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“Green math” Mathematics and Environment Dr. Ilana Levenberg Dr. Dorit Patkin ICOLACE –SINGAPORE July 2012 LEVENBERG - PATKIN ICOLACE 2012

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“We must affect a change in the way mathematics is taught by making its applications an integral part of the learning process.” (N.C.T.M., 2000) LEVENBERG - PATKIN ICOLACE 2012

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“Adding creativity to daily instructional practices will ensure that students are given opportunities to develop all of their potential ….” (Burke Adams 2007) LEVENBERG - PATKIN ICOLACE 2012

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A NEW REFORM IN TEACHING MATHEMATICS Development of multi-disciplinary thinking. Acquaintance with subject matter outside of the school curriculum Reinforcement of logical thinking. Breaking down the framework of conventional thinking. Encouragement of creativity and originality. Exposure to mathematical initiations in various fields. LEVENBERG - PATKIN ICOLACE 2012

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“GREEN MATH” PROJECT “GREEN MATH” PROJECT To integrate interdisciplinary activities within the mathematical instruction in order to achieve a higher level of understanding. To enrich the practical application of mathematical instruction through activities that challenge the student’s imagination. To raise the students awareness to the Environmental quality LEVENBERG - PATKIN ICOLACE 2012

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Who took part in our project? Students from two Teacher College 300 Students Pupils –grade 5 and 6 80 pupils 80 pupils LEVENBERG - PATKIN ICOLACE 2012

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Activities within the “Green math” LEVENBERG - PATKIN ICOLACE 2012 Air pollution Motor Transportation, Factories Water Saving Rational use of electricity Sewage treatment Garbage Recycling

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Green- Math Bottles Recycling Encourage the students to drop empty used bottles to a container for recycling You can drop two size of bottles, ½ liter and 1 liter ½ liter and 1 liter For ½ liter bottle you can get 5 cents For 1 liter bottle you can get 10 cents LEVENBERG - PATKIN ICOLACE 2012

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Green- Math Bottles Recycling Make a list of possibilities to get different amount of money! Start with: 5 cent, 10 cent, 15, 20, 25,…….. Think about: Numbers of bottles you need and the type of the bottles and the type of the bottles Mind the order of the coins you will get from the “ recycling machine” ! LEVENBERG - PATKIN ICOLACE 2012

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List of possibilities LEVENBERG - PATKIN ICOLACE 2012 Amount of money Type and No` of bottles of bottles No` of Possibilities 5 cent 1 10 cent 2 15 cent ? 20 cent ?

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List of possibilities Can you guess the number of possibilities to get 40 cent? LEVENBERG - PATKIN ICOLACE 2012

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Green- Math Bottles Recycling If you did it correct You will get the list of possibilities : 1,2,3,5,8,13,21…….. What can you say about the series of numbers you found? Do you see any pattern? LEVENBERG - PATKIN ICOLACE 2012

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Fibonacci ( ) Fibonacci was an Italian mathematician (Leonardo from Pisa) In mathematics, the Fibonacci series are the numbers in the following integer sequence 1,1,2,3,5,8,13,21,34,55,89,144….. Each number is the sum of the previous two. Fibonacci Published in 1202 his book “LIBER ABBACI “-Book of Calculation LEVENBERG - PATKIN ICOLACE 2012

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What about the durability of the natural energy resources? LEVENBERG - PATKIN ICOLACE 2012

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Studying “Green” Symmetry LEVENBERG - PATKIN ICOLACE 2012

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In what area did “Green math” answer your expectations? LEVENBERG - PATKIN ICOLACE 2012

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Students Feedback “ We had a chance to see Math outside of the classroom”. “We learned Math together with biology, history, geography, physics, economics and more.” “The activities were interesting and challenging”. “We would like to have more activities like this”. LEVENBERG - PATKIN ICOLACE 2012

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Pupils and Students green math Field Trip LEVENBERG - PATKIN ICOLACE 2012

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What did we learn from our PROJECT What did we learn from our PROJECT? The importance of presenting applications for mathematics terms. The importance of building a comprehensive, challenging learning environment for student teachers. The importance of different levels of activities -from the gifted children to others with special need. The importance of teaching mathematics together with materials from other disciplines. The importance of team work in launching complex projects. The importance of educating our students for keeping our environment. LEVENBERG - PATKIN ICOLACE 2012

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We Got the Whole World in our hands LEVENBERG - PATKIN ICOLACE 2012

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