Abstract:

Many countries and universities try to increase the number of students studying Information Technology and Computer Science. It means also that we now need to teach students with a weaker average level than before. They need more tasks on elementary topics, more detailed and timely feedback about their decisions, constructions and transformations. The necessity to provide them with immediate feedback makes us look for a possibility to use computers for applicable types of exercises.

Curricula in computing-related specialties usually contain at least some elementary introduction to graph theory and relations. Simplest level of computer-assisted exercises can be assigned in form of quiz questions (under some general-purpose or mathematical quiz system) where the student enters only the answer and the program accepts it or displays an error message. There exists also courseware for several more advanced topics: graph algorithms, proofs of the properties of relations. The paper describes our pilot project for creating interactive solution environment for exercise types that are routine but need a more special approach than the quiz systems: the answer itself is a complex structure (graph, matrice etc), for creating intelligible feedback it is desirable to analyze solution steps or the answer together with some reasoning etc.

In our project we have extracted 13 exercise categories that are first candidates for computerization. Among them are transforming a graph from one data representation (sets of vertices and pairs, graphical representation, adjacency matrix, incidence matrix, …) to another, marking/building of definite subgraphs (paths, cycles, cliques, complement graphs, …), building a graph having given values of quantities (number of vertices and edges, degree sequence etc), …, building relations having certain subset of classical properties (reflexivity, symmetry, antisymmetry,…), building result of relation operations (set-theoretical operations and composition) or closure of a relation.

Our package consists of teacher and student programs. For building them we have designed user interface panels for entering and editing of different mathematical structures: matrices, graphs, degree sequences etc. At current pilot stage 11 exercise types are implemented for experiments. These types cover different input panels but authors have also tried to implement some mathematically or algorithmically nontrivial tasks (application of Erdös-Gallai theorem, detection of isomorphism).

The paper presents our choice of task types, graphical interface panels, task composition, solution interface, checking of answers/solutions, random generation of concrete task instances, teacher tools for reviewing student solutions and mistakes.

Keywords:

Interactive exercise environment, graph theory.