Steven Jones recently had a paper titled “Identifying graphical forms used by students in creating and interpreting graphs.” published in the conference proceedings for the PMENA conference. Steven has answered a few questions about this paper below:
Who were your co-authors on this paper?
Jon-Marc Rodriguez
Who would you say is the target audience for this paper?
Secondary/tertiary mathematics education researchers
What is the big problem you hoped to address with this paper?
There is a substantial research literature on students’ understanding of and reasoning with graphs. However, most of this work is on misconceptions and difficulties, and little work has been done on documenting the productive knowledge elements students do have that they can use in graphical activity. This paper was meant to relate a framework for identifying such productive knowledge elements and to empirically catalogue a fleshed out set of these elements.
What are some of the key ideas in the article?
A “graphical form” is a specific aspect of a graph (e.g., steepness, going up toward the right, U-shape) together with an intuitive conceptual meaning for that specific aspect (e.g., rate of change, increasing, minimum value). The lens of graphical forms was used to understand how students created graphs for a variety of real-world contexts, as well as how they interpreted graphs. A significant range of forms were identified, which were clustered according to related graph aspects. For example, a point cluster included the forms, “point as instance,” “big dot as focal event,” “open/closed dot pair as existence,” and “connecting dots as transition”. In another example, a smoothness cluster included the forms “straight lines as idealized/simplified”, “curved means realistic”, “smoothness as strength of relationship”, and “jagged implies empirical data.” Other clusters were a slopes cluster, a cardinal direction cluster, a global trend cluster, a two-graphs cluster, a local feature cluster, and a position cluster.
What are some of the main ideas you hope your audience will take from the article?
We hope the audience will see that students have many productive knowledge elements about graphs that can be leveraged to create and/or interpret graphs. Increasing expertise with graph usage may include helping students activate and use these knowledge elements at appropriate times.
Abstract:
In this paper, we describe a framework for characterizing students’ graphical reasoning, focusing on providing an empirically-based list of students’ graphical resources. The graphical forms framework builds on the knowledge-in-pieces perspective of cognitive structure to describe the intuitive ideas, called “graphical forms”, that are activated and used to interpret and construct graphs. As part of the framing for this work, we provide theoretical clarity for what constitutes a graphical form. Based on data involving pairs of students interpreting and constructing graphs we present a list of empirically documented graphical forms, and organize them according to similarity. We end with implications regarding graphical forms’ utility in understanding how students construct graphical meanings and how instructors can support students in graphical reasoning.