Abstract:

Mathematics is one of those subjects, in which teaching requires illustrations of abstract theoretical concepts and relations in a suitable way on examples, with aim to help students in better understanding of connections and enable them to attain better insight to presented problems. Dynamic mathematical programs are educational tools enabling visualization of mathematical entities in the form of dynamic models. Direct interactive manipulations with models offer possibilities of heuristic approach in acquiring knowledge, while learning of theoretical data is directly connected with their practical application in the respective dynamic model. Generation of model itself and also work with it during study require a new attitude to the role of teacher and student in the educational process, change of the form of educational environment and contents of the educational process.

Active learning methods and how to introduce these in engineering mathematics is a real pedagogical challenge, as mathematical subjects are mostly accepted as necessary assumption to be fulfilled in order to graduate successfully from some engineering study program, not as a useful tool and symbolic language, or effective method for solving applied engineering problems.

Geometry courses are important for engineering studies in particular, as future engineers will work with various CAD systems, in which a steady geometric knowledge and space understanding is required, in order to manipulate generated 3D models and use these software products mostly based on commands reflecting geometric relations, objects and transformations. Therefore, it is necessary to prepare engineering students for their future work already during their university studies, using interactive applets and educational videos as didactic materials and tools using ICT.

Visualization can be regarded as a certain form of application, therefore development of visual models is also a kind of evaluation of the knowledge depth and level of understanding of the presented concept, fostering acquired knowledge and its usage, transfer of knowledge into a different context. Development of dynamic models is also an inspiration how to utilize information technologies meaningfully in the role of didactic tool, which can not only attract learners, but also enable them to realize their own creative work. Both subjects of the educational process act in this didactic situation more as equal partners, not as it is usual in the classical forms of didactic situations, where the role of teachers is active presentation of new facts and data, while role of learners is usually passive, just receiving presented facts.

Active participation of students in educational process in interesting form can contribute to better understanding and more positive approach to learning itself, which becomes more a discovery of dependencies and investigation of activities and processes than memorizing of a huge amount of incomprehensible facts and not connected data. Dynamics opens way to discover connections, and to understand mutual dependencies, which is often more important than a detailed fragmented knowledge.

We will discuss some of new challenges of teaching by introducing active learning methods, present some examples of interactive applets in dynamic mathematical software and educational videos used in teaching basic courses of university mathematics and geometry at technical university.

Keywords:

Didactics of mathematics, active learning, visualization, educational videos, interactive applets.