Tuning Georgia, Mathematics

1. Tuning Georgia, Mathematics Ramaz Botchorishvili Tbilisi State University 28.02.2009

2. Members of SAG Mathematics , Tuning Georgia • RamazBotchorishvili, I.Javakhishvili Tbilisi State University • George Bareladze, I.Javakhishvili Tbilisi State University • Omar Glonti, I.Javakhishvili Tbilisi State University • GiorgiOniani, A.Tsereteli Kutaisi State University • ZazaSokhadze, A.Tsereteli Kutaisi State University • NikolozGorgodze, A.Tsereteli Kutaisi State University • GiorgiKhimshiashvili, I.Chavchavadze University • TemurDjangveladze, I.Chavchavadze University • David Natroshvili, Georgian Technical University • Leonard MdzinaraSvili, Georgian Technical University

3. Academics Involved in Discussions, TSU specific • I.Javakhishvili Tbilisi State University • Ramaz Botchorishvili • George Bareladze • David Gordeziani • Elizbar Nadaraya • Tamaz Tadumadze • Tamaz Vashakmadze • Ushangi Goginava • Roland Omanadze • George Jaiani • Razmadze Mathematical Institute • Nino Partcvania • Tornike Kadeishvili • Otar Chkadua

4. First Meeting with Tuning, Year 2005 • Faculty of Mathematics and Mechanics, TSU • 9 Chairs • Each chair had a stake in the curriculum • Typical arguments: • this module is very important, therefore it must be mandatory • if this chair has X teaching hours then other chair must have at least Y teaching hours • Result: • too many mandatory courses • in some branches elective courses were offered before mandatory foundation courses

5. Tuning SAG Mathematics Document Why this document is important? It gives logically well defined way towards a common framework for Mathematics degrees in Europe

6. Towards a common framework for Mathematics degrees in Europe • One important component of a common framework for mathematics degrees in Europe is that all programmes have similar, although not necessarily identical, structures. Another component is agreeing on a basic common core curriculum while allowing for some degree of local flexibility. • To fix a single definition of contents, skills and level for the whole of European higher education would exclude many students from the system, and would, in general, be counterproductive. • In fact, the group is in complete agreement that programmes could diverge significantly beyond the basic common core curriculum (e.g. in the direction of “pure” mathematics, or probability - statistics applied to economy or finance, or mathematical physics, or the teaching of mathematics in secondary schools).

7. Common core mathematics curriculum, contents • calculus in one and several real variables • linear algebra • differential equations • complex functions • probability • statistics • numerical methods • geometry of curves and surfaces • algebraic structures • discrete mathematics

8. Implementation • It took almost 4 years to implement step by step • core curriculum during first two years • allowing diversity after second year • Impact by Tuning Georgia project • generic and subject specific competences • questionnaire, consultations with stakeholders • 4 workshops (training, discussions) • linking competences to modules

9. Consultation with stakeholders • 3 questionnaires were sent out: • generic competences • subject specific competences • TSU specific • Can we relay on surveys? • do stakeholders understand well what is meant under competences? • analysis, subject specific competences

10. Learning outcomes, Knowledge and Understanding • Knowledge of the fundamental concepts, principles and theories of mathematical sciences; • Understand and work with formal definitions; • State and prove key theorems from various branches of mathematical sciences; • Knowledge of specific programming languages or software;

11. Learning outcomes, Application of knowledge /Practical Skills • Ability to conceive a proof and develop logical mathematical arguments with clear identification of assumptions and conclusions; • Ability to construct rigorous proofs; • Ability to model mathematically a situation from the real world; • Ability to solve problems using mathematical tools: • state and analyze methods of solution; • analyze and investigate properties of solutions; • apply computational tools of numerical and symbolic calculations for posing and solving problems.

12. Learning outcomes, Generic / Transferable Skills • Ability for abstract thinking, analysis and synthesis; • Ability to identify, pose and resolve problems; • Ability to make reasoned decisions; • Ability to search for, process and analyse information from a variety of sources; • Skills in the use of information and communications technologies; • Ability to present arguments and the conclusions from them with clarity and accuracy and in forms that are suitable for the audiences being addressed, both orally and in writing. • Ability to work autonomously; • Ability to work in a team; • Ability to plan and manage time;

13. Subject specific competences Modules

14. Generic competences Modules

15. Levels, tuning document • Skills. To complete level 1, students will be able to • understand the main theorems of Mathematics and their proofs; • solve mathematical problems that, while not trivial, are similar to others previously known to the students; • translate into mathematical terms simple problems stated in non- mathematical language, and take advantage of this translation to solve them. • solve problems in a variety of mathematical fields that require some originality; • build mathematical models to describe and explain non-mathematical processes. • Skills. To complete level 2, students will be able to • provide proofs of mathematical results not identical to those known before but clearly related to them; • solve non trivial problems in a variety of mathematical fields; • translate into mathematical terms problems of moderate difficulty stated in non-mathematical language, and take advantage of this translation to solve them; • solve problems in a variety of mathematical fields that require some originality; • build mathematical models to describe and explain non-mathematical processes.

16. Teaching methods and assesment • Teaching methods • lectures • exercise sessions • seminars • homework • computer laboratories • projects • e-learning • Assesment: • midterm and final examination • practical skills : quizzes, homework • defense of a project

17. Next steps Every teacher involved in a program redesigns its own syllabus according to planning form for a module in order to link learning outcomes, educational activities and student work time. What if this is not done ?

18. Thank you for your attention