### More funky maths stuff

[tex]y=xsin(x^2)[/tex]

[graph]x*sin(x^2)[/graph]

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…

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

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…

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 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 …

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

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 …

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…

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:

If so, we really need to distinguish between actual skills which are applicable in a range of conte…

Very nice jonesieboy. I even used sweary words when I viewed it for the first time. (in i nice way of course) I'm going to shout on Samantha to see what she thinks.

ReplyDeleteOh dear Boys and their toys. Do you not pity those blog widows out there who have lost their husbands to the world of blogging.

ReplyDeleteHa ha. I tricked her into commenting on a blog for the first time. The only way is up. I think I'd better buy a second computer for her.

ReplyDeleteHi Samantha!

ReplyDeleteIt's only for the benefit of the kids, honest! It works in comments too:

[tex]y=x^2[/tex]

[graph]x^2[/graph]

Have a go! Just type [ graph ] without any spaces, then the rhs of the function - x^2 in the example I did, then [/ graph ] again without spaces.

Wow, it works. That's the easiest graph I've ever drwn.

ReplyDeleteI've got to try this... [graph]3*x+2[/graph]

ReplyDeleteMind you, I could have sworn I typed (without the spaces) [ graph ]3x+2[ /graph], and that's not the graph I'd have expected. There must be more to the syntax than I thought.

ReplyDeleteIt stopped working whilst I fixed it so that it can cope with a plus sign! The original plugin I was using was basically broken, so I switched into geek mode and have hopefully fixed it now.

ReplyDelete[tex]x^3+3x-2[/tex]

[graph]x^3+3x-2[/graph]

[graph] x^3+5[/graph]

ReplyDelete[graph]x^3[/graph]

ReplyDelete[graph]x^3+2[/graph]

ReplyDelete[graph](x^3)+2[/graph]

ReplyDeleteI must've typed something wrongly on my very first one. Please feel free to delete these. It is cool though :)

ReplyDeleteFingers crossed i can get it to work..

ReplyDelete[graph]3xsin(x)[/graph]

oh dear .. :S

ReplyDeleteHow about now?

ReplyDeleteYou just missed the brackets in sin(x) - I put them in for you, and it works now :)

ReplyDeleteWhat's going on with the time on this blog. Is it an hour ahead?

ReplyDeleteYeah - I'm still on BST :)

ReplyDelete[graph]3x-2[/graph]

ReplyDeleteHi jonesie!

ReplyDeleteHow are you!

Just pottering about and came across this wee graph thing. I've got a wordpress blog too but can't get this to work in mine. Is there anything I might be missing??

Hi Michael! Very well thanks. I've tweaked the plugin a bit - I'll email you a copy of exactly what I use.

ReplyDelete