2D and 3D Coordinate Geometry: Bottom-up learning using ''Autograph''

Abstract

Learning Mathematics can be like a house of cards - it can all be wasted if there is no solid foundation. There is growing evidence that the imaginative use dynamic software such as ?utograph?can help students firm up these foundations using a step-by-step approach from the bottom up. For example:

Quadratics [progressing from y=1, y=1+x, y=x? y=1+x+x?to y=ax?bx+c and the factorized form]; the link between completing the square and the vector translation of a quadratic; forming a quadratic from three points, ... etc.

Differential equations [progressing from y'=1, y'=x, y'=y, to the implicit forms: y'-y=0, y'-y=1, y'-y=x, ... etc. Likewise 2nd order from y?0 to the general damped second order].

The transition from 2D to 3D coordinate geometry can also be made easier by visualising the 2D principles first: eg the vector [a,b] perpendicular to the line ax+by=c, followed by the vector [a,b,c] perpendicular to the plane ax+by+cz=d. Likewise, a firm understanding of conics in 2D will make 3D equations such as x?y?z [paraboloid] easier to understand.

All the these ideas will be available as TurboDemo tutorials on the web for this conference, re-establishing the principle "Author once, learn anywhere!" , at www.tsm-resources.com