Математичне моделювання процесу вироблення електроенергії газотурбінними електростанціями

Наведені результати дослідження процесів вироблення електроенергії автономними газотурбінними електростанціями, з використанням обґрунтованої математичної моделі лінійних випадкових процесів, а також результати статистичної обробки реалізацій вироблення електроенергії.The results of investigations of self-power generation gas turbine power plants, using reasonable mathematical model of linear random processes with discrete time and the results of statistical processing implementations generate electricity

Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction

Structural induction is a proof technique that is widely used to prove statements about discrete structures. Students find it hard to construct inductive proofs, and when learning to construct such proofs, receiving feedback is important. In this paper we discuss the design of a tutoring system, LogInd, that helps students with constructing stepwise inductive proofs by providing hints, next steps and feedback. As far as we know, this is the first tutoring system for structural induction with this functionality. We explain how we use a strategy to construct proofs for a restricted class of problems. This strategy can also be used to complete partial student solutions, and hence to provide hints or next steps. We use constraints to provide feedback. A pilot evaluation with a small group of students shows that LogInd indeed can give hints and next steps in almost all cases.Comment: In Proceedings ThEdu'19, arXiv:2002.1189

Data from an experiment comparing restricted and elaborated feedback

Logs of student activity and diagnose and results of pre test and post test from a comparison of the effects of elaborated and restricted feedback in LogEx, a tool for teaching rewriting logical formulae

A Domain Reasoner for Propositional Logic

An important topic in courses in propositional logic is rewriting propositional formulae with standard equivalences. This paper analyses what kind of feedback is offered by the various learning environments for rewriting propositional logic formulae, and discusses how we can provide these kinds of feedback in a learning environment. To give feedback and feed forward, we define solution strategies for several classes of exercises. We offer an extensive description of the knowledge necessary to support solving this kind of propositional logic exercises in a learning environment

A pilot study of the use of LogEx, lessons learned

LogEx is a learning environment that supports students in rewriting propositional logical formulae, using standard equivalences. We organized a pilot study to prepare a large scale evaluation of the learning environment. In this paper we describe this study, together with the outcomes, which teach us valuable lessons for the large scale evaluation

A domain reasoner for propositional logic

Students learn propositional logic in programs such as mathematics, philosophy, computer science, law, etc. An important topic in courses in propositional logic is rewriting propositional formulae with standard equivalences, and the application of this technique in exercises on rewriting a formula in normal form, proving the equivalence between two formulae or proving that a formula is a consequence of a set of formulae. Existing learning environments for propositional logic offer limited feedback and feed forward. This paper analyses what kind of feedback is offered by the various learning environments for rewriting propositional logic formulae, and discusses how we can provide these kinds of feedback in a learning environment. To give feedback and feed forward, we define solution strategies for several classes of exercises. We offer an extensive description of the knowledge necessary to support solving this kind of propositional logic exercises in a learning environment. This description serves as an illustration of how to develop the artificial intelligence for a particular domain

A domain reasoner for propositional logic

Students learn propositional logic in programs such as mathematics, philosophy, computer science, law, etc. An important topic in courses in propositional logic is rewriting propositional formulae with standard equivalences, and the application of this technique in exercises on rewriting a formula in normal form, proving the equivalence between two formulae or proving that a formula is a consequence of a set of formulae. Existing learning environments for propositional logic offer limited feedback and feed forward. This paper analyses what kind of feedback is offered by the various learning environments for rewriting propositional logic formulae, and discusses how we can provide these kinds of feedback in a learning environment. To give feedback and feed forward, we define solution strategies for several classes of exercises. We offer an extensive description of the knowledge necessary to support solving this kind of propositional logic exercises in a learning environment. This description serves as an illustration of how to develop the artificial intelligence for a particular domain

A domain reasoner for propositional logic

An important topic in courses in propositional logic is rewriting propositional formulae with standard equivalences. This paper analyses what kind of feedback is offered by the various learning environments for rewriting propositional logic formulae, and discusses how we can provide these kinds of feedback in a learning environment. To give feedback and feed forward, we define solution strategies for several classes of exercises. We offer an extensive description of the knowledge necessary to support solving this kind of propositional logic exercises in a learning environment

An interactive tool for manipulating logical formulae

Logic is constructive in nature, and in a course on logic a student learns how to manipulate logical formulas. For example, a student has to learn how to simplify a logical formula, how to transform a logical formula into disjunctive normal form (DNF), and how to prove equivalences of logical formulae. Solving logical exercises is often done with pen and paper, but e-learning tools offer great possibilities. In particular for a distance learning university such as the Dutch Open University it is important to support the interactive construction of solutions to logical exercises. Currently all exercises and solutions can be found in our lecture notes for the courses that teach logic

Generation and Use of Hints and Feedback in a Hilbert-Style Axiomatic Proof Tutor

This paper describes LOGAX, an interactive tutoring tool that gives hints and feedback to a student who stepwise constructs a Hilbert-style axiomatic proof in propositional logic. LOGAX generates proofs to calculate hints and feedback. We compare these generated proofs with expert proofs and student solutions, and conclude that the quality of the generated proofs is comparable to that of expert proofs. LOGAX recognizes most steps that students take when constructing a proof. Even if a student diverges from the generated solution, LOGAX still provides hints, including next steps or reachable subgoals, and feedback. With a few improvements in the design of the set of buggy rules, LOGAX will cover about 80% of the mistakes made by students by buggy rules. The hints help students to complete the exercises