You make some very good points, John. Although curricula are notoriously difficult to change,I suspect that we are now caught in a cultural bind: Generations of failure have produced a society that looks elsewhere for success- how many "celebrities" of any kind have a scientific background and how many of those would admit to their maths and science having anything to do with their success? For example, Al Franken, who recently won a protracted legal battle to become the 60th Democratic senator, is renowned for his time as a comedian, not as a maths graduate. How many TV series show mathematicians or scientists as anything other than nerds, as compared with their glamorous legal counterparts?

Add to this, the maths anxiety of parents that is conveyed to their children: eg "Jill/Jack is no good at maths- I guess she gets that from me- I was hopeless at maths". What is Jill/Jack to do? if they try to break out of the bind, then they are rejecting their parents. It's easier to live down to their expectations.

I think that maths and science phobia needs to be treated like obesity- public examples of success backed up by appropriate and accessible education.

Most articles on education share the same fault. It is easy to tell teachers what their lessons lack, it is much harder to actually do better. Teachers do-not have the time to constantly come up with real world applications of content that are interesting and within the capabilities of the whole class. Until someone else actually collates a large collection of these problems, students will need to accept that occasionally being bored is part of getting an education.

Mathematics at school is the very basic level for anyone to continue to most professions incl engineering, science, BComm etc. To reduce it any further would require extending the graduate degrees.

Further more the subject is an exercise in problem solving and logic which form the basis of rational thought, and anyone that comes away thinking it is simply the memorising of formulae to plug into problems has seriously missed the point.

To those that are competent at maths the subject is a wonderful revelation to natural world and many cite it as their favourite subject. For others it at least develops some degree of problem solving ability.

Finally for those that cannot stand it, the fall back is religion.

I agree with benk's first two sentences - diagree with the rest.
The article has me intrigued, but its short on detail and the mechanics to make it work.
I was merely adequate in mathematics and, as it entirely failed to excite my interest, I did no maths at all in upper high school.
However, as the author points out, there are several facsinating stories in maths - Pi is one, Infinity, might I also suggest Longitude is another - that many people (certainly I) would find interesting. However, it was not until adulthood that I came across these.
Benk, I refuse to accept that teachers honestly believe that it is no part of their job to try to make the material engaging for their students. Boredom is not an acceptable 'cost' of teaching.
In order for someone to teach, someone has to learn. As for teachers not having the time to make their lessons engaging - don't get me started!

I disagree Mill. I'm sick to death of this ideology that all learning must be entertaining. Children are brought up these days to believe that they must be entertained first in order for them to bother learning anything. That's why we have people lapping up 'infotainment', rather than actual information. That's also why we have Gen Y thinking every aspect of every job they do must be rewarding and entertaining.

It's a frivolous world when a child is taught they shouldn't have to learn unless Kermit the Frog is teaching them using song.

DO NOT TRY TO MEMORISE THESE RESULTS only LEARN TO WORK THROGH THE RESULT YOURSELF.

Hello, the whole Coroneos styled math curriculum instills sheer phobia let alone anxiety.

Students need Mnemonics to overcome fear of math. Pure memory and mnemonics must be ENCOURAGED and students rewarded for new and exciting examples for sharing.

TWO quick examples:

Inverse trig:

BMaX-SOa: Integral 1/(B^2-a^2*X^2)^1/2 = (1/a)*sin-1(a/B*x)

Once you have one thing etched in your memory PERMANENTLY you are in a position to write it down, own it & play with it till you can prove the result in your own space.

Even NASA uses Mnemonics. Everything from LEM to ISS in the NASA lexicon is about acronyms as mnemonic devices.

And just to show it doesn't stop there:

The number of components in an n-'D'imensional Tensor of Rank R

CEEDEER(seedier): C = D^R

And believe it or not you are well into tensor analysis!

And don't forget all those Trig Integrals (you're not allowed to memorise) that bring students routinely to Catatonia:

TUNNELSEX, SECELSPOT(LT-(KewpiHX)), SinsOf Sex EndUpInCots etc

Mathematicians cannot exist without memorisation and mnemonics.

Stop telling students otherwise.