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.
- Construction av natural numbers by iteration x = x+1 with start x=0.
- Computation with natural numbers: addition, subtraction, multiplication.
- Programming av operations according to 2. Digital representation in different bases.
- 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.
- Digital representation of spatial position x: coordinate system, computer screen/pixels.
- Motion: change of position: x=x+vdt (or dx=vdt) with v velocity and dt time step.
- 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.
- 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.
- Properties of elementary functions by construction. Generalisation to more complex f, e g Newton’s law of gravitation.
- Digital representation of and operation on geometrical objects i 2d och 3d.
- Digital representation of and operation on image and sound, or other data.
- Constructi0n/programming av computer games building on 1-11.
- Calculus as solution of dx=f(x)dt.
- Linear algebra as generalisation av 10.