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CUF 1: Children's Understanding of Functions
This research project addresses how children in grades K-2 understand concepts associated with functions—particularly as these concepts relate to different representational tools (e.g., natural language, algebraic notation, tables, and Cartesian coordinate tools). Researchers will study how students are able to coordinate co-varying data and identify and express relationships with such data—particularly examining the connections between their thinking about recursive patterning and co-varying relationships and correspondence relationships.
The research goal for the project is to identify learning trajectories as cognitive models of how grades K–2 children learn to generalize, represent, and reason with algebraic relationships. The project will address immediate challenges facing PreK–12 STEM education concerning the need to understand how young children, at the start of formal schooling, make sense of core algebraic concepts and practices typically reserved for students in later grades.
We will examine the mathematical learning of children in grades K–2. In particular, using design research that incorporates classroom teaching experiments and semi-clinical interviews, we will address the following objectives:
- identify learning trajectories as cognitive models of how grades K–2 children learn to generalize, represent, and reason with algebraic relationships within core content dimensions (e.g., generalized arithmetic) in which these practices can occur;
- identify critical junctures in the development of these trajectories; and
- identify characteristics of tasks and instruction that facilitate movement along the trajectories.
Further, the this work will connect these trajectories to those identified in the PIs’ prior work on how children generalize, represent, and reason with co-varying relationships within the core content dimension of functional thinking. The larger goal is to assemble cognitive foundations of the development of young children’s practices of algebraic thinking across diverse content dimensions.