paradigm problems

The more I think about it, the more I think that our education system has things backwards. It seems to me that learning to count in decimal is fine, but why not introduce the concept of powers earlier? Or rather, when powers are introduced, why isn't it applied to our base ten counting system. This would give kids an extraordinarily powerful understanding of how number systems are formed. I can't remember it being explicit in our learning material; maybe it was. 

That said things may have changed a lot in 20 years..

By the by, I feel the same way about radians and degrees. I don't think they're harder. In fact I think that both of these concepts *could* help some kids conceptualise numbers and mathematical problems far better if they didn't have to see it from the point of view of their educator. Ask yourself how big a degree is.. then ask why. Apart from it having many possible factors it seems almost arbitrary.

Whereas radians have an iron clad concept.

Rant over. Off to my exam.

L33t Learning

Since I missed out on my calculus mark by 5%, the school of computer science looked at my application and saw that I had very high marks for programming, so they said if I hit 40% in the resit, I'd progress to year 1 of the degree this September.

This was a mixed result for me. Having been out of education for 16 years and having never studied maths to FE level, I have struggled to get my head around Calculus and Algebra as well as square away my subjects every three weeks for this year.

So for the last three to five weeks I have been on calculus overdrive. I've pushed my brain through real life pain; through threshold after threshold in a relatively short amount of time to arrive at a point where I would actually be comfortable starting the course again. I've inflicted such guilt on myself when avoiding study, that it made me quite difficult to live with I imagine.

Each tiny step up the Calculus mountain took me hours or days of study to get my head around, and during the last week I bashed said head against every past paper I could get my hands on over and over again. I studied the papers, and the solutions trying to reverse engineer the lecturers answers. Occasionally I'd hit a wall, when I could not see how the lecturer made some magical leap in his/her working out. I shed actual tears digging through notes looking for specific axioms that I had missed in the lectures. I scoured the internet, and notably bugged one of my maths lectures with (I estimate) close to 50 emails.

I sat the paper on Tuesday, and I have to say I'm really confident. I completed all 18 questions and did not hit a single point where I felt utterly lost. I couldn't believe it when I came out. It could still all go pear shaped, but I think I've done enough.

EDIT:

I passed with 68%, so the school has accepted me. :)

Boiling an Egg; As taught by your Calculus lecturer...

"y = C*E+(½E)
a = π(x/2)^2 v = ( ∫(C+E+(½E))dy)x OR ay
t = 60*3
T = t+1/10t
b=s*v*z (z = equation for boiling one unit of water)

b+T = |Yummy|

OK, that is the technique for boilination, now you try with examples 1-50!!"

While this is probably innacurate, some of it estimated and some of it is undoubtedly incorrect. It serves to demonstrate the point.

If at some point in the lesson the teacher would actually say the words; "this is applied to the real world and is not just an abstract set of numbers and letters and long words..." mathematical studies would probably be more populated at higher levels.

Now I know WHAT integration, differentiation, limits etc are defined as, (discoveries I made independent of my lectures) I feel like I've lost a lot of time for something that could just have been explained a little differently.

Any way.. back to studying.