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Math Foundations

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Math Foundations

  1. 1. Foundations in
  2. 2. Foundations in Math: Developing Mathematical Thinking & Conceptual Understanding in Grades KG-2 EARCOS WEEKEND WORKSHOP- MS. SARA GARRETT November 15, 16, 2014
  3. 3. What i learned...
  4. 4. Building math vocabulary
  5. 5. strategy: active word wall
  6. 6. collaboratively, we worked to construct meaning, & show relationships with the new vocabulary
  7. 7. this...
  8. 8. and this...
  9. 9. evolved into this...
  10. 10. and this...
  11. 11. evolved into this...
  12. 12. evolved into this...
  13. 13. and evolved into this...
  14. 14. with a growth- mindset we used inquiry & discourse to construct new meaning
  15. 15. Let’s look a little closer at some of the vocabulary
  16. 16. enactive
  17. 17. enactive
  18. 18. enactive= action-based Using coins...
  19. 19. enactive Using blocks, chips...
  20. 20. enactive Using base-ten blocks, etc.
  21. 21. ICONIC
  22. 22. ICONIC
  23. 23. ICONIC= image-based
  24. 24. ICONIC= sometimes called the pictoral stage
  25. 25. SYMBOLI C
  26. 26. SYMBOLI C
  27. 27. SYMBOLIC= language-based
  28. 28. symbolic= sometimes called the abstract stage
  29. 29. horizontal mathematization Freudenthal institute (F.I.) under the auspices of Hans Freudenthal (1905-1990)
  30. 30. horizontal mathematization= going from the world of life to the world of symbols
  31. 31. horizontal mathematization (example) Freudenthal institute (F.I.) under the auspices of Hans Freudenthal (1905-1990) The majority of pupils started off the problem by guessing, usually with the assumption that a t-shirt will cost more drink. After being asked to find another method for calculating the respective values they start to develop mathem tools to deal with situation. This primarily involved the idea of exchange i.e. 2 t-shirts + 2 drinks = $44.00 1 t-shirt + 3 drinks = $30.00 0 t-shirts + 4 drinks = $16.00
  32. 32. horizontal mathematization= the students come up with mathematical tools that can help to organize and solve a problem located in a real-life situation.
  33. 33. VERTICAL mathematization Freudenthal institute (F.I.) under the auspices of Hans Freudenthal (1905-1990)
  34. 34. vertical mathematization= the process of reorganization within the mathematical system itself, like, for instance, finding shortcuts and discovering connections between concepts and strategies and then applying these discoveries.
  35. 35. vertical mathematization= moving within the world of symbols
  36. 36. working with real examples...
  37. 37. In small groups we worked on 3 different problems to experience mathematical discourse
  38. 38. Patti made 42 friendship bracelets to sell. She sold 17 of them on Monday. How many friendship bracelets does Patti have now?
  39. 39. The rabbit jumped 17 inches further than the frog. The rabbit jumped 42 inches. How far did the frog jump?
  40. 40. Jane is climbing to the top of the bell tower. There are 42 steps in the tower. She has climbed 17 steps already. How many more steps does Jane need to climb to get to the top of the tower?
  41. 41. looking at the three different questions and the variety of answers was an eye-opening process. I was amazed at the variety in approaches to solving a problem. The richness of the mathematical discourse was thought-provoking, and helped deepen my understanding of problem-solving strategies. Reflection
  42. 42. PRODUCTIVE STRUGGLE CREATING THIS PRESENTATION WAS A PRODUCTIVE STRUGGLE
  43. 43. Additional examples
  44. 44. Foundations in
  45. 45. ● http://bruners- stages.wikispaces.com/Bruner%27s+Stages+of+Representation ● http://www.nctm.org/profdev/content.aspx?id=23609 ● http://campuspaper.blogspot.com/2012/10/horizontal-and-vertical- mathematization.html#.VJC6faSUeVI ● http://www.did.stu.mmu.ac.uk/cme/Student_Writings/RichHarrison/RichardH arrison.html resources/reference:
  46. 46. http://www.youcubed.org/
  47. 47. TO BE CONTINUED. ..
  48. 48. MR. DARYL RUAMRUDEE INTERNATIONAL SCHOOL facebook: https://www.facebook.com/pages/RIS-Elementary-School/566272910150141 Twitter: @Daryl_I linkedin: Daryl Imanishi slideshare: http://www.slideshare.net/DarylImanishi LET’S CONNECT...

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