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=(na+mb)/(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 …

The Scottish Curriculum: A Beginner's Guide

There is no universally agreed meaning for the term "curriculum" as applied to the education of children and young people. In academic circles it is a highly contested concept, and covers everything experienced by children and young people, within or without formal education. To an average parent, I guess it means "the stuff schools are going to teach children and young people". From this perspective, Scotland has no national curriculum. Scotland has no national framework which spells out explicitly what knowledge schools should teach children and young people. We used to have one, called 5-14, but it was decided that this was too prescriptive.

Instead, the Scottish Curriculum for Excellence has a series of statements called the Experiences and Outcomes, which make vague, implicit references to the knowledge we expect young people to acquire, wrapped up in highly general statements about what we expect young people to be able to do, and what we expect them to exper…