ࡱ> BDA{ @ibjbj >p؝؝,L4444444H,+,+,+8d+\+tHb`@,,:---F.F.F._______$rbRd_E44B.B.44_44--4`$===424-4-_=4_==V44/X-4, @>Y,+9V{Y&`<b`V\e^;Be0/XHH4444/Xe4CX8F./&=11F.F.F.__HH",+<dHH,+ PREPARING STUDENTS FOR TEAM COMPETITIONS IN MATHEMATICS POSSIBILITY TO WORK WITH ALL STUDENTS ILIANA TSVETKOVA Abstract: Students who possess mathematical abilities are often not able to improve them. The purpose of this paper is to present an unconventional way of involving all the students in creative mathematical activities. This is the preparation for team competitions. It provides an opportunity for every student to discover their own interests and creativeness in a particular sphere of mathematics. The methodology and the effectiveness of this way of teaching are shortly described in the present paper. Key words: Creative Process, Creative Environment, Creative Abilities, Team Work INTRODUCTION The concept of teaching Mathematics and mathematical abilities is frequently discussed in our society. Margaret Wente, in her article Do the Math? Not our Kids!, quotes Professor Sherry Mantyka, a research mathematician at Memorial University in Newfoundland: Math isn't like other academic subjects. It's more like learning to play a sport or instrument. You have to acquire the core skills through practice, drill and repetition, until you can execute them without thinking. Instead, the emphasis in modern Math education is to make it fun and entertaining, by giving students problems to solve through investigation. The process is as important (maybe more) as the answer. (Wente,2007). Indeed, Math can be attractive, interesting and exciting. One of the ways to present it from this view point is to involve all the students in creative activities such as preparing students for team competitions in Mathematics. They gather together conscious thinking, solving through investigation, fun and entertaining. Everyone has the ability to learn Mathematics, although some children learn and make connections quicker than others. (Borovik,2006). It is unfortunate that many students never get the opportunity to be taught and guided to achieve their talents. Team work provides opportunity to develop the abilities of each child who has the willingness to be engaged with Mathematics because there are much more mathematically able children than most people are prepared to believe, and everyone has some mathematical abilities. (Borovik, 2006). In Bulgaria many students between fifth and eight grade show interest in mathematics because it develops their thinking, logic and creativity skills. Most of them are not competitors; nevertheless, a lot of children take part in extra lessons with interest and enthusiasm. The abilities of each individual are different and the mathematical ones are extremely important social resource (Tabov, 2004). However, for its correct and completely fruitful usage special care is needed (Tabov, 2004). Preparation for team competitions gives the opportunity to work with all the students depending on their special creative abilities because it provides suitable creative environment. This way the realization and development of this resource are ensured. HOW THE DIFFERENT TYPES OF PREPARATION FOR TEAM COMPETITIONS CONTRIBUTE FOR THE DEVELOPMENT OF THE CREATIVITY OF ALL STUDENTS This paper is a reflection of my twenty years of experience working with students with a special interest in Mathematics, from grade 5 to 8 at the High School of Mathematics in Sofia. During the last ten of these years, it included a lot of training for competitions. Part of the work in these classes is preparation for team competitions, which have gained great popularity recently. This team practice provides a good atmosphere for working with all the students in the class. The individual qualities of each student can be improved and used during group training. During the last years teams from Sofia High School of Mathematics took part in mathematical competitions in which an important role had the team round. Examples of such competitions are Po Leung Kuk Primary Mathematics World Contest, Elementary Mathematics International Contest, Mathematical Tournament Acad. Kiril Popov, Shumen, Bulgaria. This makes the special preparation for team competitions essential. We use weekly classes, each consisting of two lessons. Every student who is interested in Math is invited to visit any lesson during the school year. Before competitions I organise a selection of the team to compete, and provide some intensive preparation. In the regular lessons students are divided into groups of four. There are several types of training that are organised: Eight problems are given to each team. They have to be separated between the 4 members within five minutes. Afterwards, each competitor solves his or her own problems and is not allowed to communicate with the other team mates. They have 60 minutes for solving and writing down the solutions. In this case it is important to dispense the problems among the participants properly, having in mind the interests and capacities of each student. It is possible that every student take responsibility for two problems but it may happen that one student solves the most difficult problem, according to the teams opinion, or someone, who does not feel confident about their knowledge, might take a problem they feel easy and interesting enough. Ten problems, eight of which are divided between the members (as in (1)) and solved within 40 min. Then the last two problems are given to the team to solve as a collaborative effort. Here, in addition to the adequate distribution of the problems, a team work on the two remaining problems is crucial because they are usually investigative and creative. Students often take a problem for two of them as they complement their interests and knowledge. For example, an algebraist and a geometer can work together as well as quick-witted student with precisely working student with a sense for the detail in the solution. Sometimes a consecutive approach is better: the whole team works on all problems, each member takes a different aspect of the problems and gets completely involved in it. In both of these types of training each member takes personal responsibility for the performance of the team. In these cases the most important stage is the correct evaluation of the creative abilities of each student. Four problems are given for team work. This is one of the favorites of the children because it is more emotional and attractive. Some of the problems involve practical work: painting, drawing or producing of an object there are creative and investigative problems. With such tasks even children without obvious mathematical abilities can take part in the teams work fruitfully and effectively by completing the practical work. At the same time everybody participate in the creative process of discussing and solving of the problems and has the opportunity to learn and teach each other. New ways of reasoning, unusual methods and analytical thinking are just few of the skills they can share and exchange. With such training every pupil can do their best for the success of the team. Every interested student has the chance to try this kind of work and to improve their interest and knowledge without realizing it. Problems that are solved in sequence. The solution of each team member depends on the answer of the one before them. In this training the order of the students is most important. Competitors are consequently arranged from the student with the poorest knowledge to the best prepared one, who becomes the team leader. Every competitor receives a different problem and the answer is used as a necessary information for the solution of the following problem. After the start given they begin solving and handing forwards the answers. The aim of each team is to produce the correct answer first. In this type of competition the responsibility of each member is equally important, which creates the sense of personal responsibility. On the other hand the team leader has the opportunity to predict the expected answer and to hand it in faster in order to save time. During all the preparations I observe the work of the teams, advice them on developing their distribution strategies and facilitate collaborative environment where every student can realize their creative ability to the maximum. This way students who usually do not participate in competitions work with pleasure, interest and enthusiasm, improve their mathematical abilities and enrich their knowledge. The analysis of this type of activity shows that it is possible to work with all participants in the classes regardless of their previous preparation level. Simultaneous training and selection of teams for competitions is much easier and more effective. CONCLUSIONS AND FUTURE WORK Preparation of the students for team competitions enables me to work with every interested student and gives opportunity for personal performance. In the selection process for team competitions, students with special abilities, who would not succeed in an individual competition, might be selected because they could be extremely important as part of a team. The creative abilities of each student can be developed through team training activities, because they offer a creative environment and participation in a creative process. APPENDIX Four problems for team work. REFERENCES Borovik, A.V. (2006). Mathematical Abilities and Mathematical Skills. World Federation of National Mathematics Competition Conference 2006, Cambridge, England "01>2, .. (2004), >41>@, ?>43>B>2:0 70 @5H020=5 8 >F5=O20=5 =0 7040G8 70 <0B5<0B8G5A:8 AJAB570=8O, 2004, !>D8O, J;30@8O Wente, M. (2007). Do the math? Not our kids! Globe and Mail, 13.02.2007. ABOUT THE AUTHOR Iliana Tsvetkova Teacher of mathematics Sofia High School of Mathematics 61, Iskar 1000 Sofia Bulgaria Cell phone: +359888979 800 -mail:  HYPERLINK "mailto:iliana_tzvetkova@yahoo.com" iliana_tzvetkova@yahoo.com APPENDIX Anne is at point A and Betty  at point B of a triangle garden with paths. How many paths are there to go from point A to point B always moving to the right?  Answer: 94. The number of prime divisors of number  EMBED Equation.DSMT4  is: Solution:  EMBED Equation.DSMT4  Answer: 5 The houses on one of the street sides are numbered with sequent odds starting from 1. On the other side with even numbers starting from 2. For the even numbers are used 256 digits, and for the odd numbers 404 digits. What is the subtraction of the biggest odd number and the biggest even number? Solution: We have 4 one-digit even numbers, 45 two-digit even numbers and x three- digit even numbers. Therefore  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  and 54-th three-digit even number is 206. By analogy  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  and 103-th three-digit even number is 305. The subtraction is 99. Answer: 99 In standard domino on the blocks there are numbers from 0 to 6. How many blocks should contain the domino, if the blocks numbers are from 0 to 12. 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