Engineering mathematics: An investigation of students' mathematical thinking from a cognitive engineering perspective

Although mathematics is considered to be a fundamental element of engineering education, little empirical research has been conducted to understand how engineering students actually use mathematics. This project takes a research-informed approach towards understanding the role of mathematics in engineering design by combining two studies of industrial engineering students' use of mathematical thinking: a mixedmethods study of engineering students' use of mathematics during capstone design projects and a study of industrial engineering students' use of mathematics during a laboratory-based design problem. In the language of cognitive engineering, the dissertation consists of a thorough user-needs analysis (the studies of engineering students' use of mathematics in capstone projects and during a laboratory-based task) and provides some insights into design specifications and recommendations for the design of a tool to support engineering students' integration of mathematics in engineering design.;Mathematical thinking is identified and categorized using Schoenfeld's five aspects of mathematical thinking: knowledge base, problem solving strategies or heuristics, effective use of resources, beliefs and affects and mathematical practices. Additionally, the engineering students' design behavior is investigated using Atman and Bursic's design process coding scheme.;The capstone study investigated engineering students' use of mathematics during one of their first real-world design projects through observations of five industrial engineering student' team meetings and individual interviews with each team member. An additional five students from other engineering disciplines were interviewed. For the laboratory based study, nine industrial engineering students "thought-aloud" while completing a three-hour design task.;Findings from the studies indicate that engineering students engage in mathematical thinking in a variety of manners throughout their design processes. For example, many students use problem solving strategies that they learned from mathematics course in their design projects. Additionally, engineering students engage in mathematical thinking far more than they believe they do. These studies also revealed a number of challenges that engineering students face, including difficulty in dealing with uncertainty and using mathematical modeling as an approach for dealing with uncertainty.;The results of this project afford rich insights into engineering students' mathematical thinking, relevant for engineering educators as they consider the integration of mathematics into engineering design.