math education at a crossroads
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KTH LTH DTU April 2008
Math Education at a Crossroads
v/ Karsten Schmidt and Steen Markvorsen
KTH LTH DTU April 2008
CrossroadsSynopsis
1. Demands
2. Coverage
3. Logistics
4. Materials
5. Coda
KTH LTH DTU April 2008
Demands
KTH LTH DTU April 2008
Demand for exams?
Example: 2-hours written exam, December 2007 -:-
KTH LTH DTU April 2008
Coverage
KTH LTH DTU April 2008
Coverage
• Via few concepts- linearity, approximation, integration
• Via computer experiments - visualize, inspect, discover, discuss, understand, explain
Synthesis and coherence
KTH LTH DTU April 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
KTH LTH DTU April 2008
Logistics
KTH LTH DTU April 2008
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 LTH DTU April 2008
Materials
KTH LTH DTU April 2008
Mathematics 1Weekly menus
• Examples
-:- Week 12 E07 -:- Week 11BC F08
• Resolver
-:- Maple for week 11BC F08
KTH LTH DTU April 2008
Mathematics 1Homework exercises
• Examples
-:- From menu 11BC F08-:- From notes p. 30 and 44
• Resolver
-:- Spherical solar cell roofs
KTH LTH DTU April 2008
Mathematics 1Thematic exercises
• Examples
-:- Linear maps-:- Forest fires (appendix)
KTH LTH DTU April 2008
Mathematics 1Project exercises
• Examples
-:- Bridge -:- Red Blood Cells -:- Cantilever-:- Chemical Reaction Chain
KTH LTH DTU April 2008
Coda
KTH LTH DTU April 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.
KTH LTH DTU April 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!
KTH LTH DTU April 2008
ExtraThematic Forestfire
KTH LTH DTU April 2008
A thematic exercise: Fire!
KTH LTH DTU April 2008
Forest fires in Canada ( >200 ha, 1959-1999)
KTH LTH DTU April 2008
Fire!Attack:
KTH LTH DTU April 2008
Fire!Strategy:
KTH LTH DTU April 2008
Fire!Head-, Flank-, and Back-Fire
KTH LTH DTU April 2008
Grassland FireTikokino, Central Hawkes Bay, New Zealand, 1991
KTH LTH DTU April 2008
Fire!Elliptic exercises
• Equation
• Parametrization
• Circumference
• Foliation
• Area
KTH LTH DTU April 2008
Fire!No wind
KTH LTH DTU April 2008
Fire!With wind
KTH LTH DTU April 2008
Fire!Without wind
KTH LTH DTU April 2008
Fire!With wind
KTH LTH DTU April 2008
Fire!No wind
KTH LTH DTU April 2008
Fire!With wind
KTH LTH DTU April 2008
Fire!With wind
KTH LTH DTU April 2008
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