Most important topic in maths?

What is the most important topic in maths.  Many, including parents, and (more worryingly government) would have you believe it is 'basic numeracy', which tends to mean 'times tables'.  I agree that a basic awareness of magnitude and the ability to add siubtract or do multiplaications in your head is important, I really don't think that it is the most important thing that maths teachers should be doing with classes.

This is not my idea, by the way, I heard it discussed (briefly) on Radio 4's rather excellent "The Infinite Monkey Cage", about a year ago, but the more I think about it, the more I'm convinced its right.

What we should do more of is probability.  Not just the stuff we do already - words, probability lines, fractions / decimals (do any maths teachers use percentages for probability, and if not, should we if the real world do?).  Not just Venn diagrams and tree diagrams, but actual probability and risk assessment.

Don't panic.  This is not risk assessment from a H and S form point of view, but from a maths point of view!


Why?


Well, every decision we make is based on probabilities and expectations.  Should I buy a lottery ticket? What car finance deal should I go for?  What stocks and shares should I buy?

Everyone needs to be able to properly weigh up the pros and cons of any situation.  We need to teach the appropriate skills to do that. Students need to be able to set up appropriate models (modelling may be the second most important thing we teach!), and interogate those models.  We then need to use our understanding of probabilities (using prior information) to make the 'best' decision.

There's a great example of this earlier on my blog - have a look at http://chrismaths.blogspot.com/2010/05/real-functional-maths.html to see why it's important.

Any other thoughts??

Dodgy Statistics - or am I being oversensitive.

I need a little help. I am a Statistician by nature, so sometimes get a little oversensitive when it comes to analysing stats - I get ... wound up? irritated? ... by dodgy stats.

Here's the latest, and you can tell me if I'm right, or if I need to shut up and get on with it.

Last years Y13 did an exit questionnaire, for ALIS. It asked them all about what teaching styles they experienced in each subject that they studied. For example ...
"Presentation of a topic by the teacher" or.../
" Practical Work (Using apparatus or Making things)."
... and so on. There were 22 catagories.

Students rate each one from 1 to 6, on the follwoing measure..
1 = never or almost never
2 = about once a term
3 = about once a month
4 = about once a fortnight
5 = about twice a week
6 = about once a lesson.

Scores for all students in each subject (sample size = 7 in my case, but that's another gripe) were then averaged (arithmetic mean for fellow stats types), and these published and compared with national figures.

Here's the problem(s).
1. My Preparing Essays scores was 1.29 (1+1/7). This means that one student thought we prepared essays about once a term. I haven't prepared an essay since my PGCE in 1996. This is a lack of awareness by the students that sheds doubt on all responses.

2. If 4 students respond "Never" and 3 respond "once a lesson" then the average is 22/7 = 3.14 which appears to be once a month despite the fact that NOT ONE STUDENT said once a month. Surely the mode (most common) response of "Never" is more appropriate?

Please help me out with this one?!