Iterative Schemes and Quake 3

Whilst taking a break from a bit of lesson planning (yes, I do plan!) for iterative schemes with my advanced higher maths class, I clicked on SumbleUpon and up came
Quake 3’s Fast Inverse Square Root Function.  Most serendipitous!

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Some Thoughts about Skills-Based Curricula

I hear a lot of talk about skills-based curricula in Scotland these days, with the general vibe being that skills-based curricula are a Good Thing™. I'm not entirely clear what people mean by a skills-based curriculum, because it is one of those phrases which has slipped into the common parlance of educators without any clear definition (see also "learner conversations"). Try searching on the Education Scotland website for "skill based curriculum" and you'll draw a blank. I guess it means a curriculum defined in terms of the competencies being developed by our learners: a curriculum defined in terms of the things we want our learners to be able to do, rather than what they know.

I can see the appeal of this, but I am wary. Here are a couple of things which would worry me if they were true:

1.  Is this curriculum seeking to develop generic, transferable skills?

If so, we really need to distinguish between actual skills which are applicable in a range of conte…
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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 …
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Planning for Learning or Planning for Behaviour?

Several months ago I found myself sitting beside a quite senior staff member from one of our colleges of initial teacher education, who complained to me that her student teachers all seemed to be obsessed with behaviour management.

I was flabbergasted, but failed miserably to put together a reasonable argument for why the students were quite right.

That conversation came back to me today as I taught a maths cover class, who were learning about the graphs of linear equations.  The class had some lively characters in it, and they were clearly struggling with the central concept: that a line on a coordinate diagram represents all the points where a particular linear equation involving x and y is true.

As they explored this concept through a series of activities, many of them experienced confusion and frustration. These are normal, healthy emotions for learners. We were able to stick with these challenging experiences partly because the pupils were operating in an environment in which mis…
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