This NSF funded CCLI Phase 1 project is a collaboration involving Portland State University (PSU) and Clackamas Community College (CCC). The project personnel include a mathematics educator (Sean Larsen, PI), a research mathematician (John Caughman, Co-PI), and a community college instructor (Mark Yannotta, Co-PI). The starting point for the project is a set of innovative abstract algebra curriculum materials that were developed by the PI over the last few years through a series of research and curriculum development projects.
The project is producing 1) an innovative set of instructor materials designed to support the successful implementation of the curriculum, 2) insight into the challenges and opportunities that emerge as different faculty implement the curriculum, and 3) new knowledge about how students learn abstract algebra and how the curriculum materials can enhance students’ learning. These outcomes will support the successful dissemination and implementation of the curriculum. Significant in their own right, these outcomes will also set the foundation for a larger follow-up project designed to carry the development to a state where the curriculum and instructor materials can be distributed widely or commercialized.
The instructional materials were designed for an introductory abstract algebra course and have been used successfully several times by the PI at PSU. The materials seemed to have a positive impact on students’ learning and stimulate an increase in the number of students choosing to continue studying abstract algebra. The materials actively engage students in the development of the 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 develop deductive proofs of important results based on formal definitions and previously established results). This combination of approaches seems to help students connect their intuitive understanding of concepts to the formal theory—something that research indicates is both important and rare (Edwards & Ward, 2004; Moore, 1994; Tall, 1992; Weber & Alcock 2004).
A subset of the materials has also been adapted successfully for use in algebra courses for K-12 mathematics teachers at PSU and is currently being adapted for use as part of an innovative transition course at CCC designed to prepare students for proof-based university mathematics courses.
The goal of this project is to develop a successful process for disseminating and implementing the curriculum materials. To achieve this goal, we will 1) identify the challenges and opportunities that are likely to arise as different instructors implement the materials, 2) develop instructor support materials to meet the challenges and take advantage of the opportunities and, 3) investigate how students’ learning is enhanced by the curriculum materials.
This material is based upon work supported by the National Science Foundation under Grant No. 0737299. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.