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Masalah Pendidikan 2006, Universiti Malaya 103 CREATIVITY IN THE TEACHING AND LEARNING OF MATHEMATICS: ISSUES AND PROSPECTS Noraini Idris Department of Mathematics and Science Education Faculty of Education University of Malaya Kreativiti dalam pengajaran dan pembelajaran matematik di dalam bilik darjah akan memberi ruang yang luas kepada perkembangan potensi pelajar seperti mengembangkan minat, mengasah bakat dan kebolehan, mengembangkan pelbagai kemahiran serta memberi kepuasan kepada indiv
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   Masalah Pendidikan 2006, Universiti Malaya 103 CREATIVITYINTHETEACHINGANDLEARNINGOFMATHEMATICS:ISSUESANDPROSPECTSNoraini Idris Department of Mathematics and Science EducationFaculty of EducationUniversity of Malaya Kreativiti dalam pengajaran dan pembelajaran matematik di dalam bilik darjah akanmemberi ruang yang luas kepada perkembangan potensi pelajar sepertimengembangkan minat, mengasah bakat dan kebolehan, mengembangkan pelbagaikemahiran serta memberi kepuasan kepada individu untuk mencapai kejayaan.Pengaliran idea yang kreatifdan inovatif dalam pengajaran dan pembelajaranmatematik liapat memperluaskan daya pemikiran kreatifpara pelajar, Penggunaan pelbagai metodologi atau perkaedahan dapat menyuburkan unsur-unsur kreativiti dalambilik darjah. Dalam era pembangunan negara yang pesat ini, teknologi telah menjadialat penyelesaian masalah dalam perindustrian dan perniagaan. Teknologi bolehdianggap sebagai alat, strategi danpendekatan untuk mengembangkan daya kreativiti pelajar dan guru dalam bilik darjah. Dalam artikel ini, penulis akan membincangkantentang apakah itu kreativiti, prosedur untuk mengukur kreativiti dan isu-isu serta prospek kreativiti dalam pengajaran dan pembelajaran matematik. In this information and communication technology age, creative and skilled manpowerare needed to support the vision of our nation. But the question is, What kind of work dostudents find totally engaging to promote creativity? Students want and need work thatstimulates their curiosity and awakens their desire for deep understanding. As for topicsthat relate to students' lives, the connection here cannot be superficial; it must involve anissue or idea that is manageable. How can we connect them? To prepare students for lifein today's highly technical society, their mathematical and science knowledge as well ascreativity must include and go beyond knowledge of the simple skills into capability tosolve more complex problems.Malaysia, like many other nations, is cognizant of the need to facilitate theeducation of smart learners capable of working competently with others in teams in aninformation technology environment and to be aware of their own learning, performance,and creativity. We need to prepare students who know how to identify problems andsolutions, work in teams, communicate well, and know how to evaluate their potential inmathematical creativity. In this article the author will discuss the definition of creativity,procedures for assessing mathematical creativity, as well as the issues and prospects of creativity in mathematics teaching and learning. The discussion will take into accountaspirations for national development in the 21st century and the implications for teachereducation.  104 Masalah Pendidikan 2006, Universiti Malaya An emerging technological society and economy makes mathematical knowledgeand creativity both essential and advantageous for students as they position themselvesto join the workforce. In Malaysia, cultivating a mathematically competent and creativeworkforce depends on the concomitant improvement of mathematical achievementamong students in order to possess the mathematical knowledge to produce, use, andmanipulate new technologies. In secondary mathematics, this would mean that the orderand treatment of most topics would need to change. Definition of Creativity and Assessment of Mathematical Creativity Literature shows there are numerous ways to express and define creativity. Some people referto creativity as a special kind of thinking, while others refer to the generation of products.There is yet to be one definition of creativity acceptable to everyone. However, severalexperts on creativity generally agree on the five phases of the creative process, namely (a)Preparation phase - acquiring skills, sensing and denning a problem; (b) Concentrationphase - focusing intensely on the problem; (c) Incubation phase - withdrawing from theproblem; (d) Illumination phase - the stage involving the emergence of an idea; and (e)Elaboration phase - testing out the idea (Guilford, 1975).Torrance (1984) denned creativity as a process of becoming sensitive to problems.He described four components for assessing individual creativity, namely: (a) fluency asthe ability to produce a large number of ideas; (b) flexibility as the ability to produce avariety of ideas; (c) elaboration as the ability to develop an idea; and (d) srcinality as theability to produce unusual ideas. Creativity has been denned as the ability to produce newthings or new knowledge (Simonton, 2000) or the ability to produce something effectiveand novel (Quigley, 1998). Standler (1998) tried to differentiate between creativity andintelligence as that between a creative person and an intelligent person; the intelligentperson has the ability to learn and to think, while a creative person does things that havenever been done before.Healy (1994) gave her definition of creativity as the ability to generate, to approachproblems in any field from fresh perspectives. All children are potentially gifted andcreative in delightfully individual ways. Similarly, Schifter (1999) defined creativity asthe ability to take existing objects and combine them in different ways for new purposes.Thus, creativity is the action of combining previously uncombined elements.The Oxford English Dictionary (1995) describes creativity as being imaginativeand inventive, bringing into existence, making, srcinating . So the word creativity seemsto describe change that can generate novel ideas. It is the capacity to get ideas, especiallysrcinal, inventive and novel ideas.According to Torrance and Goff (1990) academic creativity is a process of thinkingabout, learning and producing information in school subjects such as science, mathematicsand history. They acknowledged the difficulty in agreeing on a precise definition.Nevertheless, when we say the word creativity, everyone senses a special excitement.Children prefer to learn in creative ways rather than just memorizing information providedby a teacher. They also learn better and sometimes faster. The creative mind always hasthe ability to relate to imaginative activity; being imaginative is having the potential of interpreting something in a rather unusual way.   Masalah Pendidikan 2006, Universiti Malaya 105 In terms of teaching children in school, Cropley (1992) gave the process-baseddefinition of creativity as the capacity to get ideas. Creative ideas are especially srcinal,inventive and novel. Likewise, Higgins (1994) defined creativity as the process of generating something new that has value . He also linked creativity to innovation anddefined innovation is a creation that has a significant value . Thus, much emphasis hasbeen put on generating ideas that are novel and worthwhile.One of the characteristics of the so-called creative mind lies in the ability to think imaginatively. Being imaginative is having the potential of interpreting something in a ratherunusual way. Craft (2000) introduced possibility thinking as a core element in creativity.Possibility thinking means refusing to be puzzled by a problem, instead being imaginativein finding a way around it. This is very useful and appropriate especially when dealing withmathematical problems. Many new ideas can be generated in various fields. They can be inart, music, design, mathematics, science, problem solving, and so on.The^above discussionriias shown there is no single accepted definition of mathematical creativity. The wide variety of definitions and characteristics has createdchallenges in the identification and development of mathematical creativity.Kohler (1997) claimed that the inadequate success of students in mathematicsmight be due to lack of creative approaches in teaching and learning. Creativity-enrichedmathematical problems can be developed to assess mathematical creativity. Evans (1964)identified three aspects that elicit creative thinking in mathematics. These are fluency,flexibility and srcinality. These parameters are used for assessing general creativity inTorrance's (1966) general divergent production tests. The Torrance Tests of CreativeThinking (TTCT) (Torrance, 1974) have frequently been utilized to assess children'screative thinking.Fluency refers to the number of ideas generated, flexibility to the shifts in approaches,and novelty to the srcinality of the ideas generated. The three components can be adaptedand applied in the domain of mathematical creativity. The fluency score is the total numberof relevant responses made, the flexibility score is the number of different methodsor categories of ideas, while the srcinality score is based on the number of unusual,unique or infrequent ideas. Students' responses to mathematical creativity problems canbe assigned by fluency and srcinality scores (Prouse, 1967). Fluency may be awardedby counting the number of acceptable responses made. Duplicate responses are to beeliminated. The srcinality score is obtained by giving weight for correct responses withina range of percentage by students giving the same response (Prouse, 1967). For example,a weight of one (1) is assigned to a common response given by 25 percent to 50 percentof the students.In order to assess students' mathematical creativity, it is necessary to select suitablecreativity-enriched mathematical problems rather than routine problems. A creativity-enriched mathematical problem is one that can be solved by various approaches andpermits many possible answers. Torrance (1982) argued that tasks requiring generation of a variety of possible solutions could stimulate more creative thinking than tasks that needonly one correct response or answer.  106 Masalah Pendidikan 2006, Universiti Malaya Teaching and Learning of Mathematical Creativity   Mathematics relies on logic and creativity, and it is pursued both for a variety of practicalpurposes and for its intrinsic interest. The essence of mathematics lies in its beauty and itsintellectual challenge. Learning to know our creative ability is one of the most significantaspects of our life, for everything we do is affected by our thinking abilities.The teaching and learning of mathematics involves the use of creativity andthinking skills. Mathematical skills extend beyond the ability to calculate; they encompassreasoning, creativity, problem-solving, analyzing and many other skills. These skillsinvolve higher level cognitive processing. Mathematics is used every day by people toidentify problems, solve problems and communicate the solutions to others. Mathematicspervades almost every aspect of our lives. Hence students who learn mathematics well arebetter prepared for a future in which mathematics is commonplace.Malaysia, like many nations, is cognizant of the need to develop creative students(Ministry of Education, 2001). Schools need to prepare students who know how to identifya problem and its solution, students who are creative, able to communicate well, and knowhow to evaluate progress and learning (Meissner, 2000; Ministry of Education, 1997).When learning mathematics, students are required to be thoughtful and creative, and areexpected to be aware of their own cognition in order to monitor their own learning, as theyparticipate actively and constructively to learn with understanding.Creativity in the teaching and learning of mathematics helps students makesense of the world around them and find meaning in the physical world. They learnto reason, to connect ideas, and to think logically. However, typical school practicesassume that students must be told what to do and how to do it. In most mathematicsclassrooms, mathematics is taught to students as if it is a complete and unchangeablebody of knowledge, with all rules and procedures. Mathematics is actually a changing andgrowing body of knowledge. Students need to see how mathematics was developed, andrealize that creative individuals shaped the body of mathematical knowledge. However,it seems that students learning mathematics still rely too much on routine processes andalgorithms. Less emphasis is placed on creative ways of expressing ideas and displayingmathematical solutions.However, there are teachers who present their students with the appropriatechallenges and these teachers have observed that their students are able to invent theirown methods and arrive at more creative and confident approaches in solving problems.Probably no one is likely to believe in this possibility unless they have had an opportunityto see children actually do it.Hutcheson (2001) put forward two ancient problems that can be used to promptstudents to think broadly and creatively. The first one relates to trisecting of an angle intothree equal parts and the other relates to dividing a circle into any number of equal parts.As Craft (2000) had pointed out, activities that generate more than one conjecture providemore opportunities for mathematical creativity. In other words, students are encouragedto use various approaches to tackle creativity-enriched mathematical problems.Tanner and Jones (2000) suggested students should be given more opportunitiesto meet an appropriate range of unfamiliar problems. These include practical tasks,investigations in real life and within mathematics itself. Furthermore, these problems
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