math education at a crossroads

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