Pedagogical science has examined teaching and learning processes for centuries. There are no simple answers to the questions “how do we learn” and “how do teachers can enforce the students’ learning”. This is because education deals with specific differing purposes and contexts and with students as people, who are diverse in all aspects and ever changing ^[1]. We are always looking for appropriate and accountable teaching processes which can never be suitable for all students. Those processes respect the equality but not the equity, as they refer to the standard performance and the most preferable situations. Each special case is not a part of the “typical” or the “preferable”.

In the case of higher education, students bring with them different experiences, knowledge, backgrounds, motivations and expectations as a result of their previous school life. They are characterized by different cognitive and learning styles. Academic teachers need to take all those aspects into consideration, as their students experience the same teaching processes offered in different ways and consequently with different learning results. Student learning outcomes encompass a wide range of attitudes, beliefs, self-efficacy beliefs, knowledge and skills. Those abilities are both cognitive and affective, and they are indicative of how their learning experiences have supported students’ development as learners ^[2].

Teaching mathematics to engineering students in higher education has been discussed for many years by academics in the fields of engineering mathematics. Recently (2021), the “International Journal of Research in Undergraduate Mathematics Education” published a special issue with studies about the difficulties, the students’ performance and the intervention programs for the improvement of the teaching of mathematics in engineering courses. What is implemented is due to academics’ knowledge, beliefs and skills. Professional development is widely recognized as a necessary condition for the competitiveness of organizations ^[3]. Changes in higher education make the development of academics’ teaching skills a priority ^[4]. Insufficient professional development of academics creates a considerable risk to the quality of higher education. InA our opinion, a ppart of this discussion needs to be related to issues concentrating on how weresearchers can take into consideration students’ interindividual differences in terms of their beliefs, self-efficacy beliefs, conceptions about mathematics and their performance. Their differences in affective and cognitive aspects necessitate a qualitative differentiation of teaching processes, otherwise equal opportunity in teaching is a “myth without real context”.

2. Engineering Students’ Difficulties with Math Courses

Mathematics is one of the core subjects in engineering education and forms the foundation of all disciplines in engineering. Mathematics education for engineering students has been a topic of discussion among university mathematics teachers, mathematics education researchers and university authorities for many years. Many universities report high drop-out rates in mathematics, which has prompted university departments to offer transition courses to progress students from school to university mathematics ^[5]. According to Tang, Chau, Lau and Ho ^[6], in Hong Kong, a significant number of students are admitted to engineering programs without sufficient mathematical background, and they are often unaware of how mathematically demanding their education could be ^[7]. Many students are unaware of the relationship between math courses and the course they have chosen to attend and the implementation of the knowledge in their future profession ^[8]. As Sazhin underlined many years ago, one cannot expect engineering students to perceive mathematics in the same way as professional mathematicians usually do ^[9]. They need to understand its applicability to real-life engineering problems. They try hard if they are aware that they need mathematical concepts in professional activities ^[10]. Kaspersen et al. ^[11] measured engineering students’ mathematical identities in relation to their grades in university mathematics courses. They found that there is a significant correlation with their self-efficacy beliefs as a part of their identity. Mathematics educators have pointed out that engineering students encounter various issues, including barriers to understanding math concepts and to believing that physical concepts are more closely associated with real-life experiences ^[6]. Song ^[12] found three reasons for engineering students’ lack of enthusiasm for mathematics: (a) it is a difficult subject, (b) the teaching is boring and (c) the teachers’ inability to attract them. Bengmark, Thunberg and Winberg ^[13] found that motivations, beliefs and perceptions regarding the nature of mathematics are important factors which explain the initial performance of students in the first year of their studies. It is not easy to engage first year engineering students in a course which is not directly related to their main interest. Rahman et al. ^[8] designed teaching strategies to support students’ development of mathematical knowledge and problem solving, communication and team working skills. Saiman, Wahyuningsih and Hamdani ^[14] underline the necessity of focusing on conceptual understanding by providing a contextual basis to connect the new knowledge to the previously established and to problem-solving context. They found that most engineering students feel that conceptual mathematics is less important than procedural mathematics for their future professional orientation. Kyle and Kahn ^[15] found that mathematics and statistics are often taught in schools as a collection of rules, procedures, theorems, definitions and applications. The most successful mathematics courses in engineering are thought to be those that have been well integrated in the engineering curriculum, facilitating contextual relevance of mathematical abstracts to engineering concepts ^[16], while passive lectures are criticized for many reasons. Pedagogy underlines that active learning has a positive effect on students’ cognitive behavior ^[17]. It is not easy to engage students in a course if they have low self-efficacy beliefs about their abilities to face their respective previous difficulties. The method of peer support mechanisms for students was suggested many years ago ^[15]. Additionally, mathematics support centers have been established at universities in England (such as Manchester), which aim to offer supplementary online lectures, notes and videos for mathematics. Rensao ^[18] presents deliverable chosen mathematics episodes observed in a class of engineering in a calculus course and reveals the value of the instrumental strategies. In our opinion, tThe success of those attempts is affected by the students’ metacognitive knowledge of their difficulties, their desire to face them and their ability to activate self-regulatory strategies in order to overcome them. Any educational reform or the implementation of any teaching innovation can be based on teachers’ knowledge, skills, concepts and dispositions. Appropriate lifelong learning training is an ongoing need for teachers in all levels of education, especially in the case of mathematics ^[19]. Unfortunately, some academics teach students without having much formal knowledge of how students learn ^[1]. The continual professional development of university teachers has received much attention in recent years ^[20]. In many European countries, academics are prepared for their role as researchers but not for their teaching duties ^[4]. In the Agenda for Higher Education ^[21], it was argued that too many higher education teachers have received little or no pedagogical training, and the systematic investment in this continuous professional development remains the exception. Klingbeil et al. ^[22] proposed a model of the introduction of engineering students to mathematics. As they claimed, usually, the traditional approach to engineering mathematics education begins with the one year of freshman calculus as a prerequisite to the subsequent core engineering course. The motivation for their proposed model was the finding that only 42% of incoming freshmen who wish to pursue an engineering course at a specific university ever complete the required freshmen calculus program. Their proposed approach included the development of a novel freshman engineering mathematics course in order to increase students’ retention, motivation and success in engineering. By removing traditional math prerequisite requirements and moving core engineering courses earlier in the program, they proposed the restructuring of the engineering curriculum ^[23]. Many universities throughout the world are trying to determine appropriate training for academics in order to improve their teaching methods ^[24].