Exploring K-2 Children Understandings of Visual Representations in Algebraic Reasoning

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Algebra is a foundational topic in mathematics and STEM. As research has demonstrated how arithmetic is connected to algebra, there is more need to explore how K-2 children understand and use visual representations such as graphs and tables. 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. Generalized arithmetic involves generalizing arithmetic relationships and reasoning explicitly with these generalizations. These relationships include field properties of number and operations (e.g., the Commutative Property of Addition) as well as relationships on classes of numbers, such as evens and odds. It entails reasoning about the structure of arithmetic expressions and equations rather than their computational value. The project has three guiding research questions. First, what are trajectories of learning in how grades K–2 children understand visual representations such as tables, graphs, and diagrams of algebraic relationships? Second, what features of tasks or instruction facilitate movement in students’ thinking within the trajectories? Third, what are similarities and differences in how children understand visual representations of algebraic relationships across the content dimensions of functional thinking and generalized arithmetic? The study will use a design-based research methodological framework to organize data collection via classroom teaching experiments, semi-clinical interviews, classroom observations, and children’s written work. The research will produce cognitive models that can be used to design further interventions for algebra learning in grades K-2. The Discovery Research preK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.