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Although Mathematics is a pillar which many of the subjects of any Engineering degree are based on, and in spite of being used as a tool in almost all of such subjects, it is sometimes difficult for students to assimilate the mathematical concepts. Since this relationship between Engineering and Mathematics is unavoidable, a consortium of universities from different countries is working on a project, EngiMath, to, on the one hand, make it easier for teachers to teach Mathematics in the first years of Engineering degrees; and, on the other hand, to promote study from a “student-centric” point of view. As a previous step to the development of educational material that fulfills these purposes, a study of the students' feelings about Mathematics and their experience in studying them has been carried out.

The goal of this paper is to introduce a technique of creating self-tests that has allowed to actively incorporate university students into the learning process. The study was conducted within the framework of the Erasmus+ Project EngiMath. Partners’ peer reviews, the survey results and the students’ comments in forums and test results were used to conduct the research. The students’ overall satisfaction was in a high level. However, opportunities for some technical improvement has been emerged like the formulation of the tasks needs to be very clear and the time required to perform the tests must be limited. The following conclusions can be drawn from the study. The use of self-tests at all stages of training has intensified the assimilation of the material, i.e. increased understanding of theoretical material and developed computational skills. By completing a series of such assignments on each topic of the course, students had mastered the methodology of studying the topic and mastered specific teaching material on this topic. Feedback made, taking into account typical errors, has allowed the students to analyse their knowledge. A large number of variations for such tasks has allowed students to be involved in the process of active independent and individualized self-study.

Effective integration of virtual technologies is aimed at improving the quality of education. It is very important to form trends of study at the initial stage of education. This document presents the first steps in the project “Development of a Virtual Learning Environment in Technical Higher Education,” jointly funded by the Erasmus program, which includes institutions from four countries: Estonia, Lithuania, Turkey, and Poland, for 24 months. It aims to create a digital house simulator and a set of training materials for construction specialties freshmen. The tasks of this simulator are to give a learner the opportunity to independently obtain knowledge about the details of the structure through the internet without special equipment. Learning through the virtual house model will help students develop spatial thinking, which is necessary for success in graphics and engineering in general. This, in turn, will increase their professional competence, since spatial visualization refers to the curriculum for all industrial technologies and engineering programs.

Modern pedagogical practice emphasizes the use of technology as an opportunity to personalize the learning process and the need to take into account students' new needs. The purpose of this chapter is to offer a model of presenting online learning materials in mathematics that involves students in a continuous learning process. This model consists of textual materials, video materials, and tests in Moodle virtual learning environment (VLE). Textual materials include short theoretical materials with examples, self-control exercises, and worksheets with step-by-step solutions. The model includes five different types of videos: mini-lectures, problem solving walkthroughs, instructional videos, interactive videos, and individual videos. The testing system includes training, control, and bonus tests. Creating all parts of the model requires the use of specific didactical techniques. The students' feedback to this model has been highly positive.

At the end of the 2018, a new multinational project saw its approval as a European Erasmus+ Project. This project, named EngiMath - Mathematics on-line learning model in Engineering education, is closely related to Mathematics Teaching in Engineering Degrees. With its end planned for 2021, the steps needed to kick-start the development of this multinational project have not been easy in general logistic terms and even in more specific and particular issues. One of the first steps in its development was connected to the identification of common themes/subjects on which this project should be based in theoretical and general terms. This paper will describe, in a detailed way, all the educational needs analysis development. Its inclusion within this programme of work was due to the development, testing and deployment of a novel paradigm in the technology enhanced learning mediated environment in six geographically, socially, and culturally separate, engineering institutions. This was not a trivial task and took many resource hours to complete. Prior research to the submission of the project found no literature guiding educational needs analysis for joint-shared initiatives relating to socially, culturally, or geographically, separate locations. Therefore, this paper hopes to mark a complete list of objectives and tasks developed. It will point out several important issues to consider when designing multinational educational projects as well as other international connections made in education.

The COVID pandemic has touched many aspects of everyone’s life. Education is one of the fields greatly affected by it, as students and teachers were forced to move online and quickly adapt to the online environment. Assessment is a crucial part of education, especially in STEM fields. A gap analysis was performed by expert groups in the frame of an Erasmus+ project looking at the practices of six European countries. Specialists teaching university-grade mathematics in seven European institutions were asked about their perception of gaps in the assessment of students both before (2019) and during (2021) the pandemic. This qualitative study looks at the difference in perception of such gaps after almost one year of online teaching. The analysis of their responses showed that some gaps were present before the pandemic, as well as others that are specific to it. Some gaps, such as the lack of IT infrastructure and the need to adapt materials to an online environment, have been exacerbated by the outbreak., This research was co-funded by the Erasmus+ Programme of the European Union, project name EngiMath, ref. no. 2018-1-EE01-KA203-047098.

Parallel submanifolds in pseudo-Euclidean spaces are characterized locally by the system rh = 0. Submanifolds satisfying the integrability condition R h = 0 of this system are called semiparallel; geometrically they are 2nd-order envelopes of the parallel submanifolds. The existence and geometry of such two-dimensional Riemannian submanifolds (surfaces) are investigated and their complete classification is given. Moreover, it is shown that inE n withs > 0 do exist not totally geodesic minimal semiparallel space-like surfaces.