Abstract
There is at present a national concern about basic mathematics, particularly at school leavers' level. In this connection, this thesis is an attempt to cope with the problem of the mathematical competence of engineering students at the interface between school and university. Engineering students were given individual diagnosis by means of a test and tutorial discussion and by means of an approach through thinking aloud combined with observation and retrospective interview. A common characteristic of the two approaches to individual diagnosis is that they require the presence of a tutor for the diagnosis. In the belief that students can diagnose themselves, if they are provided with the appropriate tools, a battery of mathematics diagnostic tests was developed. The items in this battery were based on the topics and level of difficulty mentioned by lecturers in a survey carried out with the purpose of finding out the mathematics needed in first year engineering courses at university, particularly during the first term. As the battery of tests was being developed, the mathematical needs of sixth form school leavers and of newly enrolled engineering students were identified. It was found that both groups of students had difficulty with those topics which involved the use of formulae, and that the knowledge of concepts and numerical values tended to be forgotten more rapidly than other knowledge. Following this diagnosis, materials in algebra and trigonometry were developed for revision purposes, based on students' actual needs. These employed the principles of programmed learning, which were found to be useful and to have certain advantages over traditional textbooks.