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Technology and the Yin & Yang of Teaching and Learning Mathematics

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88 diapositives · 1.1K Views · Sep 25, 2014

In the realm of mathematics education, the dual forces of "hold on" and "let go" shape our teaching strategies. "Hold on" represents the need to connect with students, engage them, and foster communication, while "let go" emphasizes automation and exploration through technology. This approach highlights the essential balance educators must achieve in utilizing technology for enhanced learning. By integrating technology thoughtfully in pedagogy, teachers can transform mathematical problem-solving, foster deeper understanding, and create new learning experiences that benefit all students.

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  1. Technology and the Yin & Yang ofTeaching and Learning Mathematics B Kutzler, Austria

  2. Humans are ruled by two opposite forces: hold on let go

  3. Humans are ruled by two opposite forces: hold on (yin) let go (yang)

  4. In our context these show as hold on = connect let go = automate

  5. Automate Automate = compensate + amplify = compensate + (solve + explore)

  6. automate compensate explore solve

  7. Connect Connect= = represent + document + communicate

  8. Connect Connect = model  = represent + document + communicate model

  9. Connect Connect = model model   = represent + document + communicate  model human

  10. Connect Connect = model model human  = represent + document + communicate   model human human

  11. connect document communicate represent

  12. connect automate document communicate compensate represent explore solve

  13. connect automate document communicate compensate represent explore solve

  14. Math-Pedagogy-Technology Space technology mathematics pedagogy

  15. Math-Pedagogy-Technology Space technology mathematics

  16. With a helicopter one can reach places that one cannot reach otherwise.

  17. With a helicopter one can reach places that one cannot reach otherwise.B Waits: Tech makes some math possible

  18. With a helicopter one can reach places that one cannot reach otherwise.B Waits: Tech makes some math possible Tech makes some math pedagogy possible

  19. Not the tool, but the use of the tool is or is not pedagogical. (Vlasta Kokol-Voljc)

  20. Teacher training: Step 1: technology axis Step 2: math/technology plane Step 3: math/pedagogy/technology space Introducing teachers to technology needs as much (pedagogical) care as any other teaching

  21. (1) Represent

  22. (1) Represent Mathematical problem solving = the art of transforming representations (until the solution is visible)

  23. (1) Represent Mathematical problem solving = the art of transforming representations (until the solution is visible)such as transforming 5x-6=2x+15into x=7

  24. (1) Represent Algebraic/graphic/numeric 1+2  3 3a+4a  7a 24  2 6 24  4.89898

  25. (1) Represent Use technology to simulate a mathematician‘s mind New pedagogy (helps more students to understand)

  26. (2) Document = share your work with an anonymous person argue (= convince sb with certain level of knowledge) designdescribe

  27. (2) Document Describe/understand Newspaper articles Mathematical logic27 is divisible by 3  x(3x=27) every number is greater than its predecessor x(x>x-1) Use wordproblems to practice understanding

  28. (2) Document Argue - Examples such asExplain why one uses the first derivative to find the extreme values of a function If a curve is symmetric in both the x- and y-axes, is it then symmetric through the origin? Give a reason or find a counter-example.

  29. (2) Document With technology: Result loses importance Choosing keys/commands is mathematical work New pedagogy (shift focus fromexecuting algorithms to documenting mathematical work)

  30. (3) Communicate = impart or transmit idea, knowledge, information Documentation = „offline“ communication „Online“ communication

  31. (3) Communicate Student  teacher: - front teaching - teacher as advisor and assistant Student  student: - alone (cf traditional exam) - teamwork New pedagogy (enables new teaching/learning styles)

  32. (4) Compensate

  33. (4) Compensate

  34. (4) Compensate

  35. (4) Compensate

  36. (4) Compensate

  37. (4) Compensate