Transforming 
Technical Education for a Computational World

What is math?

1. Posing the right questions

2. Real world ⟶ math formulation

3. Computation

4. Math formulation ⟶ real world, verification

Use computers

1. Posing the right questions

2. Real world ⟶ math formulation

3. Computation

4. Math formulation ⟶ real world, verification

Use students

1. Posing the right questions

2. Real world ⟶ math formulation

3. Computation

4. Math formulation ⟶ real world, verification

maths ≠ calculating
maths >> calculating

Just today: 
16 UK lifetimes 
hand-calculating

Calculating is 
the machinary of maths

“Get the basics first”

“Mindless 
 button-pushing”

“Applying procedures
 teaches understanding”

More practical and 
more conceptual

Example: Let's teach 
calculus early

Manipulate[Show[Graphics[{color,Polygon[Table[{Cos[i 2π/n+ π angle/180],Sin[i 2π/n+ π angle/180]},{i,1,n}]]}],PlotRange->1],{n,3,50,1},{angle,0,360},{color, Red}]

Exam questions like...

What's the best life insurance policy to get?

Author: Seth Chandler, demonstrations.wolfram.com

Maths...
...can be fun

Manipulate[Graphics[{Yellow,Disk[{0,0},1],Black,MapIndexed[{Disk[#,s],Thickness[.008],Line[{#+{-.13,ey-er (-1)^First[#2]},#+{.13,ey+er(-1)^First[#2]}}]}&,{r {Sin[t],Cos[t]},r{-Sin[t],Cos[t]}}],Thickness[.02],First[Plot[-.35+a x+ b x^2+c x^3,{x,-.4,.4}]]},PlotRange->All],{{r,.5,"Eye distance"},0,1.1},{{t,.8,"Eye positions"},0,Pi},{{s,.1,"Eye size"},0,.5},{{a,0,"Mouth rotation"},-1,1},{{b,.6,"Frown/Smile"},-1.2,1.2},{{c,0,"Mouth twist"},-2,2},{{ey,.16,"Eyebrow position"},.05,.3},{{er,0,"Eyebrow rotation"},-1,1},ControlPlacement->Left]