A characterization of almost all minimal not nearly planar graphs

In this dissertation, we study nearly planar graphs, that is, graphs that are edgeless or have an edge whose deletion results in a planar graph. We show that all but finitely many graphs that are not nearly planar and do not contain one particular graph have a well-understood structure based on large Möbius ladders

The Role of Argumentation in Hypothetico-Deductive Reasoning During Problem-Based Learning in Medical Education: A Conceptual Framework

One of the important goals of problem-based learning (PBL) in medical education is to enhance medical students’ clinical reasoning—hypothetico-deductive reasoning (HDR) in particular—through small group discussions. However, few studies have focused on explicit strategies for promoting students’ HDR during group discussions in PBL. This paper proposes a novel conceptual framework that integrates Toulmin’s argumentation model (1958) into Barrows’s HDR process (1994). This framework explains the structure of argumentation (a claim, data, and a warrant) contextualized in each phase of HDR during PBL. This paper suggests four instructional strategies—understanding argument structures, questioning, elaborating on structural knowledge, and assessing argumentation—for promoting medical students’ argumentation in relation to HDR processes. Further implications of the proposed framework for other disciplines, such as science, legal, and engineering education, are also discussed