Math Foundations
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This document summarizes a workshop on developing mathematical thinking in grades K-2. It discusses key concepts like the enactive, iconic, and symbolic stages of learning math. It also covers horizontal and vertical mathematization, which refer to relating math ideas to real-world contexts and reorganizing within the mathematical system. Workshop activities focused on collaborative vocabulary building, problem solving in small groups, and reflecting on different solution approaches. Productive struggle and mathematical discourse were emphasized as aids to conceptual understanding. Resources for further learning were also provided.
Math Foundations
- 2. Foundations in Math: Developing Mathematical Thinking & Conceptual Understanding in Grades KG-2 EARCOS WEEKEND WORKSHOP- MS. SARA GARRETT November 15, 16, 2014
- 6. collaboratively, we worked to construct meaning, & show relationships with the new vocabulary
- 7. this...
- 8. and this...
- 10. and this...
- 14. with a growth- mindset we used inquiry & discourse to construct new meaning
- 15. Let’s look a little closer at some of the vocabulary
- 17. enactive
- 18. enactive
- 22. ICONIC
- 23. ICONIC
- 25. ICONIC= sometimes called the pictoral stage
- 26. SYMBOLI C
- 27. SYMBOLI C
- 29. symbolic= sometimes called the abstract stage
- 30. horizontal mathematization Freudenthal institute (F.I.) under the auspices of Hans Freudenthal (1905-1990)
- 31. horizontal mathematization= going from the world of life to the world of symbols
- 32. 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
- 33. horizontal mathematization= the students come up with mathematical tools that can help to organize and solve a problem located in a real-life situation.
- 34. VERTICAL mathematization Freudenthal institute (F.I.) under the auspices of Hans Freudenthal (1905-1990)
- 35. 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.
- 36. vertical mathematization= moving within the world of symbols
- 39. In small groups we worked on 3 different problems to experience mathematical discourse
- 42. Patti made 42 friendship bracelets to sell. She sold 17 of them on Monday. How many friendship bracelets does Patti have now?
- 45. The rabbit jumped 17 inches further than the frog. The rabbit jumped 42 inches. How far did the frog jump?
- 49. 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?
- 51. 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
- 52. PRODUCTIVE STRUGGLE CREATING THIS PRESENTATION WAS A PRODUCTIVE STRUGGLE
- 56. Foundations in
- 57. ● 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:
- 60. 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...