Transcript Tuning Georgia, Mathematics

TUNING GEORGIA,
MATHEMATICS
Ramaz Botchorishvili
Tbilisi State University
28.02.2009
MEMBERS OF SAG MATHEMATICS ,
TUNING GEORGIA
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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
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ACADEMICS INVOLVED IN DISCUSSIONS,
TSU SPECIFIC
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I.Javakhishvili Tbilisi
State University
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Ramaz Botchorishvili
George Bareladze
David Gordeziani
Elizbar Nadaraya
Tamaz Tadumadze
Tamaz Vashakmadze
Ushangi Goginava
Roland Omanadze
George Jaiani
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Razmadze
Mathematical
Institute
Nino Partcvania
 Tornike Kadeishvili
 Otar Chkadua
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FIRST MEETING WITH TUNING, YEAR 2005
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Faculty of Mathematics and Mechanics, TSU
9 Chairs
 Each chair had a stake in the curriculum
 Typical arguments:
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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
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Result:
too many mandatory courses
 in some branches elective courses were offered before
mandatory foundation courses
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TUNING SAG MATHEMATICS DOCUMENT
Why this document is
important?
It gives logically well defined way
towards a common framework
for Mathematics degrees in
Europe
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TOWARDS A COMMON FRAMEWORK FOR
MATHEMATICS DEGREES IN EUROPE
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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).
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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
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IMPLEMENTATION
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It took almost 4 years to implement step by step
core curriculum during first two years
 allowing diversity after second year
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Impact by Tuning Georgia project
generic and subject specific competences
 questionnaire, consultations with stakeholders
 4 workshops (training, discussions)
 linking competences to modules
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CONSULTATION WITH STAKEHOLDERS
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3 questionnaires were sent out:
generic competences
 subject specific competences
 TSU specific
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Can we relay on surveys?
do stakeholders understand well what is meant
under competences?
 analysis, subject specific competences
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LEARNING OUTCOMES,
KNOWLEDGE AND UNDERSTANDING
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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;
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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:
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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.
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LEARNING OUTCOMES,
GENERIC / TRANSFERABLE SKILLS
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Ability for abstract thinking, analysis and synthesis;
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Ability to identify, pose and resolve problems;
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Ability to make reasoned decisions;
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Ability to search for, process and analyse information from
a variety of sources;
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Skills in the use of information and communications
technologies;
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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.
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Ability to work autonomously;
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Ability to work in a team;
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Ability to plan and manage time;
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Subject
specific
competences
Modules
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Generic
competences
Modules
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LEVELS, TUNING DOCUMENT
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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 nonmathematical 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 nonmathematical 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.
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TEACHING METHODS AND ASSESMENT
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Teaching methods
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lectures
exercise sessions
seminars
homework
computer laboratories
projects
e-learning
Assesment:
midterm and final examination
 practical skills : quizzes, homework
 defense of a project
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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 ?
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THANK YOU FOR YOUR ATTENTION
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