Abstract:

The contribution is devoted to the experiences gained during five years of intensive mentoring of students of the first year of a technical college. For more than two decades, the authors of the article have been intensively dedicated to helping weaker and very weaker university students with the transition from secondary school to higher education.

The transition from high school to college is difficult for many students, especially because of the different teaching style. This problem is exacerbated for students whose secondary school results were not at a very high level or were weak.
For students of technical universities, mathematics is one of the core subjects, the successful mastery of which is a necessary prerequisite for mastering professional subjects, which are mostly included in higher years of study.

In the introduction of the contribution, the authors focus on the description of the situation at a specific university - Faculty of Military technology, University of Defence, Brno, Czech Republic - over the years. They then discuss the experiences gained in tutoring students and the findings from supervised mathematics mentoring for technical military students.

Their experiences are very interesting and unique in many respects, because it is the only high school of this type in the Czech Republic and, above all, the specifics of a military college allow for "ordered" teaching, which ordinary colleges cannot.

Students whose results do not reach the required standard must attend 1-2 times a week for an extra 1.5 hours of teaching, where they mainly focus on supplementing their knowledge from high school. Students are tested at regular monthly intervals, so teachers and school management have a clear overview of the state of students' knowledge.

The purpose of regular testing is to give feedback on knowledge or ignorance and to the students themselves, so that they do not live in the false belief that their knowledge is satisfactory.

The article also contains examples of students' mistakes, their ignorance, and reflects on changing teaching procedures so that the learning objectives are met, but the teaching is more attractive to students.
The aim of the paper is mainly to share the acquired experience and exchange experience with colleagues-university teachers from other countries.

Keywords:

Education, mentoring, mathematics education.