**Author(s): Dexter Lim, Bismark Akoto, Irene M. Duranczyk**

Algebra Instruction at Community Colleges (AI@CC) 1.0 and 2.0 are collaborative faculty research projects engaging community college researchers and practitioners with university research faculty and resources. Our first project sought to investigate the relationship between two characteristics of mathematics instruction at the community college level: (1) quality of teacher-student interaction and (2) quality of mathematics with student learning gains and course performance in community college algebra courses.

For this IMPACT Plus blog, the focus will be on our framework for characterizing the community college algebra instruction and providing the research documents to highlight some of our findings from data collected from 86 community college faculty and their 1368 students. Our second project builds on the AI@CC 1.0 to advance our work on understanding the connection between mathematical knowledge for teaching community college algebra and the quality of instruction in college algebra classrooms. We will only focus on the design of a new instrument to explore mathematical knowledge for teaching. Let’s get started.

A major accomplishment for AI@CC 1.0 was designing, testing, and validating the efficacy of Evaluating the Quality of Instruction in Postsecondary Mathematics (EQIPM). Performing exploratory and confirmatory factor analyses confirmed that our instrument successfully captures three hypothesized dimensions of quality of instruction that were anticipated by the conceptualization of instruction. The research on qualities of instruction in mathematics education and the instructional triangle (mentioned in the IMPACTful thoughts post on May 1) inform this framework (See EQIPM figure). Research supporting our development is at the end of this post.

In order for the EQIPM framework to assist in understanding and characterizing instructional activities, the team developed the following definitions.

This framework was used to characterize instruction by analyzing videos of community college faculty teaching lessons on linear, exponential, and rational functions. Some of the results can be reviewed in the research article listed at the end of this document. This research highlights ways which community college algebra instructors can foster student/faculty ownership of the learning environment using this framework in conjunction with the recommendations of AMATYC’s Ownership chapter in IMPACT. The principles of student discovery, responsibility, and continued learning are part of this framework.

Another outcome of AI@CC 1.0 was determining that Mathematical Knowledge for Teaching - Algebra (MKT-A) by Phelps and Gitomer (2012) was not adequate for community college algebra faculty. The MKT-A was developed to measure content knowledge for teaching Algebra 1. We made minimal language modifications to the MKT-A instrument by stripping information that suggested a school, rather than a community college setting. We administered the MKT-A to the community college algebra faculty whose lessons we video-recorded. In comparing the application of the MKT-A with 74 community college instructors to a national sample of 416 high school algebra teachers, we found the following: (1) the patterns of correct and incorrect responses to all but three items were similar in both samples, (2) there were significant differences in the proportions of correct and incorrect responses, with community college faculty significantly outperforming the high school teachers (the odd ratios ranged from 1.68 to 4.05 in 9 items, 8 of them had the form “identify the student response that best explains what is wrong”), and (3) the Item Response Theory (IRT) analysis of the participant responses revealed that community college faculty have a relatively higher level of mathematical knowledge for teaching algebra compared to the high school teachers (Ko, 2019a). Based on these results, it is obvious that the MKT-A instrument may not be capturing the knowledge specific to community college faculty and therefore it cannot reliably discriminate the knowledge level among community college faculty. In other words, MKT-A is not appropriate for community college faculty and more work is needed to create an instrument that can validly assess the knowledge needed for teaching college algebra at community colleges. We are presently designing a new framework to measure mathematical knowledge for teaching college algebra and writing an instrument for AI@CC 2.0 with the assistance of a diverse group of community college faculty. If you are interested in helping to test the individual items and/or be part of the validation process for this new instrument that we are calling MKT-CCA (Mathematical Knowledge for Teaching Community College Algebra), there are opportunities. For these efforts, you will receive a compensation of $50 for taking the new MKT-CCA or participating in a cognitive interview with a select number of items designed for the new MKT-CCA. For more information, see the VMQI description: https://z.umn.edu/VMQIa

In closing, we would like to acknowledge our growing team and as promised a list of publications related to the EQIPM instrument. We hope you have found this information helpful and take ownership of research as a community college faculty to bring IMPACT into your work to enhance community college Mathematics instruction.

**The AI@CC Team:**

Megan Breit-Goodwin, Anoka-Ramsey Community College

Anne Cawley, California State University, Pomona

April Ström, Chandler-Gilbert Community College

Randy Nichols, Delta College

Anna Bright, Patrick Kimani, Fern Van Vliet, & Laura Watkins, Glendale Community College

Angeliki Mali, Groningen University

David Tannor, Indiana Wesleyan University

Jon Oaks, Macomb Community College

Nicole Lang, North Hennepin Community College

Mary Beisiegel, Oregon State University

Carla Stroud & Judy Sutor, Scottsdale Community College

Claire Boeck, Saba Gerami, Inah Ko, & Vilma Mesa, University of Michigan

Bismark Akoto, Irene Duranczyk, Nidhi Kohli, & Dexter Lim, University of Minnesota

**AI@CC Publications of finding related to EQIPM features:**

Cawley, A., Duranczyk, I., Mali, A., Mesa, V, Ström, A., Watkins, L., Kimani, P., & Lim, D. (2018). An innovative qualitative video analysis instrument to assess the quality of post-secondary algebra instruction. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter. (Eds.). Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education. Umea, Sweden: PME.

Cawley, A., Ström, A., Mesa, V., Watkins, L., Duranczyk, I., & Kimani, P. (2019). Investigating Mathematical Errors and Imprecisions in Content and Language in the Teaching of Algebra. In Graven, M., Venkat, H., Essien, A. & Vale, P. (Eds). (2019) Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol 2). (pp. 137 – 144) Pretoria, South Africa: PME.

Gerami, S., Leckrone, L., & Mesa, V. (2020). Exploring instructor questions in community college algebra classrooms and its connections to instructor knowledge and student outcomes. MathAmatyc Educator. 11(3), 34 - 39.

Kimani, P., Watkins, L., Lamm, R., Duranczyk, I., Mesa, V., Kohli, N., & Ström, A. (2019). Exploring Relationships Between Number of Hours of Professional Development, Mathematics Knowledge for Teaching, and Instructor’s Ability to Make Sense of Procedures. In Graven, M., Venkat, H., Essien, A. & Vale, P. (Eds). (2019) Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol 2). (pp. 464 – 471) Pretoria, South Africa: PME.

Lim, D., Kimani, P., Duranczyk, I. M., Watkins, L., Gerami, S., Breit-Goodwin, M., & Cawley, A. (2020). Connecting Across Representations in Community College Algebra: Lessons From the Classroom. MathAmatyc Educator, 12, 12 - 20.

Mali, A., Cawley, A., Duranczyk, I, Mesa, V., Ström, A., & Watkins, L. (2019). Identifying sense-making in algebra instruction at U.S. post-secondary colleges. In U.T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.). Proceeding of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 2586 - 2593). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University.

Mali, A., Gerami, S., Ullah, A., & Mesa, V. (2019). Teacher questioning in problem solving in community college algebra classrooms. In P. Felmer, P. Liljedahl, & B. Koichu (Eds.), Problem Solving in Patagonia (pp. 317 - 335). Dordrecht, The Netherlands: Springer.

Mesa, V., Cawley, A., Duranczyk, I., Watkins, L., & Ström, A. (2020). Characterizing classroom interactions to assess the quality of algebra instruction at community colleges. MathAmatyc Educator. 11(3), 48 - 55.

Watkins, L., Lamm, R., Kohli, N., Kimani, P., & the AI@CC Research Group (2019). Using student and instructor characteristics to predict student success in algebra courses. In U.T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.). Proceeding of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 4145 - 4152). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University.

AI@CC 1.0 (NSF ECR #1561436)

AI@CC 2.0 (NSF ECR #2000602, 2000644, 2000527, 2000566)

This material is based upon work supported by the National Science Foundation. 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.

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