T UNING G EORGIA, M ATHEMATICS Ramaz Botchorishvili Tbilisi State University

M EMBERS OF SAG M ATHEMATICS, T UNING G EORGIA Ramaz Botchorishvili, I.Javakhishvili Tbilisi State University George Bareladze, I.Javakhishvili Tbilisi State University Omar Glonti, I.Javakhishvili Tbilisi State University Giorgi Oniani, A.Tsereteli Kutaisi State University Zaza Sokhadze, A.Tsereteli Kutaisi State University Nikoloz Gorgodze, A.Tsereteli Kutaisi State University Giorgi Khimshiashvili, I.Chavchavadze University Temur Djangveladze, I.Chavchavadze University David Natroshvili, Georgian Technical University Leonard MdzinaraSvili, Georgian Technical University 2

A CADEMICS I NVOLVED IN D ISCUSSIONS, 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 3

F IRST M EETING WITH T UNING, Y EAR 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 4

T UNING SAG M ATHEMATICS D OCUMENT Why this document is important? It gives logically well defined way towards a common framework for Mathematics degrees in Europe 5

T OWARDS A COMMON FRAMEWORK FOR M ATHEMATICS DEGREES IN E UROPE 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). 6

C OMMON 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 7

I MPLEMENTATION 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 8

C ONSULTATION 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 9

L EARNING OUTCOMES, K NOWLEDGE AND U NDERSTANDING 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; 10

L EARNING OUTCOMES, A PPLICATION OF KNOWLEDGE /P RACTICAL S KILLS 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. 11

L EARNING OUTCOMES, G ENERIC / T RANSFERABLE S KILLS 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; 12

13 Modules Subject specific competences

14 Modules Generic competences

L EVELS, TUNING DOCUMENT 15 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.

T EACHING 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 16

N EXT 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 ? 17

T HANK YOU FOR YOUR ATTENTION 18