Mathematics Teaching Innovation in Higher Technical Education JaaK Sikk Tallinn University of Technology

Mathematical culture The purpose of teaching mathematics at a technological university is concerned with the transmission of basic ideas of existing traditional ‘mathematical culture’, considered by mathematicians as crucial.

Mathematical culture Like all other social values, the values of a phenomenon, named as “mathematical culture”, have a stable core and this core is considered by mathematicians as a necessary instrument for interpretation of the surrounding world.

. An important social value for the community of engineers is “an engineering mathematics basic” – certain amount of core mathematical knowledge’s and ideas considered by the engineering community as natural. The engineering mathematics basic

Under the influence of constantly modernizing technologies the subject domain of this “basic” has been in a constant change. This continuously changing, but at the same time quite stable amount of mathematical knowledge forms the ‘core mathematics’ for engineering.

Integration and Co-operation of ideas Mathematics is at the heart of engineering, being both a language for the expression of ideas and the means of communication results. An effective study programme in mathematics is a necessary requirement for the education of qualified engineering graduates capable both of innovation and of adaptation to changing technology. The aim of the research is to integrate both “Mathematical cultures”. In mathematics

Core Curriculum aalen.de/profumit/alpers/sefimwg/frameset.htmhttp:// aalen.de/profumit/alpers/sefimwg/frameset.htm In 1992 the SEFI-MWG published an advisory core curriculum (CC) of mathematics to be followed in European institutions where professional engineers are formed. The content lenght ranging from 220 to 320 hours comprised:

Core curriculum (CC) Analysis and Calculus Linear Algebra Discrete Mathematics Probability and Statistics In the portions of about one half for the analysis and calculus and about one sixth each for the others.

Core curriculum (CC) The revised CC was published by SEFI in In many respect this retained the main features of the earlier document. New features were the inclusion of Geometry as a specific topic and the special emphasis placed upon student learning outcomes.

Core curriculum In Core Curriculum each of its three lower levels (0, 1; 2) are divided into many component parts in which lie the main topics and subtopics. Levels 0, 1, 2 are representing hierarchical progression from school towards to the first two stages of university education.

Bologna Agreement The Bologna Agreement calls for Bachelor programmes of 180 European Credits (ECTS) taken over about 3 years or 6/7 semesters, followed by 120 ECTs up to master level, or about 2 years or 4 semesters. SEFI-MWG however is worried about that Bachalor qualifications might come to mean noting that there could be a wide variety of levels and that mathematics might be put under pressure and reduced. It would also risk being undermined at the lower end of the curriculum with an increasing amount of “levelling-up” Core Zero materials.

Mathematical curriculum requirements of a Bachelor programme Firstly, as the start point level of mathematics study seems to get lower with every passing year, this need to be rationalised in terms of Core Zero and Core One of the CC. Secondly, the endpoint of study would come before the end of Core Two: this too would need to be rationalised in terms of type of programme and engineering discipline. ?Bachelor Type A (proceeding to masters), academically more capable students? ?Bachelor Type B (terminating), academically less able students?