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Ítem Combining interactive and automatic reasoning in first order theories of functional programs(SPRINGER, 2012-01-01) Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónWe propose a new approach to the computer-assisted verification of functional programs. We work in first order theories of functional programs which are obtained by extending Aczel's first order theory of combinatory formal arithmetic with positive inductive and coinductive predicates. Rather than building a special purpose system we implement our theories in Agda, a proof assistant for dependent type theory which can be used as a generic theorem prover. Agda provides support for interactive reasoning by encoding first order theories using the formulae-as-types principle. Further support is provided by off-the-shelf automatic theorem provers for first order logic which can be called by a program which translates Agda representations of first order formulae into the TPTP language understood by the provers. We show some examples where we combine interactive and automatic reasoning, covering both proof by induction and coinduction. © 2012 Springer-Verlag Berlin Heidelberg.Ítem Implementing an active learning platform to support student learning in a numerical analysis course(Institute of Electrical and Electronics Engineers Inc., 2017-01-01) Zabala F.J.C.; Parker H.E.; Vieira C.; Zabala F.J.C.; Parker H.E.; Vieira C.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónClassroom instruction in the 21st century needs to incorporate innovative, research-based pedagogies. The engineering classroom is currently experiencing a shift towards more active learning activities due to both advances in educational research, and advances in technologies that enable practices such as the flipped classroom model. Given that course transformation is a gradual process that begins at the level of the instructor, educators need access to the essential tools and training in order to introduce these changes into the curricula. This paper introduces a course re-design based on Self-Determination Theory and Constructivism; and outlines effectively implemented active learning strategies using the flipped classroom model. The data were collected from a Numerical Analysis course, which is an important course across several engineering disciplines at Universidad EAFIT. This course enables engineering students to solve complex problems using mathematical and computational methods. This paper describes the implementation of an online active learning platform called "Numérico Interactivo" for two related engineering courses: Numerical Analysis (NA) and Numerical Processes (NP). The platform was available to all students, but only NA implemented it using a flipped classroom model. NP made the platform available as an optional course tool. Informed by SDT principles, "Numérico Interactivo" includes a variety of instructional materials such as explanations, examples, frequently asked questions (FAQ), self-assessment tools, and evaluation. This study compares the two courses in terms of: (1) students' perceptions about the instructional materials of the course; (2) students' use of the platform; and (3) students' perceived usefulness of the different elements within the platform. Results suggest that students in the NA course found the classroom sessions and the homework assignments more useful as compared to the students enrolled in the NP course. In addition, in the NA course students used the platform more often for class preparation and to study before each module. The way in which the platform was implemented in NA also increased student motivation in the course. Overall, the results suggest that "Numérico Interactivo" is useful to implement course re-designs into engineering and computing education courses, but such tools need to be guided by active learning practices so that students can fully benefit from them. © 2017 IEEE.