This article reports on the empirical results and practical aspects concerning the teaching and learning of first-year engineering mathematics at a distance. The investigation over two consecutive years (2020 and 2021) is meant to yield prospects and contribute to the development of suitable pedagogies for online mathematics teaching and learning for engineering students in South Africa in the future. In 2020, lecturers were faced with a "sudden" shift from face-to-face to online teaching and the focus was to save the academic year and leave no student behind; in 2021 the situation was unchanged. Lecturers had to consider key aspects (such as the module structure, teaching theory and practice, and perspectives on "what can work") in the transition and continuation from face-to-face to fully online and developing a suitable teaching and learning approach. Approximately 1000 first-year engineering students at the University of Johannesburg, South Africa, were exposed to the newly developed online teaching and learning approach in both years. The approach includes the following key elements: an evaluation of prior knowledge by a diagnostic test; an investigation of students' attitudes towards mathematics by means of the SATM questionnaire; weekly virtual lecture and tutorial sessions; weekly homework tasks; additional online resources; discussion forums between all role players (students, tutors and lecturers); online tutor support; the use of e-textbooks and online assessments via the university learning management system and an external platform (such as WeBWorK). Both years followed a similar approach, although slight changes were implemented in 2021. Descriptive statistics from key elements were used to monitor the students' involvement and progress in both years. Results show the teaching and learning approach is effective but has room for improvement. Particularly, the results encourage addressing the needs of the students and lecturers when implementing pedagogical aspects in learning mathematics at a distance.