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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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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My TeachMeet slot - Animation in Maths

Here's what I would have said if I'd had more time:

I have grabbed one hour per week in an IT suite with my class of level B/C S2 mathematics pupils. We have spent some time using Tutpup, which has been good fun, and has caught the students' imaginations. But it does not fill an hour per week - 20 minutes is about enough at one time.

The biggest success has been the work we have done on creating mathematical stories. We happen to have been using GoAnimate, but I think this would work just as well with Comic Life, Digital Video or any medium which has some depth of skill acquisition but delivers rapid initial gratification.

Here's an (unfinished) example of one of the animations:



I am pleased with this project for several reasons:

The pupils are enjoying learning how to make animations. Enjoyment is sometimes a bit thin on the ground in maths for some of these students, despite my efforts to jolly things up, so I'm delighted to see them turning up early to the computer l…
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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)

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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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