standard introductory abstract algebra course, and a subset of the materials is currently being adapted for use in an innovative transition course at a local community college designed to prepare pre-service teacher education students for proof-based mathematics courses. In addition to developing a set of instructor guides and associated curricular implementation materials, the project plans to conduct research to gain insight into the challenges and opportunities that emerge as different faculty implement the curriculum, and to obtain new knowledge about how students learn abstract algebra and how the course materials enhance student learning. The intellectual merit of this project lies both in its grounding in the current mathematics education research literature and the way in which the instructor materials under development serve as a vehicle to communicate the project's own research findings on student learning of abstract algebra concepts back to the larger body of mathematics faculty. The project is exercising broad impact since abstract algebra and "transition-to-proof" courses are a staple of the mathematics curriculum, particularly for the large subset of students preparing to be teachers. Furthermore, the collaboration among mathematicians, mathematics educators, and counterparts at the two-year college level offers a model for other institutions working closely with their "feeder" two-year schools.

The grant period was July 2008 - December 2011

The curriculum and instructor support materials are now known as Inquiry Oriented Abstract Algebra. You may access those directly here: IOAA

The lead Graduate Research assistant of the TAAFU project, Estrella Johnson, Is now a faculty member at Virginia Tech and is the Principle Investigator of a project called Teaching Inquiry-oriented Mathematics: Establishing Supports (TIMES)

The TIMES project builds on the work of the TAAFU project by developing and studying supports for instructors implementing the IOAA materials as well as inquiry oriented curriculum materials designed for Linear Algebra and Differential Equations courses

Publications Resulting from TAAFU:

Special Issue of the Journal of Mathematical Behavior:

Larsen, S., Johnson, E., & Weber, K. (Eds). (2013). The Teaching Abstract Algebra for Understanding Project: Designing and Scaling up a Curriculum Innovation. [Special issue]. Journal of Mathematical Behavior 32 (4).

Johnson, E., Caughman, J., Fredericks, J., & Gibson, L. (2013). Implementing inquiry-oriented curriculum: From the mathematicians’ perspective. The Journal of Mathematical Behavior, 32(4), 743-760.

Johnson, E. (2013). Teachers’ mathematical activity in inquiry-oriented instruction. The Journal of Mathematical Behavior, 32(4), 761-775.

Larsen, S. (2013). A local instructional theory for the guided reinvention of the group and isomorphism concepts. Special Issue of the Journal of Mathematical Behavior 32 (4) 712-725.

Larsen, S., Johnson, E., & Bartlo, J. (2013). Designing and scaling up an innovation in abstract algebra. Special Issue of the Journal of Mathematical Behavior 32 (4) 693-711.

Larsen, S. & Lockwood, E. (2013). A local instructional theory for the guided reinvention of the quotient group concept. Special Issue of the Journal of Mathematical Behavior 32 (4) 726-742

Lockwood E., Johnson, E., & Larsen S. (2013). Developing instructor support materials for an inquiry-oriented curriculum. Special Issue of the Journal of Mathematical Behavior 32 (4) 776-790.

Johnson, E., & Larsen, S. (2012). Teacher listening: The role of knowledge of content and students. Journal of mathematical behavior 31 (1) 117-129.

Larsen, S. (2010). Struggling to Disentangle the Associative and Commutative Properties. For the Learning of Mathematics 30 (1) 37-42.