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 …
Em, I am the first to admit I am a bit thick when it comes to technical stuff; but What the **ll are you on about here? Have I missed some thing....
ReplyDeleteSorry again,
Tess :(
LOL! Sorry about that Tess. By day I'm a mild mannered maths teacher, but by night I take on a dark and sinister alter ego - web application developer! FreeMIS is a free, open source management information system for schools that I've developed. I noticed from my blog stats that quite a few visitors were coming from the freemis Web site, so I thought I should let them know what was going on.
ReplyDeleteAh, I see! Thanks for that. I wasn't sure what you were talking about. See you soon,
ReplyDeleteTess:)