Steven Jones recently had a paper titled “Students’ Reasoning about Multivariational Structures” published in the conference proceedings for the conference of the Psychology of Mathematics Education – North American Chapter. Steven has answered a few questions about this paper below:
Who were your co-authors on this paper?
Haley Jeppson, a former master’s student in our program.
Who would you say is the target audience for this paper?
Math and/or science instructors, including anyone dealing with contexts that relate more than two variables/quantities together.
What is the big problem you hoped to address with this paper?
Previous work looking at students’ reasoning of changes in related quantities has focused on only two variable relationships, such as y = f(x). However, math and science often involve contexts with more than two variables or quantities, such as A = Pert, PV = kT, F = GmM/r2, or z = f(x,y). This is termed “multivariation.” This study was meant to examine the mental actions students use in reasoning about how multiple variables/quantities change in relation to each other.
What are some of the key ideas in the article?
Reasoning mental actions consisted of (1) recognizing dependence or independence among variables, (2) reducing the multiple variable context into isolated covariations, (3) using covariational reasoning to get a handle on how the pairwise, variables related, (4) switching constants and variables, (5) coordinating multiple simultaneous changes, including relative versus absolute amounts of change, and (6) coordinating these changes in a continuous manner.
What are some of the main ideas you hope your audience will take from this article?
I hope the audience can learn what mental actions are involved in reasoning about contexts with more than two related variables/quantities. I hope instructors could better see how to scaffold their students’ interpretations of, understanding of, and reasoning about these situations. I hope that researchers gain a tool for analyzing or viewing students’ reasoning about multivariation contexts.