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Math Education at a Crossroads

Math Education at a Crossroads. v/ Karsten Schmidt og Steen Markvorsen. Crossroads. Synopsis. Demands Coverage Logistics Examples Integrator 6 Applications Examples Coda. Demand?. Demand!. KTH/ICT vision: Mathematics =. Demand?. Non-example: Non-example:. Demand?.

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Math Education at a Crossroads

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  1. Math Education at a Crossroads v/ Karsten Schmidt og Steen Markvorsen KTH Learning Lab January 16th 2008

  2. KTH Learning Lab January 16th 2008

  3. KTH Learning Lab January 16th 2008

  4. Crossroads Synopsis • Demands • Coverage • Logistics • Examples • Integrator 6 • Applications • Examples • Coda KTH Learning Lab January 16th 2008

  5. Demand? KTH Learning Lab January 16th 2008

  6. Demand! • KTH/ICT vision: Mathematics = KTH Learning Lab January 16th 2008

  7. Demand? • Non-example: • Non-example: KTH Learning Lab January 16th 2008

  8. Demand? Example: 2-hours written exam, December 2007 -:- KTH Learning Lab January 16th 2008

  9. Coverage KTH Learning Lab January 16th 2008

  10. Coverage Synthesis and coherence • Via few concepts- linearity, approximation, integration • Via computer experiments - visualize, inspect, discover, discuss, understand, explain KTH Learning Lab January 16th 2008

  11. Coverage Synthesis and coherence • Via applications- project exercises and thematic exercises • Via milestones- transparent architecture- less curriculum volume- rock solid principles - less rote work KTH Learning Lab January 16th 2008

  12. Math 1 Logistics • 550 students • 3 lecturers • 20 external senior TAs, highschool teachers • 20 TAs (students) • 10 DTU colleagues from other departments • 10 external examiners from other universities • 20 classes • 150 computer terminals (3 afternoons + 3 mornings pr. week) KTH Learning Lab January 16th 2008

  13. Math 1 Materials • Weekly menus, example: -:- • Thematic exercises, example: -:- • Homework exercises, example: -:- • Project exercises, examples: -:--:- KTH Learning Lab January 16th 2008

  14. Examples KTH Learning Lab January 16th 2008

  15. CAAS in Math1 at DTU Integrator6 – a multivariable ’Inspector’ Examples -:- KTH Learning Lab January 16th 2008

  16. Construction of hands-on ’examples’ KTH Learning Lab January 16th 2008

  17. CAAS From Maple to 3D printer KTH Learning Lab January 16th 2008

  18. CAAS From Maple to 3D printer • Production in Maple -:- • Export to ZPrint and ZEdit -:- • Examples - show KTH Learning Lab January 16th 2008

  19. A thematic exercise: Fire! KTH Learning Lab January 16th 2008

  20. Forest fires in Canada ( >200 ha, 1959-1999) KTH Learning Lab January 16th 2008

  21. Fire! Attack: KTH Learning Lab January 16th 2008

  22. Fire! Strategy: KTH Learning Lab January 16th 2008

  23. Fire! Head-, Flank-, and Back-Fire KTH Learning Lab January 16th 2008

  24. Grassland Fire Tikokino, Central Hawkes Bay, New Zealand, 1991 KTH Learning Lab January 16th 2008

  25. Fire! Elliptic exercises • Equation • Parametrization • Circumference • Foliation • Area KTH Learning Lab January 16th 2008

  26. Fire! No wind KTH Learning Lab January 16th 2008

  27. Fire! With wind KTH Learning Lab January 16th 2008

  28. Fire! Without wind KTH Learning Lab January 16th 2008

  29. Fire! With wind KTH Learning Lab January 16th 2008

  30. Fire! No wind KTH Learning Lab January 16th 2008

  31. Fire! With wind KTH Learning Lab January 16th 2008

  32. Fire! With wind KTH Learning Lab January 16th 2008

  33. Coda KTH Learning Lab January 16th 2008

  34. Coda Challenges • Laptops for every student (realised in principle at DTU pr. E07):Free movability of discussions, ideas, methods, and drive. • New exercises, formulations, and solution processes:Transparent architecture, process-oriented learning. • Theory, experiments, proofs, applications: Modelling + Solving + Interpretation = Mathematics. KTH Learning Lab January 16th 2008

  35. Links • Math 1 homepage: http://www2.mat.dtu.dk/education/01005/ • LearningLab DTU: http://www.learninglab.dtu.dk/ • Project Crossroads: http://www.learninglab.dtu.dk/projekter/frikoebsprojekter/MAT1.aspx Thank you for your attention! KTH Learning Lab January 16th 2008

  36. KTH Learning Lab January 16th 2008

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