Bárbara Brizuela

This project is studying how young children in grades K-2 understand mathematical concepts that are foundational for developing algebraic thinking. Researchers are contributing to an ongoing effort to develop a learning trajectory that describes how algebraic concepts are developed. The project uses teaching experiments, with researchers talking directly to students as they explore algebraic ideas. They explore how students think about and develop concepts related to covariation, representations of functions, relationships among variable, and generalization.

This project will explore how children in grades K-2 understand visual representations of algebraic concepts. For instance, children might create tables or graphs to organize information about the relationship between two quantities. They might use graphs and diagrams to explain their mathematical thinking and develop their understanding of relationships in numbers and operations. The project will use data gathered in K-2 classrooms and via interviews with children to describe their use of the visual representations. This exploratory project aims to develop learning trajectories as cognitive models of how children in grades K–2 understand visual representations for algebraic relationships.

This project will use classroom-based research to teach children about important algebraic concepts and to carefully explore how children come to understand these concepts. The primary goal is to identify levels of sophistication in children's thinking as it develops through instruction. Understanding how children's thinking develops will provide a critical foundation for designing curricula, developing content standards, and informing educational policies.

Effective “early” algebra interventions in elementary grades that can develop all students’ algebra readiness for later grades are needed. This study will use an experimental design to test the effectiveness of a Grades K–2 early algebra intervention when implemented in diverse classroom settings by elementary teachers. The broader impact of the study will be to deepen the role of algebra in elementary grades, provide much-needed curricular support for elementary teachers, and strengthen college and career readiness standards and practices.