Engaging students in conjecturing through homework in Real Analysis and Differential Equations

TL;DR

This paper discusses implementing discovery-oriented, conjecture-based homework tasks in Real Analysis and Differential Equations courses, highlighting their design, student engagement, and positive assessment outcomes.

Contribution

It introduces a new, simplified task design for conjecturing activities suitable for homework in advanced mathematics courses.

Findings

Students engaged in conjecturing, refuting, and proving tasks.

Positive feedback and assessment outcomes from students.

Tasks are adaptable for homework due to limited complexity.

Abstract

In this note we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task-design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework assignments. In addition to several concrete examples we also discuss feedback and assessment outcomes of our students.