The discussion about first-year engineering students’ difficulties in mathematics is continuous in the fields of engineering, mathematics and higher education. The present study aimed to examine the initial barriers academic math teachers need to have in mind if they want to improve students’ performance in engineering math courses through appropriate teaching practices in order to face their initial interindividual differences. During the first phase of the study, we examined first year engineering students’ initial beliefs about the nature of mathematics, their self-efficacy beliefs about mathematics and their basic mathematical knowledge. The math school grade was used for their previous mathematical performance. Results indicated the predominant role of the previous mathematical knowledge and the important role of the formalistic disposition toward mathematics. The lack of experience of using mathematics for problem-solving situations within an engineering framework prevented students from recognizing and appreciating the value of mathematical courses during the engineering studies. The second phase of the study examined, through an interview with a group of students, their perceptions of the teaching practices which were introduced after their teacher attended a training program. The discussion concentrates on how academics can use teaching processes for equity and not equality in order to motivate their students.

Self-efficacy beliefs in mathematics, as a dimension of the affective domain, are related with students’ performance on solving tasks and mainly on overcoming cognitive obstacles. The present study investigated the interrelations of cognitive performance on geometry and young students’ self-efficacy beliefs about using representations for solving geometrical tasks. The emphasis was on confirming a theoretical model for the primary-school and secondary-school students and identifying the differences and similarities for the two ages. A quantitative study was developed and data were collected from 1086 students in Grades 5–8. Confirmatory factor analysis affirmed the existence of a coherent model of affective dimensions about the use of representations for understanding the geometrical concepts, which becomes more stable across the educational levels.

Problem-solving has been at the core of mathematical education for decades. However, the objectives set for understanding mathematical concepts and developing problem-solving strategies within a realistic and interdisciplinary framework have not been achieved to the expected extent. Over the past decade, the need for persistence in mathematical problem-solving has been emphasized as a process of self-regulation in cognitive behaviour, helping learners overcome obstacles that require flexibility and adaptive actions. Learners often seek external assistance when facing difficulties in solving mathematical problems. Recently it seems that at the secondary and higher education levels, artificial intelligence has taken on this role. Research findings highlight students' willingness and expectation to acquire the necessary knowledge and skills to utilize Artificial Intelligence (AI) tools for learning, developing strategies, and enhancing problem-solving abilities to become more proficient problem solvers. We must acknowledge the advancements in AI and leverage its capabilities in an ethical and effective manner, including adaptive assessment and self-assessment tools, immediate feedback, identification of errors in mathematical thinking, and suggestions for alternative courses of action. The use of appropriate AI tools by cognitively mature individuals can positively contribute to the development of metacognitive skills that improve mathematical ability. The effective use presupposes the relevant teachers' knowledge, skills and high self-efficacy beliefs about the use of AI tools either in teaching or in learning. We present a position paper on the issue and we discuss our main concerns we have to take into consideration, under a pedagogical perspective and the challenges we have to face the following up years.

The present study examines the role of everyday play-based activities, planned and implemented by parents, on the development of children’s mathematical thinking at the age of up to 3 years old. Parents’ knowledge and beliefs were measured by using an online questionnaire, while a nonformal training program was developed and implemented with the participation of a group of parents using technological tools. The aim was to improve their knowledge on how to use relevant play-based activities and the understanding of their role. Results indicated that parents asked for the contribution of experts in order to acquire the relevant knowledge and skills and develop positive self-efficacy beliefs about their role. They found the training practical, through the use of digital tools, as well as useful for collaboration and communication. The shared examples by them indicated that the training has to concentrate further on the use of daily activities outside of the school-based context, which is more known to the parents.

Engineering education for sustainability extends beyond environmental awareness. It is aimed at the cultivation of resilient and self-regulated learners capable of continuous growth. The present work draws upon empirical data from three complementary investigations on first-year engineering students’ affective behavior, mathematical difficulties and the use of online quizzes as self-assessment tools. By integrating these findings, the paper proposes a framework for sustainable learning practices in engineering mathematics. The results highlight that affective factors, such as confidence, self-efficacy and motivation, interact significantly with students’ self-regulatory strategies and performance outcomes. Digital self-assessment tools, when purposefully designed, can promote metacognitive reflection and foster a sustainable cycle of feedback and self-improvement. The study argues that sustainable education in engineering must include pedagogical approaches that empower students with interindividual differences to manage their own learning, overcome affective barriers and develop adaptive resilience in demanding quantitative subjects. The proposed model offers practical implications for designing assessment systems that support long-term learner autonomy and well-being, aligning engineering mathematics education with the broader goals of sustainable development. In alignment with SDG 4.7 and the European Skills Agenda, which both emphasize lifelong learning, learner autonomy and the cultivation of adaptive competences for sustainable futures, the proposed framework positions self-regulation and resilience as core sustainability-oriented outcomes in engineering mathematics education.