MST for Basic School

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I am now testing a version of MST with a group of students in grade 4 (10 years old) at Lugnets Grundskola in Hammarby Sjöstad, Stockholm in the form of  Matematik-IT.

The plan of the program takes the same form independent of level, from basic through high-school to university:

Goal: Interactive digital simulation of real  and imagined worlds = computer games.

Language: Formal mathematics + programming.

Tools: Phantasy, brain, eyes, fingers och computer/iPad.

Content:

  1. Construction av natural numbers by iteration x = x+1 with  start x=0.
  2. Computation with natural numbers: addition, subtraction, multiplication.
  3. Programming av operations according to 2. Digital representation in different bases.
  4. Digital construction av rational numbers as solutions  x to the equation px=q with p and q natural numbers. Programming av operations for rational numbers: addition, subtraction, multiplication och division.
  5. Digital representation of spatial position x: coordinate system, computer screen/pixels.
  6. Motion: change of position: x=x+vdt (or dx=vdt) with v velocity and dt time step.
  7. Change of velocity: v = v+adt (or dv=adt) with a acceleration. Newton’s 2nd law: a = f/m where f is force and m mass.
  8. Digital construction av elementary functions (polynomials, sin, cos, exp, log, et cet) by programming of time stepping of a=f/m, v=v+adt, x=x+vdt with simple f.
  9. Properties of  elementary functions by construction. Generalisation to more complex f, e g Newton’s law of gravitation.
  10. Digital representation of and operation on geometrical objects i 2d och 3d.
  11. Digital representation of and operation on image and sound, or other data.
  12. Constructi0n/programming av computer games building on 1-11.
  13. Calculus as solution of dx=f(x)dt.
  14. Linear algebra as generalisation av 10.

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