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This work presents six research-based elements that align with building algebraic fluency from conceptual understandings in the teaching and learning of algebra. The six elements are: symbol sense, processes/relationships of algebra, process as an object, anticipating solution strategies, anticipating solution formats, and relationships among representations. 

The Thinking With Algebra (TWA) project, which consists of a developmental algebra curriculum and supporting professional development, has been integrated into diverse algebra courses to support undergraduate students’ success in college algebra (Feikes et al., 2024). This paper examines the equity-oriented instructional practices integrated into TWA to support strengthened equity outcomes among students. This project draws on sociopolitical equity scholarship (Rubel, 2017), including a framework consisting of achievement, access, identity, and power (Gutiérrez, 2012). Instructor and student data indicate positive changes in student achievement and identity outcomes. Future directions include expanding the integration of equity-oriented instructional practices and investigation of student equity outcomes. Applying an equity lens to TWA is critical given the barriers students, particularly minoritized students, face in algebra. 

The Thinking With Algebra (TWA) curriculum, a National Science Foundation Project (DUE 2021414), applies a sociopolitical equity framework (Gutiérrez, 2012) to strengthen student participants’ mathematics achievement outcomes and mathematics identity development. Instructor and student data indicate improvements in these two dimensions. This project also expands knowledge about creating equitable math learning environments that support underrepresented students’ mathematical success. 

s research brief will share insights from using the curriculum, Thinking With Algebra (TWA), a National Science Foundation Project (DUE 2021414). The focus will be on the value of using this curriculum when working specifically with students who have taken Algebra I and Algebra II in high school, but were not prepared for college algebra or precalculus. This curriculum is specifically designed for STEM-track students who place below the level of college algebra when they enter college. The authors have found that TWA helps instructors honor the mathematical knowledge and ideas that students bring into the classroom. The curriculum units give instructors the freedom to choose the topics that suit their objectives. TWA also offers a variety of approaches to help students connect with mathematics in a new way. This brief will expand on these them students that the authors observed when teaching with this curriculum. 

Algebra readiness and algebraic structure have been core ideas in our curriculum development work to help students develop conceptual understandings of algebra. This research brief uses Kaput’s (2008) definition of algebra to describe algebra readiness and algebraic structure, as they relate to thinking about algebra and thinking with algebra. 

Thinking with Algebra (TWA) is a project to develop algebra curriculum for college classes. The overall goal is to develop curricular materials that will help prepare students conceptually for college algebra. The project is described and the importance of algebraic structure as a theoretical consideration is explained.