How Students Construct Sophisticated Differential Equations to Model Real-World Contexts

Steven Jones and a former BYU Master’s student, Omar Naranjo, recently published an article titled “How Students Construct Sophisticated Differential Equations to Model Real-World Contexts” in the International Journal of Science and Mathematics Education. Steven has answered a few questions about this article below:

Who would you say is the target audience for this article?

Mathematics, Science, and Engineering Educators

What is the big problem you hoped to address with this article?

Modeling real-world phenomena with differential equations is often a complicated endeavor, with lots of ideas, reasonings, meanings, symbols, and relationships that have to be managed. This paper attempted to better understand the actual student cognition involved in constructing a DE model for a given real-world context.

What are some of the key ideas in the article?

We examined students modeling different types of contexts, including a mechanical context, a hydraulic context, and an electrical context. We looked at (a) students' "readouts", or how they "read" a context and extract information from it, (b) students' "inferential nets", or how they make inferences from readouts to knowledge elements, or from one knowledge element to another, and (c) students' overall strategies that guided their work. Our results identified many specific readouts and knowledge elements used in the students' work, and we constructed knowledge use flowcharts to document the students cognitive activity. We also identified four distinct guiding strategies the students used, including a diagram-based strategy, a components-based strategy, an equation-based strategy, and a math-operation-based strategy.

Abstract:

Differential equations (DEs) are a powerful tool for modeling real-world contexts. Most research in this area has examined students’ understanding and reasoning with pre-packaged DEs, with little attention being given to setting up sophisticated DEs to model complicated real-world situations. This study contributes through a collective case study on how individual students constructed DEs for various real-world systems, including a mechanical, a hydraulic, and an electrical system. We examined the students’ readouts (how they “read” a context), their inferential nets (inferences across knowledge resources), and their strategies (what guided their work), according to coordination class theory. Our study contributes the foundation of a knowledge base in students’ DE modeling that further research and teaching work can build on.