Maths Education and Regression to the Mean

[Stranger]

Great article on maths education and a good example of regression to the mean:-

http://tinyurl.com/h98fwj9

[Hope]

Now, its some time since I even made an attempt to teach maths in a scholl - mostly to non-English speaking children so often teaching the language of maths than necessarily the principles of the subject.  However, I do remember the Head of Maths dropping into one such class (one of the pupils was a Yera 10 student who was extremely bright and had managed to crack the linguistic code that is English within 6 months of arriving in the UK - but struggled with anything to do with Maths.  I don't recall the actual problem we were dealing with, but it probably involved some multiplication and division, as I remember the teacher taking me tone side at the end of the class and saying something along the lines of 'I wish I was allowed to bounce from one way of division to another like you've just done.  In mainstream, we have to teach things in a specific way; the fact that there are 4 ways of doing (and therefore teaching) division is irrelevant; we have to stick to a particular way'.

That is why I found Gove's prescriptiveness so pointless, as different children learn maths (& spelling & writing &, for all I know, science) in different ways.  Kinesthetically, visually, by means of touch and through hearing/listening.

[ProfessorDavey]

I remember the teacher taking me tone side at the end of the class and saying something along the lines of 'I wish I was allowed to bounce from one way of division to another like you've just done.  In mainstream, we have to teach things in a specific way; the fact that there are 4 ways of doing (and therefore teaching) division is irrelevant; we have to stick to a particular way'.

That simply isn't true today - actually quite the reverse. The current approach is to provide a variety of methods to 'solve the problem' allowing the kids to find the one that works best for them.

[jeremyp]

Great article on maths education and a good example of regression to the mean:-

http://tinyurl.com/h98fwj9

The speed camera thing is a great demonstration of regression to the mean. My brother (a professional statistician) told me a story of one of his colleagues who gives talks to police officers about statistics.

He would be giving a talk to a room full of policemen (say about 30) and he would hand each one a dice. Then he would tell them that each officer represented a road and they should roll their dice. The number rolled is the number of road fatalities they experienced in a year. Mean number of fatalities 3.5 (roughly).

Then he would give a picture of a speed camera to every office who rolled a five or a six to represent the placing of a speed camera on the road and calculate the mean number of fatalities for the dangerous roads (5.5).

Then he would ask everybody to roll the dice again for the next year and recalculate the mean number of fatalities for the roads with speed cameras. As often as not, it would decrease from somewhere around 5.5 to somewhere around 3.5. And this effect was caused just by putting a picture of a speed camera in the hands of somebody pretending to be a road.

[jeremyp]

One thing that made me smile was one of the comments on the Simon Jenkins article. Somebody said "with everything on one side of the equals sign being the same as everything on the other side, students could be forgiven for thinking maths is a tautology".

It made me smile because everything in pure maths actually is a tautology.

[Stranger]

And this effect was caused just by putting a picture of a speed camera in the hands of somebody pretending to be a road.