Steven Jones recently published an article titled “How Students Understand Graphical Patterns: Fine-grained, Intuitive Knowledge Elements Used in Graphical Thinking” in the Journal for Research in Mathematics Education. Steven has answered a few questions about this article below:
Who were your co-authors on this article?
Jon-Marc Rodriguez, University of Wisconsin
Who would you say is the target audience for this article?
Any math or science instructor who uses or teaches graphs.
What is the big problem you hoped to address with this article?
A lot of research on graphing has looked at "large" ideas, such as misconceptions, covariational reasoning, or disciplinary practices. But, Knowledge-in-Pieces theory claims that there would be many, small-sized, intuitive knowledge resources students develop and use in graphing practice. We call these "graphical forms." Graphical forms would constitute an important part of students' graphical thinking and reasoning, and understanding them would help instructors know what student thinking consists of, and even how to develop these ideas.
What are some of the key ideas in the article?
Using data of students constructing and interpreting a range of graphs in various contexts, we were able to identify and catalogue a large set of these "graphical forms." These forms were implicit, intuitive ideas students associated with different parts of a graph. They used these forms, often subconsciously, to piece together a graph for some scenario, and to interpret graphs. We listed and organized this large body of graphical forms in clusters according to what features of graphs they attended to.
We demonstrated how these graphical forms were key aspects of the students' activity, beyond covariational reasoning and social practice. We also showed how graphing "misconceptions" can even be re-interpreted as just using an otherwise productive graphical form at the wrong time.