ࡱ>  @-ebjbj F؝؝.8L*</|rrl.n.n.n.n.n.n.$1Ro3.4j"44.d[/   4l. 4l.  ,h-f XWH-.\q/0/ -_4_4 -_4-,D: ~z..X CREATING COMMON LANGUAGES IN PEDAGOGY: MENTAL MODELS AND STRUCTURAL NICHES IN APPROACHING CONCEPTS FOR THE HARMONIC DEVELOPMENT OF GIFTED TALENTED STUDENTS EUGENIA T. MELETEA Abstract: Creativity is dealing with (rational and/or irrational) products, but the role of the scientific knowledge is to be an art in human harmonic/balanced development. Quality is the measure of harmony, and can also be the measure of creativity, in both theory and praxis. Key words: Creativity, Definitions, Gifted Talented Students, Terminology in Pedagogy INTRODUCTION This presentation delivers some of the outcomes (mental models and/or structural niches) that the author has organized, in order to support the research focusing in the target group of gifted talented students. This may also help educators to approach concepts and create common languages in Pedagogy. Following are some examples in theory and praxis. 1. CREATING COMMON LANGUAGES IN PEDAGOGY Common languages form the basis for human communications. Activities, like definitions and linguistic rolls can be useful in creating a common environment of understanding. Universal languages are multicultural universal processes help to approach the understanding of concept and the meaning of their (name) term. The relationship between names and concepts was addressed by Aristotle. To indulge the name is the beginning of wisdom,     . 1a. Terminology: creating myths for approaching concepts or approaching myths for creating concepts? Terms are basic structures, which humans need to create in order to communicate, in both oral and written form. Experimental views come from the author s mother tongue: The word  name =   or    = the law These give an idea of how language can be related to mathematics and/or how the term  creativity (in witch the present conference focuses), can be equivalent to mathematic creativity or/and to linguistic creativity etc. Aristotle in Topika, stated that the construction of any word (name/term) tried to put in any words the most important characteristics. Human beings have various common ways to communicate. These include common languages such as mathematical, musical, sign languages, body languages etc. Another experimental case to Professor Artemiadis (2001) who taught the author Pure Mathematics. Apart from the applied (in teaching and writing) knowledge he gave the author, he also made some comments, which have influenced the author deeply (both personally and professionally). Comments like: mathematics are also a from of fine art, the beauty of a theory means that this theory is truth, As the application of these instructions can also be useful if we transform them to the need of qualitative algorithms in computer programming. We can then suggest the need for such diachronic instructions (from teacher to student). Mathematicians have a common language, but in education more concepts (like the creativity in mathematics) are needed, for a discussion for new concepts, new terms/names. In our life we need to use names, terms, words etc to approach communication (common). As in some other periods the same word has had different meaning (like the word music: While there were 9 female figures called Muses, one for each of the 9 different arts, music was named after Muse, because it was thought to contain all arts in it. In our era we certainly do not share that opinion about music (and neither do other languages, which have borrowed the term music. This example demonstrates that the same word can have different meanings in different time periods and different places. In relation to the concept of creativity in mathematics, the authors view is presented in the following paragraph 1b (as her position in the dialogue hypothesis for the definition of concepts) and in paragraph 2a (where the term creativity is taking a only place (see figure 1: levels of behave and define talents). 1b. Elements of a Definition Theory There have been long discussions of some other similar problems common to human sciences, for approaching concepts like giftedness, Intelligence, creativity etc. Trying to explain why there are so many different definitions and opinions, the author ended up beyond a theoretical approach to the concepts, that in the case of gifted talented students - are useful, but not as useful as focusing on developing innovations, which will be available to those pupils, as well as for all other pupils, as and we needed. Aristotle in  After the Physics agreed that the    inductive research directs to the  Total definition - Global definition ,     . Concepts can be expressed in every language with a. Typical definitions (e.g. the mathematical notion of  function means the same in all languages). b. Descriptive definitions: Generalizing concepts like talent, giftedness, etc. and taking them out of context can create chaos. (As illustrated from the following example, if a 5 year old boy from Alaska and one from Sahara are asked what snow is, their answers will be determined by their experiences, personality, environment and aesthetics). c. Working Definitions: These can be helpful for certain groups of people but they may mean nothing to the rest of the population). d. Symbols (e.g. numbers in various numerical systems, words and their semantics, translations of foreign words such as the word theatre which comes from the Greek word theater meaning view, can remain the same if translated). Having worked on the issue of the gifted talented education in an international scale, I have noticed that there are some common goals and common activities, which do not share common definitions nor terms. An example of using different terminology to refer to the same group of people is the following: Educators use the term student, pediatricians use the term child, while psychologists the term people. 2. APPROACHING CONCEPTS FOR THE GIFTED TALENTED STUDENTS It is the time for educators and facilitators to be able and adapt in order to develop innovations reflecting on the students needs that are always changing, as the rhythm of the students needs are in dynamic interactivity, we must investigate the future of the educational process. Even students who we would call gifted in mathematics or those who appear to be gifted in mathematics but have some weaknesses, for which we cannot determine the causes. For instance, a 10-year old student with high scores in IQ tests has writing difficulties. Are these caused by possible dyslexia or has the student developed some different thought patterns, which do not correspond to those of writing? This is one of the main reasons why most countries have developed programmes for supporting the unique needs of gifted talented students. What could we propose to such a student? This only one of the many similar questions and possible answers that arises. It is therefore imperative that we can identify the students talents, interests as special abilities and, based on those, to help them formulate a harmonic/balanced personality. A classification that describes the interaction (student - teacher/etc), and/or (children - parents) etc, - proposed by (Meletea, 2003) - in order to obtain the necessary information from the students behavior to identify their talents is described below (in figure 1). Figure 1: bd Model, A Classification of the Levels in Behave and Define Talents We propose, at least, the next two axes (and the four directions) that mathematicians need to focus on at any time, for any student and in any topic (Meletea, 2003). Axis 1: Investigating traditional values - Suggesting the future Axis 2: Student (Inner) Environment (outer) 3. TRADITIONAL SOURCES OF HUMAN COGNITION IN PEDAGOGY Issues relevant to pedagogy according to Aristotle: Criteria for human virtue and development. Aristotle, in volume eight of his  Politics , and especially in  Ethics Nikomachea , presents his views on pedagogy. It is the first time in history that there is mention of statutory  common and individualized    , pedagogy, through which humans become active citizens, embrace virtue and happiness and, through logic, reach perfection. According to Aristotelian research in his  Politics (2, 10-13) the main functions of pedagogy are INNER: Autonomy, OUTER Economy ( - ) () Politics (which Aristotle thought to be the foremost science), urging ... to be involved with politics lest the wicked prevail. The management of a household and the division of labour within it, become easier when educated citizens are involved. Pedagogy should not aim at oppressing students. Despite the fact that Aristotle does not admit that youths learn through playing    ,     , he advocates that pedagogy should be a source of oppression. Therefore, the joy of learning and the playful nature of education, which are some the modern, progressive pedagogical methods, hail back to Aristotles way of thinking. The purpose of pedagogy should be to achieve happiness, but not only in the form of enjoying material or spiritual goods, but also in the form of soul energy, which draws us closer to perfection. Thus, pedagogy mission is to assist in fulfilling the very purpose of existence, which is the achievement of happiness. Aristotle in Physics (introduction) he stated, Humans are choosing to know their origin. An Axiomatic approach for human harmonic/balanced development in the figure 2 (Meletea, 2003), The system (Justice - freedom - equilibrium) works in two directions.   Figure 2: A7+ Model, An Axiomatic approach for Human Harmonic Development Using the semantic of the term in Greek, justice, means divide, freedom, means past the limit. To achieve harmonic development it is necessary for the two systems (INNER OUTER) to have balance (equilibrium,  - ). When these two systems are opposed (ambiguity), this can even lead to their destruction. To achieve harmonic development it is necessary for the two systems (INNER  OUTER) to have balance ( - ). 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Knowledge transformation in mathematics (theory and praxis), assisted by other activities (such as photography, poetry, theatre), and also by existing utilities of the Information and Communication Technologies (ICT), is expected to completely transform the existing educational environment in the future. 4. EPILOGUE Educators need to create their own golden rules for their professional development and success in promoting creativity for all students, in mathematics education for expanding scientific knowledge for qualitative life. REFERENCES Aristotle  After the Physics ( 4, 1078b and A 6, 978b). Aristotle  Ethical Nicomachien (1, 1-3 and 6, 10-11). Aristotle, Physics, ntroduction. Aristotle, Poetics (2, 10-13). Aristotle, Politics. Aristotle, Topika. Artemiadis, N. K. (2001). Speaches from the rostrum of the Academy of Athens,  Mathematics Are Art) , pp.30 - 52. (ACADEMY OF ATHENS). Meletea, .T. (2003). APLOYN  Development of Pedagogical Speech to Support Gifted-Talented, Pupils. Axiomatic Foundation, Exploratory Dialogue: Gifted and Talented Pupils: A Pedagogical Approach, 9.2.2003, Athens, Greece. ABOUT THE AUTHOR Eugenia T. Meletea Director of APOLLON - International Interactive Educational Network Researcher in the School of Medicine of the National and Kapodistrian University of Athens P.O. Box: 61123, 15110, Marousi, Athens, Greece Cell phone: +2111199133, Website: www.apollon.edu.gr -mails: evmeletea@med.uoa.gr emel@apollon.edu.gr  PAGE 554 PAGE 554 PAGE 554 PAGE 558 PAGE 554    Eugenia T. 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V-{@Times New Roman- G2 O(aiProceedings of the Discussing Group 9 : Q4C;;;C%JC4!C,!%J<!`%4;J44%JC!`4CJD!C!,! 2 ai Dia'j2 L?aiPromoting Creativity for All Students in Mathematics Education Q4CgC%%JC!Y4;C%%<%%;!,C4!Y%%!J&JC;J&4!%J!vC%J<gC%%;4"YCJ;C%%CJ! 2 Lai Cia'@Times New Roman- 2  ai "ia'-b2 2 :aiThe 11th International Congress on Mathematical Education QJ;!CC%J!4J%;4JC%&CJC%!YCJC4;44!CJ!vC%J;gC%%;C%!YDJ;C%%CJ! 2 2`ai Cia'-12 aiMonterrey, Mexico, July 6vCJ%;44;;!"v;C%<C!!CJ%;!C 2 } ai-,2  ai13CC2 / ai, 2008!!CCCC@Times New Roman- 2 } ai -ia'@BMonotype Corsiva-2 aiICME 11,=bI33 2 > ai, Mexico, 2008b(1(/3334- 2  ai -ia',-2 ,8933- 2 , .,''{@Times New Roman-  2 }E ai H- 2 j7ai -j@Times New Roman-D2 @^&aiCREATING COMMON LANGUAGES IN PEDAGOGY:lldld;lu&luuk&dllulludS&:l&\dlluuul2 2 @ai QF2 a'aiMENTAL MODELS AND STRUCTURAL NICHES IN dldld&tlddS&lll&Sellldmlld&m:ludS&:l& 2 aai RD2 &aiAPPROACHING CONCEPTS FOR THE HARMONIC l\\lullu:mu&lulld\dS&\ul&duc&uklul:l& 2 ai QF2 ]'aiDEVELOPMENT OF GIFTED TALENTED STUDENTS ldlddu\dld&u\%u:\ddl&dlddlddl'SdlleldS 2 ai R@Times New Roman- 2 ai ? 2 aiEN%2 kaiUGENIA T. MELETEAT[NT.TNnNNNNNT 2 + ai ?@Times New Roman- 2 $ ai 5@Times New Roman- 2 c aiAbstract: N;- .;3!'@Times New Roman- a2 9ai Creativity is dealing with (rational and/or irrational) 5M.3; !3! 45!.4;3; !:;5M! ;5&.: ;::!5:;: ;.4!--; !::; &2 c aiproducts, ;-:;;3 .g2 =ai but the role of the scientific knowledge is to be an art in !;:!! ;4!-:!3!;!! ;4!.3!3; !!4!3::N!3;:4!!. !; ;4!:;!:-!!!:j2 ,c?aihuman harmonic/balanced development. Quality is the measure of ;;S;;;:.T::!4 :; ;:44;;443 ;;T3;!T;:! !4 . ;4 T4:-;-4 : p2 cCaiharmony, and can also be the measure of creativity, in both theory o;:.T:;4;:;3:;; -;:4 ;4T3:.:.4;!3.4: !4 !4!::; ;!:4:.32 7c aiand praxis. ;:;:-;3!. 2 7ai <- 2 3c aiKey words: N44KN:.:.'K- G2 3(aiCreativity, Definitions, Gifted TalentedN.3:!!3!!4KT4 !: ! :;.KT! !4;K@; 4:!3;2 3 ai Students, K; :;3:!-/2 caiTerminology in Pedagogy A4.T :; ;:4 ;G4::;:;4 2 =ai <- 2 7ai ?2  aiINTRODUCTION.TNT[TTTN.[T 2 w ai ?-t2 7FaiThis presentation delivers some of the outcomes (mental models and/or G; .Q;'3.3; 4 !:;Q:4! ;4&.Q-;Y4Q;'Q!:4Q;:!3;Y4.Q(Y4;!4 RY;;4 .Q4:; :&2 07Saistructural niches) that the author has organized, in order to support the research .!&;3!:'4!%:!4:4.'% ;3!& ;4&3; :;'&:4.%;&;3;!34;%!;%;&;4'%!;%.:;:;&!& ;4&'3.43'3:[2 75aifocusing in the target group of gifted talented stude';3;- ;;8!:9 ;48!4&:4!8;'::;9:'9:!&!4;8 4!3;!3;8. :;3/2 l aints. This may also help ; .9G:!.9Y5994!.:9;3 :w2 <7Haieducators to approach concepts and create common languages in Pedagogy. 4:;43!;&.:!:;3;;&;34;;3:;43; .;3:;;4&34!4:4;ZY;;;!3;:;3;4-; ;;@4:4::;9V2 72aiFollowing are some examples in theory and praxis. A; ;T ;;4&4-;Y45;4Y;!4.!;!:4;'94:;;&4:!. 2  ai 42 7ai  2 ai 6-iiaahh``gg__ff^^ee]]dd\\cc[[bbZZaaYY ` `X X  _ _W W  ^ ^V V  ] ]U U  \ \T T [[SSZZRRYYQQXXPPWWOOe ՜.+,D՜.+, hp|  zRUTo. KABOUT SOME BASIC PRINCIPLES OF THE EXTRACULLAR WORK WITH TALENTED STUDENTS INTRODUCTION)1. CREATING COMMON LANGUAGES IN PEDAGOGY%1b. Elements of a Definition Theory :2. APPROACHING CONCEPTS FOR THE GIFTED TALENTED STUDENTS RIt is therefore imperative that we can identify the students’ talents, interestQFigure 1: bd Model, A Classification of the Levels in Behave and Define 73. TRADITIONAL SOURCES OF HUMAN COGNITION IN PEDAGOGY QFigure 2: A7+ Model, An Axiomatic approach for Human Harmonic Develop4. EPILOGUE ?Aristotle “After the Physics” (Μ 4, 1078b and A 6, 978b).?Aristotle “Ethical Nicomachien” (Β1, 1-3 and Β6, 10-11).#Aristotle, Physics, Ιntroduction."Aristotle, Poetics (Α2, 10-13). Aristotle, Politics. Aristotle, Topika. TMeletea, Ε.T. (2003). APLOYN – Development of Pedagogical Speech to Support Gift Title HeadingsH 6> MTWinEqns   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry FWData 1Table4WordDocumentFSummaryInformation(DocumentSummaryInformation8CompObjj  FMicrosoft Word Document MSWordDocWord.Document.89q