Thursday, September 17, 2009

On teaching

With the Bratii over the weekend and just for fun*  I showed Major the algebraic proof of the Pythagorean Theorem because I think it's the easiest one to grasp; he knew the theorem, but hadn't been taught the proof.

Now baring the notion of complimentary angles all you need to know is how to calculate the area of a square and a triangle and to be able to multiply two two-term equations i.e. (a+b)²; for those who've forgotten it expands thus (a+b)(a+b) = a*a + a*b + b*a + b*b in other words multiply the first term by the terms in the other bracket then repeat with the next resulting in a²+b²+2ab (a*b and b*a being the same thing).

He's 13 and had trouble grasping it. Simplifying it down to "Big square minus the four triangles leaves the small square" helped to the point that Minor (8) could grasp it.

On another tack Minor boasted of his Quick Maths skills yep it's a lesson called Quick Maths. Basic multiplication so I threw some easy ones at him such as 7*8 etc. then moved into one set of double digits with the easy 6*11 which caused a pause... no wait not a pause but a repeat of the question. That's his trick if he doesn't instantly know the answer he'll repeat the question back at you. Anyway I moved to 7*12 which stumped him. One piece of paper later and I'd shown him how to break down the number into easier multiplications i.e. 7*10 + 7*2 which resulted in him being mightily chuffed when he used that to multiply 8 by 12 to give the correct answer (80+16).

However what came out of this was the question of why I used "Indiana Jones' sevens". Caused me to blink for a second but I realised I use, what I've always been told were called, continental sevens; that is the standard 7 with a horizontal bar. He told me off and told me to do it the "proper way" because he could mistake them for the letter F. Upon asking how you could confuse the letter F (I wrote one) to the letter 7 (with bar) I was informed I wrote "weird F's".

Now okay I was taught to use the vanilla 7, but changed somewhere about the age of 11 when I realised I couldn't be arsed in slowing down my hand to match my brain (despite the plaintive crying of my teachers) and this was resulting in confusion between ones and sevens even for me, so I've no hang-up with that; but being told you could confuse it with an F? How? Even I with my scrawl have never confused the two.

I can't suggest dyslexia as he's quite capable of reading and these things are looked out for much more these days; I can't suggest unfamiliarity as he both identified and named it; so where did the suggestion that this form of 7 shouldn't be used come from?

I shall approach the subject on my next visit in a roundabout way.

* Yes I do have a non-standard definition of "fun"


Dan H said...

In primary school in Scotland I was repeatedly told off for doing my 2 the way my Grandma taught me: with a little curl in the bottom-left corner. I've created an example image in my picture gallery. The school way doesn't use a hook on the 1, so it's not confused with the non-continental 7. They also teach the cursive F, which has that funny shape I can just about see getting confused with a continental 7. I never saw the point in continental 7 at school, but started writing them as an undergrad because I thought they looked nicer, as well as because of the 7/1 confusion.

Since leaving school I print almost everything I write, so the F thing doesn't matter. I've also changed back from doing the triangular 4 (which also got me into trouble at school) to the two-stroke kind, again because I think it looks nicer.

Lately I've tried changing my 3's to the kind with a horizontal stroke at the top leading to a sharp point at the right-hand end, but didn't care about it enough to change my habits.

FlipC said...

I was thinking of how much the teaching things the 'right' way was down to orthodoxy and how much down to reasoning. Given your cursive F I can see both how it could be confused for a continental 7 and why my reverse seven F would be seen as weird.

Interesting that though you were taught the open 4 and I was taught the closed we've both ended up using the same version. I do end bar my ones though and my cursive F can be mistaken for a pound sign.

I'll post examples.