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

Uses of Technology in Lower Secondary Mathematics Education: A Concise Topical Survey

Mathematics Education; Learning; Teachin

Empirical Definition of Object-oriented Programming Competencies

International large-scale educational investigations and the focus on learners' competencies powered a veritable revolution in teaching and learning approaches as well as in educational research methodologies. In the relatively young field of computer science education research, however, there is a considerable lack of empirical studies on the definition and measurement of competencies. The central goal of the presented research project is to identify, describe, and measure competencies for object-oriented programming, in particular for implementing abstract data types. We use an automated assessment system to evaluate and score a large number of students' solutions of programming tasks. Item Response Theory analyses of the results identify subsets of tasks suitable for defining typical programming competencies. Further qualitative analyses reveal the internal structure of the competencies and allow a classification in a competency structure model. This article presents in detail our rigorous methodology and exemplary results for the empirical definition and decomposition of the competency named "Ability to implement the abstract data type Binary Search Tree"

Ask-Elle:an Adaptable Programming Tutor for Haskell Giving Automated Feedback

Ask-Elle is a tutor for learning the higher-order, strongly-typed functional programming language Haskell. It supports the stepwise development of Haskell programs by verifying the correctness of incomplete programs, and by providing hints. Programming exercises are added to Ask-Elle by providing a task description for the exercise, one or more model solutions, and properties that a solution should satisfy. The properties and model solutions can be annotated with feedback messages, and the amount of flexibility that is allowed in student solutions can be adjusted. The main contribution of our work is the design of a tutor that combines (1) the incremental development of different solutions in various forms to a programming exercise with (2) automated feedback and (3) teacher-specified programming exercises, solutions, and properties. The main functionality is obtained by means of strategy-based model tracing and property-based testing. We have tested the feasibility of our approach in several experiments, in which we analyse both intermediate and final student solutions to programming exercises, amongst others

A domain reasoner for geometry exercises

With advances in ICT around the world, digital tutors are an increasingly attractive option to provide education to a large audience inexpensively. Important components of a digital tutor include the exercises or a method to generate exercises, an algorithm for finding and verifying solutions to exercises and a method of providing hints to a student while the student is working on an exercise. The domain reasoner models all paths from the proposition(s) of an exercise to the solution(s). This enables the digital tutor to provide hints from any situation the student might encounter. This thesis contributes a method to generate a domain reasoner from an exercise solution in the domain of high school level geometry exercises. The program representing a solution to an exercise is first represented as a directed acyclic graph of which the edges represent steps in the solution. Each edge uses a formal rule to execute a step and human-readable hints are attached to these rules. Since an algorithm for generating solutions from the formal description of an exercises currently exists, this domain reasoner enables the generation of hints from just that formal description of an exercise. The exercise-specific domain reasoner enables feedforward, feedback and worked-out examples as well as a degree of adaptivity to a student's knowledge by providing hints for steps composed of smaller steps