Math Education at a Crossroads
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Transcript of Math Education at a Crossroads
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Department of Mathematics KTH Learning Lab January 16th 2008
Math Education at a Crossroads
v/ Karsten Schmidt og Steen Markvorsen
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Department of Mathematics KTH Learning Lab January 16th 2008
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Department of Mathematics KTH Learning Lab January 16th 2008
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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
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Department of Mathematics KTH Learning Lab January 16th 2008
Demand?
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Department of Mathematics KTH Learning Lab January 16th 2008
Demand!
• KTH/ICT vision: Mathematics =
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Department of Mathematics KTH Learning Lab January 16th 2008
Demand?
1. Non-example:
2. Non-example:
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Department of Mathematics KTH Learning Lab January 16th 2008
Demand?
Example: 2-hours written exam, December 2007 -:-
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Department of Mathematics KTH Learning Lab January 16th 2008
Coverage
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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
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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
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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)
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Department of Mathematics KTH Learning Lab January 16th 2008
Math 1Materials
• Weekly menus, example: -:-
• Thematic exercises, example: -:-
• Homework exercises, example: -:-
• Project exercises, examples: -:- -:-
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Department of Mathematics KTH Learning Lab January 16th 2008
Examples
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Department of Mathematics KTH Learning Lab January 16th 2008
CAAS in Math1 at DTU
Integrator6 – a multivariable ’Inspector’
Examples -:-
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Department of Mathematics KTH Learning Lab January 16th 2008
Construction of hands-on ’examples’
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Department of Mathematics KTH Learning Lab January 16th 2008
CAASFrom Maple to 3D printer
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Department of Mathematics KTH Learning Lab January 16th 2008
CAASFrom Maple to 3D printer
• Production in Maple -:-
• Export to ZPrint and ZEdit -:-
• Examples - show
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Department of Mathematics KTH Learning Lab January 16th 2008
A thematic exercise: Fire!
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Department of Mathematics KTH Learning Lab January 16th 2008
Forest fires in Canada ( >200 ha, 1959-1999)
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Attack:
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Strategy:
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Head-, Flank-, and Back-Fire
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Department of Mathematics KTH Learning Lab January 16th 2008
Grassland FireTikokino, Central Hawkes Bay, New Zealand, 1991
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Elliptic exercises
• Equation
• Parametrization
• Circumference
• Foliation
• Area
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!No wind
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!With wind
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!Without wind
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!With wind
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!No wind
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!With wind
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Department of Mathematics KTH Learning Lab January 16th 2008
Fire!With wind
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Department of Mathematics KTH Learning Lab January 16th 2008
Coda
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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.
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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!
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Department of Mathematics KTH Learning Lab January 16th 2008