CAREER: Covariational and Algebraic Reasoning: A New Path to Algebra

Covariational reasoning, or the ability to reason about relationships as quantities change together, is one way of thinking that can provide a foundation for students to build their more abstract algebraic knowledge. This research builds a foundation for integrating education and research at the intersection of students’ developing algebraic knowledge, covariational reasoning, and new educational technologies to create a new path into algebra. This path can help remove barriers that have historically restricted access to mathematics and STEM coursework and careers.

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For many students, algebra presents challenges that have long-term economic and social impacts, as algebra can serve as a gatekeeper for future STEM coursework and careers. Thus, it is critical for K-12 education to support all students in developing algebraic knowledge. Covariational reasoning, or the ability to reason about relationships as quantities change together, is one way of thinking that can provide a foundation for students to build their more abstract algebraic knowledge. The research builds a foundation for integrating education and research at the intersection of students’ developing algebraic knowledge, covariational reasoning, and new educational technologies to create a new path into algebra. This path can help remove barriers that have historically restricted access to mathematics and STEM coursework and careers.

To develop this new path into algebra, the project extends prior research exploring how middle-school students can reason covariationally to develop understandings for ideas critical to algebra. Two research questions guide the project: (i) How can middle-school students’ covariational reasoning serve as a foundation for their development of algebraic reasoning and knowledge? (ii) What general paths support students to develop algebraic reasoning and knowledge via their covariational reasoning? The project addresses these questions by enacting multiple phases of small-group and whole-class design-based research cycles with middle-school students. Each phase will produce new insights into students’ learning by characterizing ways individual students build their algebraic knowledge via their covariational reasoning. Comparing and contrasting individual students’ progressions will support the articulation of general paths students progress through as they develop their algebraic knowledge via their covariational reasoning. In each phase, the project will iteratively generate and test tasks situated in the free, publicly-available, Desmos platform to create a research-based sequence of Desmos activities, including teacher support materials, that have been effective in supporting students’ algebraic and covariational reasoning. These efforts will also allow for the development of principles for designing dynamic digital tasks to support students’ covariational reasoning and algebra learning.

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