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Showing posts from June, 2017

Knowing and Understanding in Mathematics

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 coordinate the convention that capital letters represents points and bold lower case letters represent corresponding position vectors how to multiply or divide a vector by a scalar how 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