Elements of Good Problem-Solving Tasks in Thinking Classrooms

Engineering is an interdisciplinary field that requires extensive knowledge of STEM topics. The ability to apply mathematical concepts in engineering applications is no exception. Some undergraduate engineering students struggle with early course work typically entrenched in learning underlying mathematics. Students are often able to understand engineering principles, but are unable to understand the mathematics behind the principles. This is due to students finding it difficult to make connections and apply mathematics outside of routine computational calculations.

Traditional instruction of mathematics has relied predominantly on teacher-centered pedagogies or passive learning (e.g lecture). Active learning differs in that it includes student-centered approaches and has been shown to increase student understanding in STEM courses.

The purpose of this study is to explore and discover what elements lead to good problem-solving tasks in an active learning mathematics focused classroom. Elements were determined using interviews with mathematics instructors that currently use active learning techniques and problem-solving tasks in their classrooms. Instructors were asked to describe the process they use for creating tasks. An instructor’s guidebook will be created and made available based on the findings and discoveries of this study on how to create problem-solving tasks.

The three main categories of emergent themes were task structure, task development, and problem-solving environment. The emergent themes in task structure are useful for understanding what elements make a good problem-solving task. Knowing the particular challenges previous instructors faced in creating an active-learning environment will help instructors avoid common pitfalls. These elements of creating a problem-solving environment will also be included in the guidebook as a class cannot have good problem-solving tasks without an environment conducive to active learning.