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The National Agency for Higher Education was asked by the government to survey the organisation and implementation of teaching for students beginning higher education, in particular in connection with mathematics courses at higher education institutions with programmes in mathematics, technology or the natural sciences. This task also involved working out proposals to enable the institutions to improve their presentation of mathematics and student learning. The study covered bachelor´s and master´s programmes in engineering and the programmes in the natural sciences that include more than 5 credit points of mathematics during the first year. The survey took the form of site visits, telephone interviews with representatives of the higher education institutions and also a questionnaire on student attitudes to mathematics and the teaching of mathematics.

During the years a number of inquiries have taken place into the standard of mathematics among beginner students in addition to this one. In every case it has been determined that many students are poorly equipped when they begin their studies. For many years, several higher education institutions have required beginner students to take a diagnostic test. All of the inquiries have shown that levels of knowledge have declined and that there are grave shortcomings in many students´ knowledge of fundamental elements of basic upper-secondary programmes in mathematics. It is particularly alarming that many students have a poor understanding of arithmetic and algebra. Several inquiries indicate that mathematics teachers often take these teaching problems seriously and show great commitment to their work. Emphasis is also placed on the importance of strong links between mathematics teaching and courses in engineering. Inquiries made since 2000 indicate as well that modern aids such as computers are not adequately incorporated into the teaching. The majority of students have a positive attitude to mathematics as a subject. But even if the overall picture is positive there remain a not inconsiderable minority with a negative approach even though they have opted for programmes in technology and the natural sciences. Attitudes to the mathematics teaching they receive follow basically the same pattern.

One interpretation of the student´s own conceptions is that they rate their own knowledge and skills in mathematics higher than their teachers do. Just under half of the students in their second semester consider that they have had great use or very great use of their mathematical skills in other subjects. About 15 per cent of the students in their sixth semester in the bachelor´s programmes in engineering consider that they have had little or no use for their mathematics. The students also consider on the whole that the links between the teaching offered in mathematics and the profile of their programme are non-existent or very weak. Many feel that these links should be stronger than is currently the case.

Tne thing that has come to light during our interviews and site visits is that mathematics is acquiring increasing significance while at the same time student interest in the subject is waning. At many higher education institutions the formal qualifications for admission to bachelor´s and master´s programmes in engineering have been or will be lowered to the upper-secondary school D-programme. For some programmes the C-programme is the entry qualification required.

On the whole the contents of the basic compulsory courses are the traditional ones. Elementary algebra, analysis and linear algebra predominate. It has turned out to be difficult in practice to link the contents of mathematics courses to the profiles of programmes. More and more attention is focused on revision and confirmation of knowledge from the upper-secondary school. Experiments have been made with introductory courses of varying extent or slowing down the pace of study to deal with the shortcomings of many students in elementary mathematics.

Many teachers feel that they have lowered the level demanded for pass grades. This has often resulted from the fragmentation of the material but also through reducing the difficulty of the final tests. After three attempts, the proportion passing is somewhere between 60 and 80 per cent.

As a rule the use of calculators is not permitted during tests in the initial courses and computers are not normally integrated into the teaching of mathematics. Methodological issues are becoming increasingly important and the teachers are working with commitment to solve them. Changes in the student population and their knowledge on arrival have meant that mathematics departments have devoted a great deal of work to the development of new teaching and examination methods. Educational development work is undertaken at the moment with very restricted resources or none at all. The mathematics departments attach a great deal of importance to cooperation with the upper-secondary schools. In many cases there is great ambition to establish contacts with the upper-secondary schools. But these endeavours often fade away as neither the upper-secondary schools nor the higher education institutions allocate resources for this purpose.