Why Has Mathematics Become a Nightmare at Technical Universities?

Practice Paper Recommended citation: Gabková, J., Gužela, Š., & Halaj, M. (2025). Why Has Mathematics Become a Nightmare at Technical Universities?. In Kangaslampi, R., Langie, G., Järvinen, H.-M., & Nagy, B. (Eds.), SEFI 53rd Annual Conference. European Society for Engineering Education (SEFI), Tampere, Finland. DOI: 10.5281/zenodo.17631335. This Conference Paper is brought to you for open access by the 53rd Annual Conference of the European Society for Engineering Education (SEFI) at Tampere University in Tampere, Finland. This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License. WHY HAS MATHEMATICS BECOME A NIGHTMARE AT TECHNICAL UNIVERSITIES? Jana Gabková a, 1 , Štefan Gužela b, Martin Halaj c a Slovak University of Technology, Bratislava, Slovakia, 0009-0006-4947-3564 b Slovak University of Technology, Bratislava, Slovakia, 0000-0003-0975-2498 c Slovak University of Technology, Bratislava, Slovakia, 0000-0002-7432-7423 Conference Key Areas: Teaching mathematics and physics in engineering education Keywords: mathematics teaching, technical universities, students drop-out ABSTRACT In this paper, we would like to highlight the discrepancies between the entry requirements for applicants to study at a technical university and the requirements for completing mathematics courses in the first year of bachelor's studies. In secondary schools (especially secondary vocational schools), the time allocation for teaching mathematics is very limited, and only a small proportion of students graduate from mathematics. The composition of students applying to technical universities has changed, with graduates of secondary vocational schools currently prevailing. On the other hand, mathematics still represents the theoretical basis for most engineering courses at the bachelor's and engineering levels of study, so the faculty's engineering departments require a certain level of knowledge in mathematics from students moving on to higher years. This contradiction is manifested in the large number of students who have problems with successfully completing basic mathematics courses at the bachelor's level of study, which complicates their further studies and, in some cases, even leads to dropping out of studies. Using the example of the Faculty of Mechanical Engineering of the Slovak University of Technology, we present an overview of measures to overcome this contradiction. These include the introduction of various supporting teaching activities, the wider use of activating teaching methods, the modification of study plans and course information sheets, and the like. The text shows that despite the various activities of the faculty, which have several positive effects, the problem of students' prerequisites for successfully completing mathematics courses remains unresolved and require systematic intervention by the state. 1 Corresponding Author Jana Gabková [email protected] 1 INTRODUCTION The issue of teaching mathematics at technical universities has already received a lot of attention. This is understandable, as mathematics is one of the basic pillars for mastering engineering courses. Knowledge of mathematical procedures, principles, methods, and mathematical thinking are required at all levels of higher education. However, there is an increasing discrepancy between the readiness of secondary schools graduates to master the requirements of university mathematics at technical universities, the expectations and demands of these schools, the student's abilities to master the study requirements, as well as the procedures and approaches to help students overcome the pitfalls of university mathematics. We are talking here mainly about bachelor's degree students, where this discrepancy is most pronounced and results in a very undesirable phenomenon - drop-out of bachelor's students. Using the example of the Faculty of Mechanical Engineering of the Slovak University of Technology (FME STU) in Bratislava, we are trying to point out the fact that even though the faculty takes various types of measures to increase the pass rate of students through mathematical courses in bachelor's studies, the faculty's internal capabilities are limited and cannot fully compensate for the need for measures from the state, nor can they respond flexibly enough to changing external influences on the knowledge and abilities of applicants for study at technical universities. 2 APPLICANTS FOR STUDIES AT TECHNICAL UNIVERSITIES Currently, one in five Slovak university students studies abroad. Since 2017, the number of Slovak students studying abroad has remained roughly at the same level of around 32,000 students. Studying abroad is a popular phenomenon, which is thoroughly investigated by respective state authorities, as the number of students studying abroad has an undesired impact on the Slovak academic system. Approximately 70 percent of Slovak students who go abroad, study in the Czech Republic (Skvarenina, 2023). It is mainly highly motivated students with above-average socio-economic backgrounds who go abroad to study. In other words, students with above-average secondary school results often go abroad, which necessarily has an impact on the overall level of study prerequisites of bachelor's degree students who remain to study in Slovakia (Martinak, Varsik, 2021). Approximately half of Slovak secondary school graduates who decide to study at Slovak universities prefer to study social sciences. As can be seen from the data from the universities‘ admissions process for the academic year 2023/2024, only about 11.5% of all admitted applicants intend to study at a university of technical sciences (see Table 1). Of these, the vast majority aim at studying computer science. Table 1 illustrates the number of applicants and then students who come to the STU and its FME. Table 2 shows the composition of students who started studying at the FME STU in the academic year 2023/2024, according to the type of secondary school they came from. In that academic year, 37.2% of secondary grammar school graduates and 61.8% of secondary vocational school graduates started studying. However, the same table also shows the very unfavourable fact that 40.2% of secondary grammar school graduates and up to 62.5% of secondary vocational school graduates left the faculty after the first year. In both cases, this is an alarming number, which, however, has been approximately repeated for almost the entire last decade, as is the ratio of dropouts according to the type of secondary school they studied at. The main reason for dropping out is the failure to master mathematics in the courses of the first year of the bachelor's degree. In the last four academic years, STU Academic Information System indicates that the number of students failing in mathematics exams always exceeded the number of students who left the FME in the first academic year. This fact confirms that passing mathematics is one of the major concerns in successful completing the first academic year at the FME STU. Table 1 Applicants and students at the FME STU for 2023/2024 (Antalikova, 2024) Plan Applicants Accepted Enrollment Enrolled/Admitted STU in Bratislava 4680 4193 3207 2476 0.77 FME STU 530 331 257 211 0.82 Table 2 Success rate of studies at the FME STU in the academic year 2023/2024 Secondary grammar school Secondary vocational school Another type of school Total Number of studies initiated 82 136 2 220 Dropped out after the 1st semester 12 57 2 71 Dropped out after the 2nd semester 21 28 - 49 Dropped out after first year / % 40.2 62.5 100 54.5 Let's take a closer look at the issue of insufficient knowledge of mathematics among applicants to technical universities, which is reflected in the high dropout rate of students in the first year of bachelor's studies. We will demonstrate this issue using the situation with students at the FME STU. 3 KNOWLEDGE OF MATHEMATICS AMONG UNIVERSITY APPLICANTS A survey by the Slovak Mathematical Society among the technical universities representatives was conducted in Slovakia in 2019 on the mathematical knowledge and skills requirements of university applicants (Bederka et al., 2019). In summary, they are required to: 1. know the essence of mathematical knowledge - understanding is most important, 2. use the language of mathematics to express mathematical ideas, 3. master the capabilities for solving tasks and mathematical problems, 4. know the application of specific mathematical courses outside of mathematics, 5. be able to justify the truth of statements using specific examples, 6. have the belief that mathematics is a universal activity necessary for the development of society. The content of the secondary school Matura (see following text) is in line with these requirements, so one can assume that after successfully completing the high school Matura, the student will have no problem completing mathematics at university. 3.1 Matura in mathematics Matura is a Latin name for the secondary school graduating exam in various European countries, Slovakia included. Of course, successful passing of Matura in mathematics is not the only criterion by which a student's prerequisites for successfully completing mathematics at a technical university can be characterized. However, it provides a very clear insight into how popular mathematics is among secondary school graduates and how many of them dare to take an exam in it, certifying their acquired knowledge. Student of a secondary grammar school (that prepares for the further university study) takes Matura in mathematics as an optional exam (student selects mathematics from a group of scientific subjects) or as a voluntary exam (mathematics exceeds a mandatory number of four Matura subjects). Student of the secondary vocational school (that prepares for direct employment at the labour market) can take the Matura in mathematics as a voluntary exam only (Cipkova Hamplova et al., 2024). The Minister of Education announced in 2025 that the ministry wants to extend a compulsory Matura in mathematics to all secondary grammar schools and secondary vocational schools with a technical focus. Since other measures are also linked to the compulsory Matura in mathematics, the expected timeframe for the introduction of a compulsory Matura in mathematics is approximately 10 years (Ministry of Education, Research, Development and Youth of the Slovak Republic, 2025). In 2024, a total of 40,950 students graduated, of which 36.8% were from secondary grammar schools, 57.8% from secondary vocational schools, and the rest from other types of schools (National Institute for Certified Educational Measurements, 2025). The Matura in mathematics was taken by 4,779 students, which is only 11.7% of all secondary school graduates. Of these students, 74.2% were from secondary grammar schools, and 24.8% from secondary vocational schools. An analysis of the 2024 Matura in mathematics results revealed that, at a strong significance level, the following holds true: a. secondary grammar school students achieved better results than secondary vocational school students, b. students graduating with mathematics as an optional exam achieved better results than students taking Matura in mathematics voluntarily. For comparison, in 2009, a total of 9,250 students took the Matura in mathematics, which is approximately 15.2% of all 60,732 secondary school graduates. At the same time, students from secondary grammar schools achieved better results than students from other secondary schools at the medium level of significance. If we summarize the information from 2009 and 2024 (which is a time span of 15 years), only half of the students currently graduate in mathematics as they did fifteen years ago (in absolute numbers), while at the same time, the difference in results between students from secondary grammar schools and secondary vocational schools has increased significantly compared to fifteen years ago. 3.2 Time allocation for teaching mathematics in secondary school The state curriculum for secondary grammar schools prescribes that 12 hour of mathematics be taught (per week) throughout the entire study period. Moreover, students can add additional mathematics hours in the third and fourth years within the available hours, and a mathematics seminar in the final year. This means that there is a space to prepare students for the Matura in mathematics. In secondary vocational schools, there are only 6 hours of mathematics and computer science per week for a total of 4 years, additional hours can be added from the 28 available hours. However, these are primarily used for other courses, not for teaching mathematics. There is no space here for preparation for the voluntary Matura in mathematics. Moreover, the school does not receive any financial resources to introduce, for example, an optional course for preparing for mathematics. And here comes the problem. The student applies for university, but the content and scope of mathematics teaching, especially at secondary vocational schools, do not correspond to the preparation for university, nor can it, because the study is supposed to be preparation for practice. However, this student is accepted to university because he/she successfully passed the Matura. Technical universities usually do not conduct entrance exams, and then there is a problem for all parties. 4 TEACHING MATHEMATICS AT THE FME STU At the FME STU, in total 12 courses related to mathematics are taught at the bachelor's level. In total, there are 27 hours per week for the entire study period in the case of compulsory and compulsory elective courses and 14 hours per week for elective courses. They have different time allocations, and a different number of credits are obtained to complete them. In any case, the biggest problem for bachelor's students at the FME STU is completing two basic courses in the first year - Mathematics I (winter semester) and Mathematics II (summer semester). In terms of content, these two courses are related to each other. The course Mathematics I in the winter semester is a mandatory course for all firstyear students of the bachelor's degree. The curriculum covered is directly related to the areas of Matura in mathematics. The syllabus of the course Mathematics I therefore assumes a certain level of entry knowledge, on which the students build and based on which new curriculum is covered. The success of completing the course Mathematics I is therefore directly correlated with the level of knowledge that students bring from their previous studies at secondary school. The compulsory course Mathematics II is taught in the next semester, and it follows Mathematics I. Since the topics covered are not based on the initial knowledge from secondary schools, the determining factor for successfully mastering this course is the successful completion of the previous course Mathematics I. As the study results statistics show, students do not have any major problems with completing other mathematics courses. Therefore, all efforts related to increasing the students' progress to the next year are largely focused on successfully completing Mathematics I and Mathematics II. As an example, take a successful passing the course Mathematics I in the first semester of bachelor's studies in the academic year 2024/2025. Of the 314 students who started studying the first year of bachelor's studies, only 158 students (50.3%) met the requirements for taking the exam in Mathematics I at the end of the semester, 139 students (44.3%) did not meet those requirements, and 17 students dropped out during the semester (5.4%). Of the 158 students who met the requirements for taking the exam, 81 students (51.2%) successfully passed the exam, 32 students (20.3%) failed on three exam dates, 30 students (19%) did not use all the retake dates, and 15 students (9.5%) are allowed on an additional retake date. Therefore, only 25.8% of the students who started their studies at the beginning of the semester passed the Mathematics I on the regular exam date! 5 SUCCESSFUL MASTERY OF MATHEMATICS 5.1 Influences on successful mastery of mathematics Let us summarize here the individual influences that affect the ability of secondary school graduates not only to successfully complete their studies in mathematics at the bachelor's level of study at technical universities but also to choose such studies: a. Secondary school graduates with the best study prospects often go abroad. b. Low interest in studying technical subjects at universities prevents a thorough examination of entry knowledge and the sorting out of applicants with insufficient study prerequisites. The vast majority of technical faculties do not hold entrance exams and accept all applicants for study. c. Graduates of secondary vocational schools, where the number of hours allocated to teaching mathematics is very low, mostly apply to technical universities. There are fewer graduates of secondary grammar schools than in the past. d. A low percentage of secondary school graduates complete the mathematics exam, and there is a large difference in the results achieved between graduates of secondary grammar schools and secondary vocational schools. e. Distance learning during the COVID-19 pandemic has a specific impact, with this impact continuously being felt by students entering higher education institutions. Among other restrictions, the Matura was also cancelled at this time. Added to these are the objectively existing general influences on students brought about by changing times. The following points are observed at the FME STU by university teachers at most of the study courses, and fully apply to mathematic courses. These observations are regularly discussed at the faculty and university fora and also widely confirmed in personal exchange with teachers from the other technical universities in Slovakia. These are then also reflected in their poorer ability to master mathematics: a. Available technical means – currently, students have the initial impulse to search for all information and solutions on the Internet or to use artificial intelligence to solve problems. For example, the abolition of final theses is being considered. Students' first impulse is not an effort to think but an effort to use existing solutions with the least effort, the so-called "looking at the Internet" b. Reduced number of direct teaching hours per week – in the past, the faculty had approximately 30 hours of direct teaching per week; now it is approximately 20 hours of direct teaching hours per week. The emphasis is shifting from direct teaching to indirect teaching, which, with evident problems of some students with learning, further exacerbates the problems of a large group of students not fulfilling the requirements of teachers. c. Students don't know how.to learn. After moving from secondary school to university, they have problems with organizing their studies, adhering to a regular schedule of indirect teaching, different demands at university, a higher pace of knowledge acquisition, and an emphasis on independent study. d. Reduced ability of students to independently solve problems, read with comprehension, and formulate general tasks using mathematical means. This is manifested mainly in follow-up engineering courses that require students to solve their problems and formalize general tasks into a mathematically solvable form e. Reduced ability of students to synthesize knowledge from multiple learning areas and transfer it within or outside mathematics. This is also related to the low ability to use previously learned material in the later stages of the semester. However, the problem is often also on the university's side: a. Insufficiently flexible adaptation to the changing composition of incoming students, the level of their initial knowledge, study prerequisites, and abilities. b. Ambiguous definition of the content of mathematics studies at the bachelor's level. Almost all bachelor's level students continue to engineer studies, so in higher grades, a different composition of mastered mathematics knowledge is required than when students complete their studies after the bachelor's level. 5.2 What can and does the faculty do? The low passing rate in mathematics in the first year of study regularly and frequently appears at meetings of various faculty bodies. The faculty management has been paying due attention to this problem for a long time and is trying to define measures to manage the unfavourable situation. Regular consultations are held with mathematics teachers as well as with students, while appropriate forms of support for students are constantly sought. The principle of maintaining the established level of students' knowledge and not lowering qualitative requirements is constantly emphasized, and support mechanisms are being sought to help students. In the academic year 2023/2024, the following measures came into effect: a. In parallel with the courses Mathematics I and II, the elective courses Supplementary Exercises in Mathematics I and II are taught. The aim is to supplement any deficiencies from secondary school, deepen the understanding of the subject matter covered, and prepare for the mathematics exam. b. In September, before starting studies, the faculty offers a week-long course in secondary school mathematics, five hours a day. Students pay for their participation themselves (50 euros per week). The course was generally well received, but the problem is that in several cases students who supposedly did not need it participated, but there were fewer students who needed such a course. c. In addition to the elective courses, informal tutoring is organized, which many students have started to attend. This tutoring is led by a university mathematics teacher and is not included in the official study plans. d. In mathematics teaching, activating teaching methods are widely introduced (especially EduScrum, problem-based learning). These methods are also addressed in several grant projects at the faculty, while faculty staff are also successfully involved in international research teams in this area. Future measures include: a. Introduction/strengthening of an introductory seminar before the start of studies. b. In the new study program structure being prepared, the mathematics curriculum will be divided into more semesters than now, with the first semester intended to consolidate students' initial knowledge of mathematics and the start of teaching new mathematics topics will be postponed to the second semester. c. Grading of students according to the mathematics entrance test will be introduced, and students with weaker results will be required to have some additional mathematics instruction. d. The content of the course taught is updated to more effectively meet the changing requirements of engineering courses in later years of study. e. The widespread application of modern teaching methods will also be supported. f. Consultations with secondary school mathematics teachers are planned to better connect the requirements of universities with the possibilities of secondary schools. 5.3 Has there been any improvement yet? The measures introduced are just beginning to take effect and have not yet significantly changed the situation. Signs of improvement can be seen rather in the more positive attitude of students and an increase in their positive motivation: a. Improved grades of students who successfully passed the math exam, b. Students attend additional math exercises to a greater extent, but they also attend more consultations and informal math education. What is important is that they have realized that they need to solve examples to acquire specific skills. c. Students' independent work on mathematics exercises has improved. d. Activating teaching methods are being used more widely. EduScrum is a group method in which students have become accustomed to group problem solving, so they now form more groups and help each other solve examples before the exam and prepare for the exam together. e. Students have access to a variety of support materials in the university's academic information system, which they increasingly use for independent study. 5.4 What should the state do? According to (Vancikova, 2020), when teaching mathematics, it is necessary to define, adopt, and implement systematic measures aimed at: 1) teachers at all levels of schools (teacher training and increasing their number); 2) teaching mathematics (modern practices, increasing the efficiency of education); 3) students (supporting the improvement of study results); 4) legislative framework (increasing the hourly subsidy at secondary vocational schools, mandatory mathematics graduation). These are also the measures that representatives of technical universities, together with directors of secondary vocational schools, are calling for the most at present. This is especially point 4, which is fully in the hands of political representation. Recruiting mathematics teachers at universities is also becoming a major problem. It cannot be stated that the situation with the knowledge of secondary school graduates applying for studies at technical universities has improved significantly since 2019. The fundamental problem is the overall insufficient emphasis of the state on supporting technical education. Support in this direction must begin in elementary schools. Even though universities regularly comment on the readiness of secondary school graduates to study at technical universities, employers also express their views, the situation has not changed yet. 6 CONCLUSION The paper describes the situation with the problem of a low pass rate of bachelor's students at the FME STU through mathematical courses. Changing entry requirements (students' knowledge and skills, composition of applicants for study), external influences (hourly allowance for teaching mathematics, required knowledge and skills), and technical progress (available software tools, artificial intelligence), all necessarily affect the approach of teachers and faculty management to teaching mathematics and requires a high degree of flexibility of teachers at the faculty to cope with these changes (not only in mathematics). At the same time, it is true that even a high degree of flexibility of the faculty cannot replace some necessary state interventions (subsidy of mathematics hours in secondary schools, Matura in mathematics), so the argument about the insufficient adaptability of universities to the changing conditions in which they operate does not hold up. The problems with completing mathematics courses at the bachelor's level of study at the FME STU also confirm the generally valid conclusion (Vancikova, 2020) - the quality of higher education in the coming years will not be determined by the quality of incoming students but by its ability to adapt to new conditions so that universities are able to provide quality education and at the same time serve an increasingly diverse group of students. Authors intend to refer to the adopted measures and their effectiveness at the next SEFI events. 7 ACKNOWLEDGMENT This paper was created with the support of the Cultural and Educational Grant Agency (KEGA), grants number 025STU-4/2024 and 016STU-4/2025.