Middle School Students Graphing from the Ground Up (Collaborative Research: Paoletti)

Graphical representations are common in STEM fields for modeling, communicating, and analyzing phenomena, and understanding graphical representations is critical to student success in STEM fields. Yet, research indicates that many students struggle to develop an understanding of graphical representations. We contend that students’ understanding of coordinate systems, an understanding required to construct and interpret graphs, underlies their struggles to understand graphical representations and, moreover, lays the foundation necessary for developing that understanding. In this project, we examine middle-school students’ understandings of coordinate systems and frames of reference prior to examining their graph construction and interpretation. This focus allows us to design instructional materials that can support students’ graphing understandings in ways that avoid or mitigate how persistent challenges in students’ graphing understandings identified in the research literature.

The overarching goals of this project are to advance knowledge of middle school students’ developing understandings of graphs “from the ground up” with attention to underlying coordinate systems and frames of reference that comprise the coordinate systems. Three research questions guide the project: (1) What are the ways of thinking through which individual students create and interpret frames of reference, coordinate systems, and graphs? (2) In what general progressions do students develop these ways of thinking? (3) What sequence of instructional tasks support and build on students’ varied ways of thinking in their development of graphing understandings? The project addresses these questions by leveraging a design-based methodology in which we will engage in cycles of intervention and revision to develop, test, and refine cognitive models, constructive itineraries, and instructional tasks. Through several iterations of clinical interviews and small-scale teaching experiments, we intend to produce a theory that explains students’ developing graphing understandings and accounts for their varied ways of thinking. Through this process, we will iteratively design instructional tasks and task sequences that support students developing understandings for frames of reference, coordinate systems, and graphs in the widely used and freely available Desmos platform.