In order to investigate the current debate about knowing and understanding sparked by David Didau's
post, I want to examine one small part of mathematics, which I happen to be teaching to a Higher maths class at the moment: finding the point which divides a line segment in a given ratio.
One way to approach this is to teach a formula:
The position vector of P, where P divides AB in the ratio m:n, is given by
p=(n
a+m
b)/(m+n)
If you know
how to convert a position vector to a coordinatethe convention that capital letters represents points and bold lower case letters represent corresponding position vectorshow to multiply or divide a vector by a scalarhow to add vectors together
then can probably now solve a problem such as:
Given that the point P divides S(3,4,-1) and T(5,8,11) in the ratio 3:1, find P.
At this point, a student knows how to find a point which divides a line segment in a given ratio. They may have no idea why this rule works. They may have no idea what a position vector …
Hi Rober - If you thought that was good. Check this out http://dummies.book.cover.imagegenerator.org/ David Muir put me on to it! See you soon. Ollie
ReplyDeleteHi Ollie - you got a dodgy "t" on your keyboard or what? ;)
ReplyDeleteNice link - how about http://www.customsigngenerator.com/ - so much fun to be had :)