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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Learning styles are a myth and I am not an auditory learner

Image
I switched on Radio 6 this morning, and the track they were playing had a drum sound which caught my ear. It reminded me of a rototom - a tuned drum which was quite popular in the 80s. I had a set of three in my drum kit.



I doubt many listeners would have made that connection. I suspect many listeners would not even have particularly distinguished that drum sound. I think many people just hear songs in a much less differentiated way, unless they make a real effort. I, like most musicians, tend to hear the guitar, the drums, the bass, the keyboard and the vocals separately.

In other words, I am extracting more information from the audio than some might.

It would be tempting to imagine, therefore, that I would learn better through hearing than through other senses. But that is nonsense. Imagine trying to learn about the physical geography of a country through hearing about it without a map!

But this is exactly the argument made by people who insist they are "visual learners" d…
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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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