Online assessment is intended to enhance the learning experiences of students and improve the manner in which feedback is delivered. This paper reports on an international project, in three countries, to examine the beliefs of self-efficacy, and constructs of expectancy, held by engineering mathematics lecturers, and provides a comparison with those beliefs held by students, in the first year of undergraduate Bachelor of Engineering programmes. The interviews were semi-structured to stimulate conversations around a set of pre-determined themes. The thematic inputs to the lecturer interviews resulted from interpretative phenomenological analysis of the beliefs, experiences and perceptions of 127 students, gained from a series of questionnaires, and interviews. The aims of the engineering mathematics lecturer interviews were to examine current practices in terms of assessment of mathematics, and the provision of feedback, in both online and face-to-face formats, with a view to determining if the self-efficacy of students is a considered within the process. The research highlights differences in understanding of the assessment process held by lecturers, and students particularly in the early stages of the first semester. Evidence that students' meta-cognitive functions evolve over the first year of study to minimize the differences is provided. The implications of these findings are discussed.