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This full paper is focused on research into how educators might use concept mapping to explore and design learning experiences in a problem-based learning environment. Attempts to incorporate more open-ended, ill-structured experiences have increased but are challenging for faculty to implement because there are no systematic methods or approaches that support the educator in designing these learning experiences. In the reported work, we present an exploratory study toward a systematic approach for comparing and manipulating problems. The approach combines concept mapping with Jonassen’s characterization of problems and the forms of knowledge required to solve them. We explore manipulation pathways for a problem that can be pursued by an instructor who is interested in impacting the dimensions of structuredness and complexity. We compare similarities and differences among two problems taken from introductory aerospace engineering courses. We consider manipulation of structuredness and complexity and the change propagation in forms of knowledge and solution pathways. 

Introduction: The work reported here subscribes to the idea that the best way to learn - and thus, improve student educational outcomes - is through solving problems, yet recognizes that engineering students are generally provided insufficient opportunities to engage problems as they will be engaged in practice. Attempts to incorporate more open-ended, ill-structured experiences have increased but are challenging for faculty to implement because there are no systematic methods or approaches that support the educator in designing these learning experiences. Instead, faculty often start from the anchor of domain-specific concepts, an anchoring that is further reinforced by available textbook problems that are rarely open in nature. Open-ended problems are then created in ad-hoc ways, and in doing so, the problem-solving experience is often not realized as the instructor intended. Approach: The focus in this work is the development and preliminary implementation of a reflective approach to support instructors in examining the design intent of problem experiences. The reflective method combines concept mapping as developed by Joseph Novak with the work of David Jonassen and his characterization of problems and the forms of knowledge required to solve them. Results: We report on the development of a standard approach – a template -- for concept mapping of problems. As a demonstration, we applied the approach to a relatively simple, well-structured problem used in an introductory aerospace engineering course. Educator-created concept maps provided a visual medium for examining the connectivity of problem elements and forms of knowledge. Educator reflection after looking at and discussing the concept map revealed ways in which the problem engagement may differ from the perceived design intent. Implications: We consider the potential for the proposed method to support design and facilitation activities in problem-based learning (PBL) environments. We explore broader implications of the approach as it relates to 1) facilitating a priori faculty insights regarding student navigation of problem solving, 2) instructor reflection on problem design and facilitation, and 3) supporting problem design and facilitation. Additionally, we highlight important issues to be further investigated toward quantifying the value and limitations of the proposed approach.