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Mathematics Competitions Vol 23 No 2 2010, in doing mathematics which we define as solving problems that for him. or her are new and original, Every year new and exciting competitions are organized to cover new ar. eas seen as crucial be these by age group by geographical region or by. the type of problems content level of difficulty format included In. 2008 in Latin America we were told about the Brazilian Math Olympiad. for Public Schools that had more than 18 million participants In 2009. the Colombian Math Olympiads founded an interuniversity competition. for Latin America similar to the IMC with the participation of universi. ties from 6 countries in its first version and a second version to be held. in Brazil in 2010 WFNMC has been instrumental in giving support and. recognition to those doing this work as well as serving as a multiplier. through its congress and journal to inform others whose own work can. benefit from analyzing the design the activities and the problems posed. Peru has been able to obtain the backing of the Ministry of Education. for its math Olympiad which has meant an increase to about 3 million. students in the event This is another important area that of signifi. cantly increasing the number of students who benefit from the Olympiad. experience where the work of WFNMC continues to be influential. Similar activity abounds in virtually all geographical regions around the. globe and in the days to come we will hear from several speakers how. new events have given new impulse to students and sparked favorable. changes in math education in their countries or regions. Our Federation should continue to be instrumental in bringing the Olym. piad experience to students in all corners of the globe accompanying. new national transnational and regional events approaching new groups. such as those organizing the primary or elementary school Olympiad on. the international level as well as the organizers of the IMC and similar. university competitions to extend the reach of mathematical competi. tions to ensure that they also enrich the mathematical experience of the. youngest students and undergraduates alike, WFNMC also serves as an avenue for competitions covering new aca. demic territory Two years ago we learned about an optimization compe. tition in Russia named Construct Investigate Explore held in the same. mode as distance learning and serving students from the sixth form to. Mathematics Competitions Vol 23 No 2 2010, postgraduate level In this congress we will hear about an International. Internet Competition for University Students the Australian Interme. diate Mathematics Olympiad a Statistics Olympiad in Iran and several. One area that must be strengthened is that of formal research to supple. ment our professional appreciation of the impact of competition activity. The Federation should look to encourage its members to engage in. research that can provide solid evidence of the impact of competitions. on the student and on the educational system as well as on the field. of mathematics research that provides a foundation for practice in a. variety of ways, The American Mathematical Society for example published in 2008 a.

study done by Jim Gleason using models developed by psychologists. and thus pertinent and acceptable to educators in other areas of research. in mathematics education such as PME International Group for the. Psychology of Mathematics Education that shows that in fact designing. an Olympiad with a first round that includes multiple choice questions. as many of the popular Olympiads do is a process that responds to the. objectives and corresponds to the aims that such events profess and. that the great majority of the problems posed in a popular unnamed. nationwide competition are in fact well designed to fulfill its aims and. objectives, The Mathematical Sciences Research Institute of UC Berkeley commis. sioned a study to analyze the educational history of students with out. standing results in the Putnam Competition a case study whose 2005. report by Steve Olson revealed several critical moments in the attraction. of young students to the field of mathematics, There is no doubt that this line of research and action is seen by IMU. for example and by all those present as vital to the continuing task. of attracting talented young people to the field of mathematics not. only enriching the lives of these future mathematicians but also thus. furthering mathematics itself The afternoon of talks given by former. IMO medalists at the 50th IMO last year in Bremen showed brilliantly. the key contribution being made,Mathematics Competitions Vol 23 No 2 2010. During the time Petar Kenderov and I had the opportunity to serve on. the ICMI Executive Committee this role of mathematics competitions. was highlighted by a concern of IMU referred to as the pipeline issue. The math education community represented by ICMI has slowly focused. on the issue coming up with an intermediate case study eight countries. that has yielded some very useful information There will be a report. at the IMU meeting in India in August Nevertheless the question of. whether or not there is a real decline in the number of people choosing to. follow a career in mathematics has not been answered by the study and. under the current design and objectives no attempt to gather complete. information will be made, As we all know this is the same concern that prompted Hilbert in the. early twentieth century to draw up his famous list of problems yet to. be solved Young people must know that there are still open questions. in mathematics so that they will find the field not only attractive but. irresistible Certainly events such as the IMO have led a large number. of talented young students to devote themselves to doing mathematics. Its power and beauty are exposed the student feels himself part of the. sublime human endeavor that is mathematics, The Federation must be active in proposing and supporting research.

regarding the solidity of practice and the depth and extent of impact of. competitions and in publishing its findings Our journal must reflect. these aspects of the work of the Federation as well as the fine job it. has done offering articles on the design academic planning problem. creation organization and realization of competitions. As we have seen in the past and will see again in the days to come. the problems posed in math competitions often link the work of the. Federation and its members to research in mathematics This is one. of the most important aspects that link the Federation to research the. original problems created for math competitions often correspond to new. results that is to say results of effectively doing research in elementary. mathematics Another important link stems from new results in research. on the frontier of mathematics that can and have lead to the formulation. of original problems for the highest level competitions such as the IMO. More than a dozen of the talks given at this congress speak to results of. this nature,Mathematics Competitions Vol 23 No 2 2010. WFNMC can and should stress this aspect of its work and the work of its. members before the international community making clear its links to. important areas of research in mathematics and mathematics education. on many different levels, There is a second line of research and development that we wish to sug. gest for future action of the Federation that is the designing planning. organizing and carrying out of research relating to the nature of math. ematical thinking and of how the experience of the average math class. can be brought closer to developing the mathematical thinking of stu. dents in ways that will be personally satisfying and fun and enable the. student to leave all options open when making life choices from career. to personal finance to exercising the rights of a citizen. This line of development will link the work of the Federation with other. areas of research in mathematics education and will involve looking at. both teacher education and the curriculum, The idea that all students can enjoy challenging and enriching experi. ences in mathematics is not new, When beginning to prepare this talk I remembered Plato s dialogue. Meno in which Plato wishes to gain adherents to his explanation of how. learning is possible and in which Socrates actions have been famously. taken to illustrate what we call the Socratic method however I wish to. look at them as an example of mathematics teaching involving challenges. In the Meno the pupil s condition as a slave is meant to assure us that. he has no prior mathematical knowledge and that all for him is new. The problem set by Socrates is to draw construct a square whose area. is twice the area of a given square, The slave begins by suggesting that we double the length of the side and.

Socrates drawing in the sand or dust shows that the resulting figure has. four times the area of the original, We reproduce on the next pages from a copy of Plato s Collected Di. alogues and Letters the only illustrations in more than 1700 pages of. Mathematics Competitions Vol 23 No 2 2010,Mathematics Competitions Vol 23 No 2 2010. The slave s second suggestion is to increase the sides a distance of half. the length of the given side, In each instance Socrates disproves the conjecture using diagrams or. proofs without words and then finally he draws the diagonal of the. given square and leads the slave to see that again proof without words. the square constructed on the diagonal as side fulfills the requirements. of the problem posed, The problem is fresh requiring thought the attempts by the slave to. solve it are respected but firmly shown to be in error the solution arrived. at through questioning is diagramatic conclusive and elegant. We are not trying to promote the Socratic method but rather illustrate. how 2400 years ago it was thought that anybody even a slave with. no prior knowledge can solve interesting and challenging problems in. mathematics if and when that person is given a chance. What have we here An excellent problem a superstar teacher a. superlative way of exhibiting the solution that instantly convinces the. learner of its correctness, Every child shows his or her originality and creativity outside the math.

classroom how must we set our goals and build the possibility of their. realization into our schools so that every child is given the chance to show. his or her creativity within the confines of the mathematics classroom. When we speak of giving a child or youngster the opportunity to meet. more challenging mathematics as an essential component of school math. ematics we are in fact proposing three things give the child student. exposure to a mathematical situation or problem that is beyond what. he or she has already met and practiced provide tools to grasp the prob. lem and think about it assist the child to find ways of expressing his or. her thoughts progress and solutions, We cite four fundamental and interrelated reasons for establishing a. role for the Federation in giving renewed impulse to the evolution of. mathematics as presented to the student in school and indeed even. at university although we will develop only one of them under the. Mathematics Competitions Vol 23 No 2 2010,Mathematics Competitions Vol 23 No 2 2010. premise that math competitions and competition mathematics have. shown how careful planning analysis original problems and non stan. dard representations can counteract the separation that some sectors. have attempted to foster between elementary mathematics and school. mathematics between mathematics and math education. These four reasons concern the rights of the student the nature of. mathematics itself the way technology is changing the way we do. mathematics and indeed the way we think and the needs of the. Mathematics Competitions Vol 23 No 2 2010,knowledge based society. Several countries and school systems have long since taken note of the. fundamental change that must take place Many have built a rich. mathematical culture For example professor Konstantinov will be. talking during this Congress of the Russian system under the title Math. Classes in Russia, Other systems are beginning to take note of the desirability of structuring. a more challenging curriculum for all, In the USA the state of Connecticut has put forth the following precept.

Every student needs and deserves a rich and rigorous mathemat. ics curriculum that is focused on the development of concepts the. acquisition of basic and advanced skills and the integration of prob. lem solving experiences The Department of Education encourages. educators to provide such challenging mathematics opportunities to. foster the growth of intelligent thoughtful and mathematically lit. erate members of society, What is interesting about the Connecticut statement is that it stresses. the importance of a challenging mathematical education for the student. and future citizen This is an essential emphasis it is what every student. needs and deserves Furthermore in a recent Summer 2010 article Ed. The Magazine of the Harvard Graduate School of Education thought it. appropriate to emphasize that access to a more exacting mathematics. curriculum albeit in the form of better ways of teaching a. many years In 2008 she was elected at the WFNMC mini conference in Mon terrey as the president of WFNMC Abstract Two fundamental lines of research and action for the World Federation of National Mathematics Competitions are pro posed complementing the traditional areas of problem creation and competition design Links to the work of other international groups and to areas of research and

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