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

2. “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

3. “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

4. 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

5. “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

6. 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

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

8. 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

9. 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

10. 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 ?

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

12. 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

13. Fibonacci (1170-1250)  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

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

15. Studying “Green” Symmetry LEVENBERG - PATKIN ICOLACE 2012

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

17. 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

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

19. 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

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