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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?. - PowerPoint PPT Presentation
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Department of Mathematics KTH Learning Lab January 16th 2008
Math Education at a Crossroads
v/ Karsten Schmidt og Steen Markvorsen
Department of Mathematics KTH Learning Lab January 16th 2008
Department of Mathematics KTH Learning Lab January 16th 2008
Department of Mathematics KTH Learning Lab January 16th 2008
CrossroadsSynopsis
1. Demands
2. Coverage
3. Logistics
4. Examples
5. Integrator 6
6. Applications
7. Examples
8. Coda
Department of Mathematics KTH Learning Lab January 16th 2008
Demand?
Department of Mathematics KTH Learning Lab January 16th 2008
Demand!
• KTH/ICT vision: Mathematics =
Department of Mathematics KTH Learning Lab January 16th 2008
Demand?
1. Non-example:
2. Non-example:
Department of Mathematics KTH Learning Lab January 16th 2008
Demand?
Example: 2-hours written exam, December 2007 -:-
Department of Mathematics KTH Learning Lab January 16th 2008
Coverage
Department of Mathematics KTH Learning Lab January 16th 2008
Coverage
• Via few concepts- linearity, approximation, integration
• Via computer experiments - visualize, inspect, discover, discuss, understand, explain
Synthesis and coherence
Department of Mathematics KTH Learning Lab January 16th 2008
Coverage
• Via applications- project exercises and thematic exercises
• Via milestones- transparent architecture- less curriculum volume- rock solid principles - less rote work
Synthesis and coherence
Department of Mathematics KTH Learning Lab January 16th 2008
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)
Department of Mathematics KTH Learning Lab January 16th 2008
Math 1Materials
• Weekly menus, example: -:-
• Thematic exercises, example: -:-
• Homework exercises, example: -:-
• Project exercises, examples: -:- -:-
Department of Mathematics KTH Learning Lab January 16th 2008
Examples
Department of Mathematics KTH Learning Lab January 16th 2008
CAAS in Math1 at DTU
Integrator6 – a multivariable ’Inspector’
Examples -:-
Department of Mathematics KTH Learning Lab January 16th 2008
Construction of hands-on ’examples’
Department of Mathematics KTH Learning Lab January 16th 2008
CAASFrom Maple to 3D printer
Department of Mathematics KTH Learning Lab January 16th 2008
CAASFrom Maple to 3D printer
• Production in Maple -:-
• Export to ZPrint and ZEdit -:-
• Examples - show
Department of Mathematics KTH Learning Lab January 16th 2008
A thematic exercise: Fire!
Department of Mathematics KTH Learning Lab January 16th 2008
Forest fires in Canada ( >200 ha, 1959-1999)
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Attack:
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Strategy:
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Head-, Flank-, and Back-Fire
Department of Mathematics KTH Learning Lab January 16th 2008
Grassland FireTikokino, Central Hawkes Bay, New Zealand, 1991
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Elliptic exercises
• Equation
• Parametrization
• Circumference
• Foliation
• Area
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!No wind
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!With wind
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Without wind
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!With wind
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!No wind
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!With wind
Department of Mathematics KTH Learning Lab January 16th 2008
Fire!With wind
Department of Mathematics KTH Learning Lab January 16th 2008
Coda
Department of Mathematics KTH Learning Lab January 16th 2008
CodaChallenges
• 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.
Department of Mathematics KTH Learning Lab January 16th 2008
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!
Department of Mathematics KTH Learning Lab January 16th 2008
