Algebra Research

Wladis, C., & Mesa, V. (In Press). What Can Happen When Community College Practitioners Lead Research Projects? The Case of CUNY. Review of Higher Education.

Abstract: Although the majority of college freshmen enroll at community colleges, very few research studies focus on this context. In addition, what research does exist often overlooks important practitioner concerns, such as instruction. In this essay we argue that supporting generalizable education research conducted by community college practitioners can address this gap. We seek to start a conversation about the benefits of such research, to both the education research community and to educational practices at community colleges. We draw on findings from a large community college system where this kind of research has been systematically supported for the last 15 years.

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Wladis, C., Offenholley, K., Licwinko, S., Dawes, D. & Lee, J. K. (2018). Development of the Elementary Algebra Concept Inventory for the College Context. In T. Fukawa-Connelly, N. Engelke Infante, M. Wawro,S. Brown (Eds.), Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education. San Diego, CA.

Abstract: This study describes the creation and validation of the first concept inventory for elementary algebra at the tertiary level. A 22-item multiple choice/multiple answer instrument was created through a combination of literature review, syllabus review, and collaboration with instructors. The instrument was then revised and tested for content, construct and concurrent validity as well as composite reliability, using a circular process that combined feedback from experts (mathematicians, instructors, and mathematics education researchers), cognitive interviews with students, and field tests using both classical test theory and item response theory. Results suggest that the inventory is a valid and reliable instrument for assessing student conceptual understanding in elementary algebra, as conceptualized in this study.

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Wladis, C., Smith, J., & Duranczyk, I. (2017). Research on Non-university Tertiary Mathematics. In G. Kaiser (Ed.), Proceedings of the 13th International Congress on Mathematical Education. Hamburg, Germany: Springer International Publishing, 693-694.
Abstract: This paper summarizes the research presented and discussed at the ICME Research on Non-university Tertiary Mathematics Research Group.

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Wladis, C., Offenholley, K., Lee, J. K., Dawes, D., & Licwinko, S. (2017). An instructor-generated concept framework for elementary algebra in the tertiary context. In T. Dooley, V. Durand-Guerrier & G. Guedet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education, 557-558. Dublin, Ireland: Institute of Education Dublin City University and ERME.
Abstract: This study presents a framework generated by a group of experienced elementary algebra instructors describing what the fundamental concepts of elementary algebra are. An action research spiral was used to generate subsequent revisions of the framework collaboratively, in conjuction with specific conceptual assignments used with students.

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Wladis, C., Offenholley, K., Licwinko, S., Dawes, D. and Lee, J. K. (2017). Theoretical Framework of Algebraic Concepts for Elementary Algebra. In T. Fukawa-Connelly, N. Engelke Infante, M. Wawro, S. Brown (Eds.), Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education, 1510-1516. San Diego, CA.
Abstract: The long-term aim of this study is to develop a conceptual framework outlining the concepts necessary for college students to be able to successfully complete fundamental tasks of elementary algebra. The first stage of this research, which is the focus of this paper, focuses on instructor perceptions of what concepts are fundamental to successful completion of elementary algebra tasks. The framework presented here is the result of an action research project that was a collaboration among five college instructors who teach elementary algebra. Future stages of the research will include an extensive exploration of the literature as it pertains to those concepts identified by the instructors in the first stage of the research (and to enumerate concepts that might have been overlooked by the instructors) as well as cognitive interviews with students using concept-inventory-type questions to pinpoint specific aspects of student thinking included in the framework.

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