Exercises are held as part of a university course, and belong to a lecture. An exercise consists of combinations of the following forms:

  • Supervised "group exercises" with a group of approximately 15 course participants,
  • "Central exercises" for the participants of the course,
  • "Homework exercises" handed out in regular intervals and completed by the participants on their own.

The goal of exercises is to have students learn the syllabus-relevant skills and methods through practical experience and by working out the exercise tasks.The students themselves are actively involved in working out the problems so that they can strengthen their knowledge of how to handle the course’s subject matter.The students learn cooperative learning methods and work methods, voice their solution methods through active dialogue, and explain and discuss alternative methods. This fosters their soft skills.Through the exercises, students learn how to independently handle the typical problems based on the course’s subject matter. This skill helps them prepare for their subsequent examinations and tests.

Throughout the entire course, the exercises are designed to give students continuous feedback about how well they master the subject matter.

Different variations of exercises are currently offered. Each variation has a distinct configuration and combination of three components - group exercise, central exercise, and homework. Here we describe two variations, whose elements can also be combined:

A. Supervised classroom problems: During each group exercise session, a series of classroom problems is handed out, each of which can be solved in a very short time. These problems are solved together by several small groups of 3 to 5 students. The students discuss the problems and solution approaches and devise the solutions together. The instructors act as moderators and consultants. Some of the classroom problems can also help the students prepare for completing their independent homework, and they can address typical errors that students made in their homework. The contents of the accompanying lecture can be addressed without losing any time. The goal of this type of group exercise emphasizes active and cooperative learning.

The purpose of group exercises is not to present solutions for the homework. This is done in the central exercises, where the methodological aspects are also presented. Central exercises should not just show sample solutions, but also recapitulate the subject matter, answer subject-related questions and stimulate discussion. Sample solutions are made available in typically or electronic form. The students receive annotated feedback on all or some of the solutions they wrote for the homework problems. If the students are able to independently review their solution methods on the basis of the annotations or the model solution, then a central exercise for conveying this information is no longer necessary.

B. Homework Discussion: This type of exercise emphasizes dealing with the homework. In addition, subject matter from the lecture can be recapitulated, and the students can ask questions on the lecture’s subject matter. In particular, dealing with the homework entails developing and discussing the methodology of the solutions. Sometimes sample solutions are shown to present complete, formally exact solutions. The instructors encourage the participating students to present their own solutions and solution approaches and to open them for discussion. The instructor also corrects the written solutions and comments on them. If many students participate in the group, only some of the tasks are selected for review. In this type of exercise, a central exercise is not necessary. The goal of this type of group exercise emphasizes teaching the students how to methodically develop solutions of even very complex tasks whose scope would go above and beyond the range of classroom tasks.

Exercises can also entail hybrid forms made from variations A and B that combine the elements "discussions of subject matter," "review of selected homework problems" and "working out classroom problems" or handle them in alternating one- or two-hour tutorial sessions. One of the reasons why these hybrid forms are a fitting alternative is that this more diverse exercise type is more attractive to students.

As a rule, group exercises are supervised by tutors, academic assistants or university instructors who have participated in at least one training course on how to design exercise groups and moderate small group work. These training courses are offered by the institute once per year. The overall supervisor of the work groups encourages his team of instructors to participate in these training courses.Central exercise sessions are held by university instructors or by academic assistants.When preparing the exercises, the group supervisor ensures that the topics and issues of the exercises are closely related to the contents and time frame of the accompanying lecture (or the course that conveys the subject matter).If the course subject matter requires or strongly recommends that certain tools are used, these tools are practically applied in the exercises and not just mentioned on the side.The homework’s volume and level of difficulty are in reasonable relation to the number of hours that the exercise sessions are held. As a general guideline, we estimate this to be twice the amount of the weekly semester hours for a lecture plus the accompanying exercise. This means that for a course with V4 Ü2, an average participant in the target group should spend approximately 6 additional hours per week on pre-and post-processing the lecture and completing the homework.The homework assignments also help the students prepare for the final examination because they directly reflect the type of exam and its level of difficulty. To increase the students’ motivation for completing the homework, the instructor might include one homework problem in the final exam and announce this beforehand to the students.