The aim of this study was to establish whether there are differences between the computer self-efficacy of pupils and teachers (N = 507) in the context of the classroom, as a developing workplace of the teacher in elementary education. The survey covered 184 teachers and 323 pupils in elementary school. The results show that there is no statistically significant difference in the Basic Computer Skills dimension. In other words, both pupils and teachers assess their own self-efficacy in Basic Computer Skills equally. Further, the results show a statistically significant difference of the medium effect size in Media-Related Skills. In other words, pupils assess their self-efficacy in this dimension higher than the teachers. The results also reveal a statistically significant difference in the medium effect size concerning the self-efficacy dimension of Web-Based Skills, i.e. the pupils' assessment of self-efficacy in the skill of internet use is higher than the teachers' assessment of self-efficacy in the same area. The results also show that pupils generally assess their computer self-efficacy more highly than the teachers do, which may be explained by the fact that these pupils are digital natives, belonging to what is known as the Net Generation, while their teachers are known as digital immigrants. This paper explains the implications of these results for modern multimedia student-centred classes, and the role of the pupil and teacher in such classes. [This paper was published in: "E-Learning at Work and the Workplace: From Education to Employment and Meaningful Work with ICTs." Proceedings of the European Distance and E-Learning Network 2014 Annual Conference (Zagreb, Croatia, June 10-13, 2014). p517-526. ISBN 978-963-89559-7-5.]