Crossing the Threshold of Problem Solving: Electrical Engineering vs. Chemistry

We are conducting educational research in determining whether an abstraction threshold exists for students enrolled in different EE courses.

A Capacity Building Project in STEM (Science, Technology, Engineering and Mathematics) Learning is proposed to form the foundation for studying abstraction capacity in problem solving among undergraduate students in different STEM disciplines. The project defines the concept of an abstraction threshold as a hypothesized gap in reasoning ability that is able to be crossed by students, and seeks to characterize reasoning ability applied to problem solving using a cognitive processing model called Representation Mapping, which accounts for reasoning in terms of two main processes, rules and similarity.

The study tests two hypotheses: 1) Many students do not have fully mature processes for abstraction, i.e., cognitive supply, and it is possible to measure what their processes are and the degree to which they are capable of reasoning using abstraction. 2) Somewhere in each undergraduate STEM curriculum there exists enough of a shift on the cognitive demand side where a typical student’s current capacity for abstraction is not matched to the complexity of the problems being posed, and this impacts student performance (see Figure below).

The research questions that this Capacity Building project seeks to study are:

The arc to utility of this pursuit is two-fold: 1) if there is a course in which the abstraction threshold is most prominent, targeted interventions could increase students' proficiency in abstraction, facilitating transition across the abstraction threshold and greater success in problem solving in upper-level undergraduate STEM courses, and 2) faculty can be helped to develop stronger skills in creating assessments that build students' abstraction capacities.

Abstraction Threshold picture2.jpg Abstraction Threshold picture2.jpg Abstraction Threshold picture2.jpg Abstraction Threshold picture.jpg

The project approaches the cognitive supply hypothesis by applying the Representation Mapping framework to determine degrees to which abstraction is present in students' approaches to solving problems, and the cognitive demand hypothesis by analyzing operational tasks expected by experts (faculty) on problems students are expected to solve in their courses. With a basis in the findings from the research, the project intends to provide implications for enhancing students' development of abstraction capacities and their application to problem solving, and for faculty professional development to assess in ways that build students' abstraction capacities.

The study will be achieved through an interdisciplinary two-year Capacity Building project involving faculty and undergraduate students in electrical engineering at the University of Nebraska-Lincoln and in chemistry at the University of Massachusetts Boston. The study will examine two courses that typically occur in the sophomore and junior years of the electrical engineering curriculum and two courses that typically occur in the sophomore and junior years of the chemistry curriculum for evidence of the hypothesized abstraction threshold. This project is intended to build the capacity of the research team to conduct a more expansive study of abstraction thresholds in undergraduate STEM curricula that would be suitable for a CORE Research Proposal.

Associated Publications