A Phenomenological Study of Expert Problem Solving

I initially became interested in knowledge transfer after observing my students' general inability to use mathematical knowledge and skills in an applied (engineering) context. My personal belief was that the students should have an understanding of basic basic mathematical concepts, like integration, and be able to use them correctly to solve problems. Clearly, something was missing in my students' understanding or perhaps memory that was causing them problems in this regard. In my initial work on knowledge transfer, I found that many students did not even recognize the need to transfer knowledge and for example, to integrate to solve a problem framed in an engineering context unless they were prompted to do so. Concerned by this troubling observation, coupled with my belief that engineers should be able to both understand and apply mathematical concepts in their coursework and careers, I determined to investigate the cause of the problem and, if possible, evidence a potential solution to help students transfer mathematical knowledge into an applied (engineering) context. In this study, I examine an expert (faculty) approach to problem solving using a semi-structured, think-aloud interview protocol coupled with a thorough thematic analysis for phenomenological themes. This analysis, grounded in an existing framework of knowledge transfer, provides a rich, thick description of the knowledge transfer, and problem solving process employed by the faculty expert and serves as a useful comparative case against which student approaches to problem solving and knowledge transfer can be judged. Important findings of this study relate to the extensive use of reflective and evaluative practices employed by the faculty member at all stages of the problem solving process. These internal checks and balances are rarely observed among novice problem solvers and perhaps represent behaviors that we, as educators, should seek to impart in our students if they are to become more adaptable engineers who are better equipped to transfer their knowledge and skills across a range of contexts.