ࡱ> rtq @?bjbj >Z؝؝5jjj8,<NzN|N|N|N|N|N|N$PRSN@@@N4N($($($@"zN($@zN($($IL  QxSYjb J"M|N0NJSv"ZSDLSLl4($,PNN j#Xj PROMOTING CREATIVITY FOR ALL STUDENTS IN MATHEMATICS EDUCATION FAYEZ MINA Abstract. The purpose of this paper is to express the writers views concerning promoting creativity for all students in mathematics education. The paper defines creativity and mathematics creativity. Two theories of creativity exist; creativity for the elites and mass creativity. The writer supports the second one. The paper includes some means to promote creativity in mathematics and requirements to achieve mathematics creativity. Key words: Creativity, Mathematical creativity, Relative creativity, Cultural historical approach INTRODUCTION Some thinkers summed up the emerging new world system in four principles; Universalism, globalism, interdependence and creativity (Eid, 2000, p.22). So, creativity is seen as a basic requirement to live in our era. We live in a time of extraordinary and all celebrating change . The need to understand and to be able to use mathematics in everyday life and in the workplace has never been greater and will continue to increase . All students should have the opportunity and the support necessary to learn significant mathematics with depth and understanding. There is no conflict between equity and excellence (NCTM, 2000, pp.4-5). Although excellence and creativity are not synonymous, it seems that they have some aspects in common. If we consider, however, what Hemiar pointed out that creativity is the activity that distinguishes man (Hemiar, 1993, p.78), we would accept the possibility that every individual can be creative rejecting confining creativity to some elites, and that creative thinking is developmental under certain conditions (eg motivation, appropriate environment etc). When thinking about mathematics education, the question which may arise is whether mathematical creativity is confined to those having mathematical intelligence according to the multiple intelligences theory (Gardner, 1983, 1999). However, these intelligences are developmental. Then the answer is that mathematical creativity can characterize those having mathematical intelligence and could characterize those who have not that intelligence. MATHEMATICAL CREATIVITY Creativity can be seen as the ability of man to establish new relationships to change reality (Eid, 2000, p.19). So, mathematical creativity can be seen as the mental activity in the area of mathematics education which is directed towards establishing new relationships which go beyond those given in a non-routine mathematical situation (Hemiar, 1993, p.100). The following are some remarks on these definitions: The purpose of the creative process is very important ie to change reality, simply because it distinguishes normal thinking from psychotic one. Traditionally, researchers use to pay much more attention to the product of the creative process. In an educational situation, emphasis should be on the process, where there might or might not be - some products of the creative process. The writer calls this phenomenon relative creativity, ie following the creative process, but not provided reaching new products. Actually, these products are new for the student, not new in mathematics. The role of the teacher is crucial in developing creativity or relative creativity. He/She is responsible to motive students, establishing a creative environment, and guide students to know their own abilities etc. Teachers have to live in a creative atmosphere, by which the writer means professionalization as a way of pre-service teacher education (Mina, 2006, p.114), establishing a career for teaching - if not existing, avoiding the short comings of the existing programmes of in-service teacher education and employing of the lecture method to the minimum (Ibid, pp. 114-115). HOW TO PROMOTE CREATIVITY ? There must be special means to develop creativity (Mina and Mohamed, 1991, p.117). For primary school pupils there is an evidence that a mathematical programme on educational games would develop mathematical creativity (Aly, 1991 and Salama, 2000, p.110), as well as a special programme based on the following (Afifi, 2007, 99.115-116); Establishing new relationships, establishing new models, predicting some mathematical ideas and possibility of their application, non-routine problem solving, criticizing mathematical ideas and facing pupils with open- ended problems. As for secondary students, there is an evidence that many approaches can be used to develop mathematical creativity such as; General problems, mathematical problems - based on non-routine problems in mathematics and the cultural - historical approach - where points of departure in mathematics are studied in their historical contexts (Hemiar, 1993, pp.167-169). Although all the above mentioned approaches have proved to be affective in developing both kinds of creativity ; in general and mathematical creativity, the cultural historical has proved to come on the top of them in developing mathematical creativity (Ibid, pp.231-232). SOME REQUIREMENTS TO ACHIEVE MATHEMATICAL CREATIVITY The writer - keeping in mind the systemic view - sees that the most essential inputs to mathematical creativity in our era are; Adopting developments in science as the student becomes a young researcher as well as paradigm shifts in education, mathematics and mathematics education, considering new classification of educational objectives than Blooms (Bloom et al, 1956; Anderson & Krathwohl, 2001 and Marzano & Kendall, 2007). Such as adoption must be strengthen by changing policies of pre- and in-service teacher education on the bases mentioned above, establishing an educational environment by teachers which is able to foster creativity - which is characterized by being free from particular means of punishment, transparency, self-education and educational activities. These suggestions must be associated with introducing radical appropriate changes in methods of teaching mathematics and means of evaluation. To clarify the present section, some lights will be thrown on paradigm shifts in science, education, mathematics and mathematics education Paradigm shift in science is from "simplification" to "complexity" (Aida et al, 1984)). Complexity can be described in terms of the following developments (Mina, 2003, pp. 23-26): The emerge of the relativity theory, the second law of thermodynamics and other scientific developments lead to realize that there is no more simple and absolute laws controlling motion and the globe. The appearance of the general systems theory and cybernetics, then the emerge of theories dealing with behaviour of systems, eg chaos theory and catastrophe theory, leads to transdisciplinarity and rejecting the linear vision. Researchers constitute a component of a research system, so it is not possible to consider research neutral. The undecidability theory of Kurt Gdel and falseiability (instead of verification) of Karl Popper make scientists suggest that thought is no more controlled by logic. Further, the Heisenberg law of uncertainty, makes people think that it is not likely to have "certain facts". In the light of the above mentioned developments, it is suggested that the main goal of science is to understand reality with the intension to influence and change it. Cohesion of knowledge and its technological applications. The development in technologies of communication, measurement and its units and scientific calculations. Three interacted characteristics distinguish paradigm shift in education; self-education, concurrent education and developing creativity. Thus, education has to move from the "traditional" type - concentrating on knowledge in the narrow sense, to education with no limits, as well as from "given certain" knowledge to criticizing knowledge and utilizing them in new senses. However, this requires developing some values of our area, e.g. respecting the other, team working , etc. (Mina, 2003, p. 6). Paradigm shift in mathematics is from seeing mathematics as the study of formal systems to seeing mathematics as a living body (Mina, 2006, pp. 40-41). This has been reflected in primary school mathematics programmes "from seeing mathematics as a large collection of concepts and skills to be mastered in some strict partial order to seeing mathematics as something people do" (Romberg, 1994, p. 3655), and in secondary school programmes from the "formal" teaching of mathematics to introducing mathematics as a human activity in order to provide a basic preparation of learners for the full participation as functional member s of society (Travers, 1994, p. 3661). Some example to be followed in programmes of teacher pre- and in-service education to cope with the above mentioned paradigms shifts are: Including a research topic in these programmes, attempting to employ complexity to deal with, and identifying some integrated areas to be subject to research that students can deal with. CONCLUSIONS AND FUTURE WORK The main conclusions and features of future work are presented as follows: Every one can be creative. The theory of multiple intelligences supports this possibility, though might be in different areas. According to the developmental natural of these intelligences, mathematical creativity can be for all. However, future work can decide upon this issue by looking for an evidence. Creativity can be seen as the ability of man to establish new relationships to change reality. Mathematical creativity can be seen as the mental activity in the area of mathematics education which is directed towards establishing new relationships - which go beyond those given - in a non-routine mathematical situation. So, the emphasis would be given to the process in the framework of relative creativity. Therefore, the role of the teacher is crucial in the area. Much more work would be directed to the role of teachers in developing students creativity and their mathematical creativity. This paper suggests professionalization in programmes of pre-service teacher education and other practical suggestions for in- service teacher education. There must be curricula or programmes designed intentionally to develop creativity. Many approaches in mathematics teaching have proved to be affective in developing creativity in general and mathematical creativity, including mathematical games and the cultural-historical approach. However, this area is open to further research, there is a need to study the effect of integrated curricula, non-rote teaching and learning, achievement an interests towards the subject in developing creativity. There are many requirements to achieve mathematical creativity, some of the most important of them are: Adopting developments in science as well as paradigm shifts in education, mathematics and mathematics education; considering new classification of educational objectives than Blooms one, changing policies of pre- and in service teacher education, establishing an appropriate educational environment and introducing radical changes in methods of teaching mathematics and means of evaluation in the area. REFERENCES Afifi, A. (2007). A suggested programme in mathematics to develop creativity for students of the fourth primary grade, An unpublished MA. Thesis, Faculty of Education, Ain Shams University, Cairo. (In Arabic). Aida S. et al (1984). The Science and Praxis of Complexity. Tokyo: The United Nations University. Aly, M. (1991). Designing programmes for mathematical games to develop mathematical creativity for pupils of the first cycle of basic education, An unpublished PhD Thesis, Faculty of Education, Ain Shams University, Cairo. (In Arabic). Anderson, L. and Krathwohl, D. (Eds.) (2001). A taxonomy for learning, teaching and assessing: A revision of Blooms taxonomy of educational objectives. New York: Longman. Bloom B. et al (1956). Taxonomy of educational objectives; Handbook 1: cognitive domain. London. Longman. Eid, I. (2000). The philosophy of creativity of Mourad Wahba. In: Mourad Wahba and Mona Abousenna (Eds.), Manifesto of Creativity in Education, 17 -24. Cairo: Kebaa House.(In Arabic). Hemiar, A. (1993). Effectiveness of proposed approaches for developing creative thinking in mathematics students in general secondary school education, An unpublished PhD Thesis, Faculty of Education, Ain Shams University, Cairo. (In Arabic). Marzano, R.& Kendall, J. (2007). The new taxonomy of educational objectives, Second edition. Thousand Oaks, California: Corwin Press, Sage. Mina, F. (2003). Issues on curricula of education. Cairo: The Anglo-Egyptian Bookshop. (In Arabic). (2006). Issues on teaching and learning mathematics. Cairo: The Anglo-Egyptian Bookshop. (In Arabic). Mina, F. & Mohamed, S. (December 1990). Creative and mastery learning: A curricular view, WCCI Forum, 4(2), 115-118. NCTM (2000). Principle and standards for school mathematics. Virginia: NCTM. Romberg, T. (1994). Mathematics : Primary school programs. In: T. Husn & T. Postlethwaite (Eds.), The International Encyclopedia of Education, Second edition, 3655-3661. Oxford: Pergamon Press. Salama, H. (2000). The effect of using educational games on developing creative thinking in mathematics for pupils of the first stage of primary education, An unpublished MA Thesis, Faculty of Education. Ain Shams University, Cairo. (In Arabic). Travers, K. (1994). Mathematics : Secondary education programs. In Husn & Postlethwaite, Op. cit, 3661-3668. ABOUT THE AUTHOR Fayez Mina, MA PhD C. Math FIMA Emeritus Professor, Department of Curriculum and Instruction Faculty of Education, Ain Shams University, Cairo, Egypt Cell phone: + 2010 681 3351 E-mail: fmmina@link.com.eg  PAGE 554 PAGE 554 PAGE 554 PAGE 558 PAGE 554    Fayez Mina Promoting Creativity for All Students in Mathematics Education PAGE 98 DG 9: Promoting Creativity for All Students in Mathematics Education, Section 1 PAGE 103 ICME 11, Mexico, 2008 Proceedings of the Discussing Group 9 : Promoting Creativity for All Students in Mathematics Education The 11th International Congress on Mathematical Education Monterrey, Mexico, July 6-13, 2008 PAGE 97 ICME 11, Mexico, 2008 ABCMNOXY   j k w x Ƿvkv]RA0k hW9hjMOJQJ^JmH sH  hW9h[FOJQJ^JmH sH hW9h[FCJaJhW9hW96CJ]aJhW9hW9CJaJhW9hjMCJaJhW9hjM56CJaJhW9hDSp5CJaJhW9h[F5CJ aJ hW9hW95CJ aJ mH sH hW9hW95CJaJmH sH hW9h_%5CJ$aJ$mH sH hW9hW95CJ$\aJ$hhnHtHhcm{6OJQJ^JmH sH  BCNO j k x O y$d\$]^a$gdW9 $d\$a$gdW9 $d\$a$gdW9$hd\$]^ha$gdW9Pd\$]P^gdW9$Pd\$]P^a$gdW9 $d\$a$gdW9gd$d\$]^a$gdW9=? >8 $ & Fqd\$]qa$gdW9$ & Fqd\$]qa$gdW9 $d\$a$gdW9d\$gdW9$qd\$^qa$gdW9 $d\$a$gdW9((i(($+@+3333333334 4!4444n5o5566666G6H6V6W6a66666M7q77188888+9K999?:I:g:: ;6;};<ܹܹܹܹܹܹܹܹܹܹܹܹܹܹܹܹܹܹܹܹܹܹ hW9hW956CJ\]aJhW9hW96CJ]aJhW9hW9@CJaJhW9CJaJhW9hW9CJaJhW9hW95CJ\aJhW95CJ\aJB !x""#$$F%;'')#+$+@++,.$ & F q0d\$]q`0a$gdW9 $d\$a$gdW9 $d\$a$gdW9d\$gdW9$ & F q0d\$]q^`0a$gdW9$ & F q0d\$]q^`0a$gdW9./1333|445v6678999Z::j;`<<<$q0]q^`0a$gdW9 $d\$a$gdW9d\$gdW9$ & F q0d\$]q`0a$gdW9 $d\$a$gdW9<<<<<<<===================================̼yuyuyuyuhRLjhRLUhRL0JmHnHu hRL0JjhRL0JUhW9hjMCJaJhW95CJaJhW9hW95CJaJhW9hW95CJaJmH sH hW95CJaJmH sH hW9hW95CJ\aJhW9hW96CJ]aJhW9hW9CJaJ)<<=>=w=============>> >I>J>K>$a$gd:$a$gd:$a$gdW9 $d\$a$gdW9d\$gdW9gdW9 $d\$a$gdW9=>>> >I>J>K>L>R>S>U>V>W>[>]>>>>>>>>>>̼̜xhThG̜xh6CJOJQJaJ'h;h6CJOJQJaJmHsHh;h6CJOJQJaJ%hU0JCJOJQJaJmHnHu hAoIh0JCJOJQJaJ)jhAoIh0JCJOJQJUaJh:hCJaJh:hCJOJQJ\aJhhW9hOJQJaJhCJOJQJaJmH sH $hW9hCJOJQJaJmH sH K>W>>>>>>>5?6?q??????$a$gd(#',&#$+D,gd$ 9r  ]a$gdIi$ 9r  ]a$gd52$a$gd|*$K'&#$+D,a$gdJ$ee]e`ea$gd|*y,&#$+D,gd|*>>>>5?6????????????????Ӿᩘyjc_ThW9hjMCJaJhRL hIihh;h(#CJOJQJaJh(#CJOJQJaJ%hU0JCJOJQJaJmHnHu hAoIh0JCJOJQJaJ)jhAoIh0JCJOJQJUaJ h-Chh-Ch56CJaJh-Ch56CJ aJ hh;hCJOJQJaJhCJOJQJaJ??? $d\$a$gdW9< 00&P 1hPa:pU. 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