Sunday, November 07, 2004

Alternatives

Health and age - Alternative medacine page
There are a lot of alternative treatments for certain ailments. The best part about this page is it tells you what vitamins and minerals you might be deficient in.

See ya!

The Matrix

Oh now I know what a matrix is...
(and listening to hall of the bandit lord?)

By the way, you must check this out (Natural Math's "An Adventure in Number Sense"

What a matrix is, is some part of the timestable. Because you are cross-multipling different corners of a rectangle in the table, they always add up to the same thing.

And all the squares you make in the times table, the values add to a square number!

Bingo! Times tables and Arithmetic Progression

Noone ever explained Arithmetic Progression to me as a kid.
Now it's so easy!! I sure could have solved some of those problems they gave me in highschool... (in fact, all of them).

Say if someone asked you to add all the numbers from 1 to 100.

Every number can be put together in pairs, for example, 100 + 1, and 99 + 2. They all equal 101. So there are 50 pairs (half of 100 numbers), so the total adds up to 101x50, which is 5050. (5000 + 50).

Arithmetic progression

I'm going to create a arithmetic progression.
It goes like this:

2 6 10 14 18 22 26 30 34 38

So there are 10 numbers.

so there are 5 pairs.

The first pair adds to 40. So 5 x 40 = 200.

Rule: To find the sum of an arithmetic progression, you add the first and the last number of the progression, and then multiply by a half of the number of numbers in the progression.

So it works for odd numbers too.
I want to find the answer to this progression for 13 numbers. So there are 6 and a half pairs.

6.5 x 40 = 220.

Seven times tables...

I get stuck on a few. Because of the terrible rote learning technique employed by my parents, half my times table memory (not half, but some of the bigger numbers) are currently wiped out and I have to rebuild.

63 is 7x9 because all the 9xs digits, add to 9.
42 is easy to remember because it also adds to 6.
21 adds to 3.

So basically 3, 6, 9 times 7, all add up their digits. So that is easy to remember.

The 4s and 8xs are all EVEN numbers.
so 28 = 7 x 4, 56 = 8 x 7.
8/2 is 4, so that is easy to remember.

So the hardest is 8 x 7. I can remember that 8 + 7 = 15. And then I take that 5, and take that 1, 1+5 = the last digit, and 1x5 = the first digit, so 56

So if I see 56, i can remember 15, and what adds to 15? Cant be less than 5, can't be 6 because of the 9xs table pattern, so its 7, or 8. 7x8.

And... 49 is 7x7
6x6 = 36 and incidentally 4x9 also =36...

Also check out:
The Resource Room

Fun and Games

Try the BBC Skillwise website for numeracy games.

For some hardcore maths needs, try the Math Centre, where you can do online excercises, and teach yourself, high school math concepts.

Saturday, November 06, 2004

Maths Trauma

I remember being told by my dad that I had to stay in the bathroom until I learnt my timestables. That was horrible and traumatising. I knew 2x, 10x, 5x, probably 4x and 3x too, but the others I could not see a pattern in. I was an intelligent child, and I can't rote learn. Of all the terrible things they have done to me, I remember this also. It was so painful.

How the timetables should be taught to kids with dyscalculia,
(quoted from the Education Standards site, UK

"One of the most frequently occurring problems for dyslexic learners and dyscalculic learners is not being able to (rote) learn the times tables, so a possible alternative is to use the facts the child knows to work out the facts they don’t know. This has an additional bonus of teaching further understanding of numbers and number relationships.
The facts that can be learnt (and the child does have to have some facts) are 1x, 2x, 5x and 10x. Other facts can be derived from these, a strategy advocated in the NNS for 4x, for example:
5x can be obtained by halving 10x facts (also useful for percentage work)
4x facts are done by using 2x twice as in 4 x 7 as 2 x 7 = 14 and 2 x 14 = 28
9x facts are derived from 10x facts using the pattern n x 9 = n x10 – n as in 7 x 9 = 7 x 10 - 7
3x facts are done by doubling the number and adding the number as in 3 x 6 = 2 x 6 + 6 = 12 + 6 = 18
6x facts are similar but using 5xn and 1xn as in 6 x 8 = 5 x 8 + 8 = 40 + 8 = 48
7x facts are computed from 5x and 2x facts as 5n + 2n, for example 7 x 3 = 5 x 3 + 2 x 3…………………
and if you teach the commutative property (e.g. 4 x 3 = 3 x 4) then there is only 8x8 left, which can be done by a triple sequence of doubling, starting with 8."

So how do I recover from Dyscalculia?

Well, I am not a child anymore, so I can't undo the things that have happened to me. I don't respect the people who did it to me, and I never will, that is my only vengeance.

Other than that, I am now finding resources to relearn what I have missed. So far, I am a more stable person, still not totally stable, I am still prone to intense periods of depression, that seem to dissapate by themselves for whatever reason.

Here are some good links to understand what Dyscalculia and Dyslexia is like, and what you can do for your own maths skills:

Misunderstood Minds: PBS special

BBC: Skillwise on Dyscalculia



How I got Dyscalculia...

At first, I never knew I had it. For a long time, I probably didn't. When I was 15 I still got 94% in Maths, but the weird thing was, the question I did get wrong, was about numbers. It was something simple, like what is a million, or 10 million, or something like that, written in numerals, but I didn't know it. I never knew it, was it relevant to my life anyway?

The point is, maybe for people with dyscalculia, a lot of things aren't relevant. I didn't get 94% in Maths because I could remember things, I got it because I could solve things logically. Same with Physics. I got a B then, and by that time I wasn't concentrating anymore (nobody found I had ADD, because it was ADHD, and I wasn't hyperactive, it didn't really show). I was still a 'good' student by school standards, but I knew my work was slipping, and my attention for anything was slipping. Meanwhile, I was falling into depression.

By the time I got to university, it only got worst. I was devoid of any maths or science, because I was doing Art, but I was devoid of any motivation too. I was introverted, and I hardly hung out with anybody, even if I wanted to. I was very reclusive, maybe because noone invited me anywhere. I was on a verge of a crisis, so I did break down. I was really miserable and lonely, and wanted to die. I went on a trip, and at the same time, left university, because emotionally I couldn't deal with it. I went away, and went home when I ran out of money.

I was having a rough time with my parents, I still do. The cause of my depression and mania has always been them, and I am pretty sure what they have done to me would constitute abuse, in one way or another.

So what I am saying is, if you connect the dots, a lot of the reason why people fall into ADD or dyscalculia has more to do with social relationships, than with genetics, attention, or maths.

I am a intelligent person. And my IQ is higher than average. And it was really, really high when I was a child. Somehow things went bad for me, and while I'm not less intelligent, I haven't been able to grow and improve as exponentially as I did as a child, and I am now hindered by basic numeracy skills which I could not get due to emotional and mental stress.

Welcome to Dyscalculia!

My name is Calculia, (C for short), and here to take you on a journey through what it's like to have Dyscalculia (which is a learning disability to do with maths).