The Calculus Concept Inventory and teaching methodology reform

textUnlike fields in the humanities and social sciences, mathematics is traditionally taught through lectures in which students are expected to passively learn material. Research has shown that this didactic method leaves students with little conceptual understanding and discourages them mathematically. The Calculus Concept Inventory (CCI) is an exam which was developed to determine the impact of different teaching methodologies on students' conceptual understanding. The results have demonstrated that teaching methods which fall under the category of Interactive Engagement have the largest positive impact on conceptual knowledge. These methods actively engage students through social interactions with their peers and instructors in addition to providing immediate feedback and time for second attempts. The purpose of this report is to describe the current status of calculus reform and the ways in which the CCI is affecting mathematics pedagogy. For example, the University of Texas at Austin Mathematics Department has implemented flipping, an interactive engagement method delivering instruction on-line outside of class and bringing homework into the classroom.Mathematic

A Dialogue on Concepts

This short dialogue, in Socratic prose, explores some of the most fundamental constructs in cognition: Concepts, thinking and analogy. In short, concepts are the atoms of thought and analogy is the 'ether' of concept formation. Therefore, thinking is the process of triggering memories through analogy

Binding Social and Cultural Networks: A Model

Until now, most studies carried onto social or semantic networks have considered each of these networks independently. Our goal here is to bring a formal frame for studying both networks empirically as well as to point out stylized facts that would explain their reciprocal influence and the emergence of clusters of agents, which may also be regarded as ''cultural cliques''. We show how to apply the Galois lattice theory to the modeling of the coevolution of social and conceptual networks, and the characterization of cultural communities. Basing our approach on Barabasi-Albert's models, we however extend the usual preferential attachment probability in order to take into account the reciprocal influence of both networks, therefore introducing the notion of dual distance. In addition to providing a theoretic frame we draw here a program of empirical tests which should give root to a more analytical model and the consequent simulation and validation. In a broader view, adopting and actually implementing the paradigm of cultural epidemiology, we could proceed further with the study of knowledge diffusion and explain how the social network structure affects concept propagation and in return how concept propagation affects the social network.Comment: 8 pages, 3 figures (v2: typos, minor corrections in section 3.2) (v3: examples, figures added

The Methodology of Political Theory

This article examines the methodology of a core branch of contemporary political theory or philosophy: “analytic” political theory. After distinguishing political theory from related fields, such as political science, moral philosophy, and legal theory, the article discusses the analysis of political concepts. It then turns to the notions of principles and theories, as distinct from concepts, and reviews the methods of assessing such principles and theories, for the purpose of justifying or criticizing them. Finally, it looks at a recent debate on how abstract and idealized political theory should be, and assesses the significance of disagreement in political theory. The discussion is carried out from an angle inspired by the philosophy of science