"The theorem says...": Engineering students making meaning of solutions to Ordinary Differential Equations.

There is a need for further studies on students' learning of Differential Equations (DEs), especially in advanced undergraduate and graduate courses. Research on the mathematical education of engineers shows a conflict between students' demands for practical, contextualized pedagogies and the need for abstract reasoning and appropriate use of mathematical results. Few papers focus on engineering students' interpretation of theorems and their use as tools in argumentation and problem-solving. This paper takes a sociocultural stance on learning and employs dialogical inquiry – a methodology rooted in Bakhtinian theory, newly developed for collaborative inquiry and qualitative data analysis – to investigate the meanings that senior engineering students made while working on a task designed to evaluate their understanding of Existence and Uniqueness Theorems (EUTs) of solutions of DEs. We identified two important epistemological disconnections that explain the difficulties that some of our students faced in making meaning of solutions of DEs and the EUT. • There is a need for more studies on the learning of Differential Equations (DEs). • Few research papers focus on students' meaning-making of theoretical results in DEs. • Dialogical inquiry methodology was used to analyze students' meaning-making processes. • Two epistemological disconnections were found that explain students' difficulties. • The use of warrants in students' dialogue was important in their meaning-making. [ABSTRACT FROM AUTHOR]