Thinking With Algebra, TWA

Brandon Sorge
Associate Professor
Indiana University Purdue University Indianapolis

Algebra is the gatekeeper to higher level mathematics and science courses (Domina, McEachin, Penner, & Penner, 2015; Long, Conger, & Iatarola, 2012). Without a rich understanding of algebra students will not be successful in STEM (RAND, Mathematics Study Panel, 2003) The Thinking with Algebra (TWA) Project aims to address a major need in the learning of algebra and the support of undergraduate instructors in the teaching of algebra.

This project has developed a complete curriculum on algebra to be used in beginning algebra courses at universities and community colleges. To address challenges students have faced learning algebra, the construct of algebraic structure is used in the materials to help students understand central algebraic concepts. The curriculum will be piloted and refined over multiple iterations. Two faculty workshops, one in-person and one synchronous online, for college instructors will be conducted in the summer of 2022.

Guiding Questions:
1. What impact does the curriculum unit have on students’ knowledge of algebra?
2. What impact does the curriculum have on students’ mathematics self-efficacy?
3 How effective is the professional development in preparing college instructors to use the unit with undergraduate students?

The project has two published abstracts:

Feikes, D., Walker, W. S., III., McGathey, N., & Kafle, B. (2022). Algebra readiness and algebraic structure as foundational ideas for algebraic learning. In W. S. Walker, III, L. A. Bryan, S. S. Guzey, & E. Suazo-Flores (Eds.), Proceedings of the seventh annual Indiana STEM Education Conference. West Lafayette, IN.

Feikes, D., Kafle, B., McGathey, N., & Walker, W. S., III. (2021). Thinking with algebra: A project and perspective. In W. S. Walker, III, L. A. Bryan, S. S. Guzey, & E. Suazo-Flores (Eds.), Proceedings of the sixth annual Indiana STEM Education Conference. West Lafayette, IN.

The project team has made seven presentations at conferences from NCTM to AMATYC.

A complete curriculum has been developed with 30 lessons and an instructor edition with solutions. The instructor edition contains front material explaining important concepts for providing instruction like small group work, whole class discussions, and understanding solutions. Also, pages of notes for problems and activities are included side by side with the student pages, which provide explanations about the mathematics being learned, guiding questions, and connections to algebraic structure.

Data collection is ongoing and findings from student interviews and preliminary assessment data will be included in the poster.

Broader Impacts:
Learning algebra through the lens of algebraic structure has the potential to impact undergraduates’ success in algebra, in higher level mathematics courses, and in other STEM related courses. Beyond implementation, we are interested in researching how peer-led team learning can enhance student achievement. Additionally, we are interested in researching the impact of the curriculum on a broad section of college students in different learning contexts (e.g. high poverty, rural and urban, and students traditionally underrepresented in STEM disciplines).


David Feikes, Purdue University Northwest, Westville, IN; William Walker, Purdue University, West Lafayette, IN; Natalie McGathey, Prairie State College, Chicago Heights, IL; Bir Kafle, Purdue Northwest University, Hammond, IN