John D. wrote in part:|
| On 08/13/2007 11:44 AM, Rauber, Joel wrote:
|
| > .... Actually
| > introduce vectors purely as geometric objects at first;
| i.e. arrows,
| > this is done briefly, but show adding and subtracting
| head-to-tail, etc.
|
| That's smart. That's important.
|
| > Then define velocity pictorially and acceleration.
|
| Yes.
|
|
| Of course the introduction should be "done briefly" ... but
| then you can spiral back to the arrows again and again,
| pounding on the point that a vector is a physical,
| geometrical object, not just a list of three numbers.
|
The spiral back part is important and useful IMHO, particularly to help
fight the tendency John mentioned for students to quickly forget the
geometric part of the discussion; of which there is a high danger if you
only do component calculations after having mentioned the "arrows".
I.e. one needs to specifically spiral back to the geometric drawings
every so often (or always) when you introduce new topics using the
vector methods.