Do I have a learning disabilty?

[whatthebutlersaw]

No? Loosely, and off the top of my head:

For A >= 0,
9 x A = B + 10 x B1 + 100 x B2 ... (where all Bi >= 0)
9 x A = B + 9 X B1 + B1 + 99 x B2 + B2 ...
A = (B1 + 11 x B2 + 111 x B3 ...) + (B + B1 + B2 ...) / 9
So since A is an integer, (B + B1 + B2 ...) must be a multiple of 9.
It is trivial to show that this sum of digits, if not 9 or 0, is less than
A, so if not 9, repeating this process will result in another sum of digits
that is 9, 0, or smaller yet, and so by recursion the recursive sum of
the digits must be 9 or 0. If it is 0, then it can only be that A was 0.
So the recursive sum of digits for A > 0 must be 9.

Yeah... what you said... *pretends to understand*

 

[Modified]

Yeah... what you said... *pretends to understand*

Well, the trick is that 10 - 9 = 1, 100 - 99 = 1, 1000 - 99 = 1, so the value represented by each digit, B, in the result can be split into (9 times something + B). The result has to be a multiple of 9, so the sum of the digits must be a multiple of 9. There isn't any complicated math required.

Alternately, to get that the sum of the digits is divisible by 9, you could start with 9 x 0 = 0, and note that adding 9 to a number will either change the ones digit from 0 to 9, or decrease the ones digit by one, increase some higher digit by one, and change all intermediate digits (if any) from 9 to 0. So the sum of the digits, if a multiple of 9, is still a multiple of 9 after adding 9 to the number. Thus, by recursion the sum of the digits of 9 x A must be a multiple of 9, and you can use the last part from my first post to show that the recursive sum of the digits must be either 9 or (trivially) 0.

 

[Dancing David]

Does everyone have learning disabilities?

Compared to whom?

If there exists a measured baseline of what constitutes "Average human ability to learn and understand subject X in time Y" I have yet to hear of it.

There is a huge amount of literature on this, mainly in developmental and education metrics. I am sure Bpesta22 could source them better than I. There are spectrums of age related skills and abilities.

We are all better at some stuff and not so good at other stuff.
Sometimes we can use workarounds , sometimes not.
That this is partly a result of experience and partly of neural structure seems fairly clear.
These days it's not considered PC to say someone is a bit dim.

Depends in schools we refer to them as the 'slow learners', they comprise about 10-20% of the given population, they rate as having IQs below 90 and above 70. They consistently fall behind the rest of their peer group. In common parlance they are referred to as the 'low' student, in that they have low abilities to perform class based skills.

the issue is that one does not just kick them out of school or ridicule them.

We prefer to say said individual has a highly specific learning disability and ascribe it to a neural structure. That way there's no blame for the person himself.

But by definition these are not the slow learners, LD means that your ability to perform in a class setting is below that expected by your overall IQ.

But what is the person himself if not the combination of neural structure and experience?
Eddie- for what it's worth, my arithmetic abilities are much like your own and my conceptual mathematical ability is very weak indeed. I not only think a lot of mathematics is just philosophical bunk, I'm not even convinced that numbers are in a deep sense "real" at all. And I'm totally incapable of explaining what I mean by that.
It's possible I have a rare and profound insight into the Nature of Reality. Or I may be just a bit dim.
I know which I think is more likely.

ETA- And I'm not losing any sleep over it.

Incidentally, I'd add that if a particular neural structure is associated with a "disability"- learning or otherwise- it may also be associated with another advantage, such as emotional stability, better verbal dexterity, ability to visualise more clearly etc- . Brain output is behaviour- and behaviour is so subtle we will be centuries categorising it all and associating it with bits of brain, if that is even possible in theory.
Being unable to count beyond thirty was no disadvantage for 99.999% of human prehistory- and given a calculator, looks to be no major problem in future. If it happens to be associated neurally with (say) the ability to appreciate the loveliness of a flower- how would we ever know?

SS, here is the deal, yes we all have strengths and weaknesses, but some people do not function well in a school environment.

This is how a learning disability is judged:

1. What is the persons overall ability, judged by IQ testing or other metrics.
2. What is the person's ability to perform in a class room situation.
3. Is there a marked difference?

The issue is not the benefit of not having a skill, but, how do you do in school ? It is specifically about skill based performance in a class room setting.

Seriously, if I had been in a different family I would very a very low skilled reader. I only learned to read with great difficulty, my brain just does not sound out the phonemes by reading them, I just can not spell things by the rules without great effort. Even in college I read very slowly.

So yes in a pre-industrial society this would not matter, but in today’s world it does matter. I would not have had any of the higher paying jobs that I have had, had I not learned how to read and gone to college. For me, learning to read is crucial to my current place in life.

 

[scissorhands]

I use the same approach, but my brain latched onto other criteria. For multiplying with 9, instead of just learning the table by heart in second grade like the rest of my class did, and which would have been much more practical, I noticed that anything multiplied by 9 could always be added down to make 9. In second grade, I never did this beyond "times 10" as it wasn't required, but as I got older I noticed it actually held:

Simple example: 9*7=63
6+3=9
Bigger example: 9*82=738
7+3+8=18
1+8=9
Bigger yet : 9*2640=23760
2+3+7+6+0=18
1+8=9

and so on. Of course, I have no proof - or any chance of understanding the math required to find a proof - for this, but it worked for everyday purposes and though I grew up to be a math doofus, at least there was this glorious moment in second grade when I actually came up with a simple theorem. The strain must have shut the math part of my brain down forever.

This meant that whenever I came across a small, multiplication (which is the only one you do in second grade) with 9 I would go one down and add up whatever made it nine. I.e for 6*9 my brain would go: one from six is five, five plus what is nine? Four. Five four. Fifty four. 6 times 9 is 54.

Other tricks I utilised to save myself the work of just learning the bally tables was to note that single even numbers multiplied by 6 tended to end in themselves: 6*2=12, 6*4=24, 6*6=36, 6*8=48, so when multiplying odd numbers by six my brain would find the higher nearest even number and then subtract six: 6*7=6*8-6=42.

The only table I couldn't find a trick for was 7 - but since I had tricks for all the other ones, I just did 7s the other way around. (Still talking kiddie school math, you understand, so not many big numbers flying about)

This meant that I calculated instead of rattling off, which actually made me slower than my classmates.

I never ever thought to share this with a math teacher and chose an all humanities package for my upper secondary because my teachers and I agreed that I did not have a math brain, since I was always lagging behind.

The process wasn't speeded up by the fact that I for some reason ascribed the single digits - only the single digits not larger numbers- personalities and disliked some of them causing me to feel some digits fared better to the expense of others, an injustice I was determined to correct. I detested the number 5, which I thought of as a disgusting goody two-shoes, teachers pet and total prigg, and would sometimes change answers if today's assignments had contained - in my opinion - too many fives, in order to let the four come out and play more often. (Four being honest, dependable and a good friend) My teacher at the time found it really weird that I would so often be exactly one off the correct answer. We came to the joint conclusion that I basically sucked at math and left it at that.

With a brain that messed up, no wonder math wasn't for me. I don't think there is a teaching method in the world that could straighten out that mess. (Although I did grow out of the "numbers have personalities" thing. These days, they are just numbers)

I have an unrequited love for math. I love to read about it - especially number theory - but I don't understand any of it. I experience it like I would dadaistic poetry and leave it at that.

Thats a great insight into the workings of a young, somewhat logically mixed up, but highly creative brain.

I think your math teacher sucked at teaching math, he/she should have picked up on your strange "one digit off" answers and dealt with your strange number 5 discrimination.

Four being honest, dependable and a good friend

Obviously not in your case.

Great post.

 

[DevilsAdvocate]

Why two Ls in functionally?

Why not? The rule is add "ly" (cruel=cruelly, functional=functionally). Exceptions are if the word ends in

"ll" (full=fully)

consonant + "le" (simple=simply, gentle=gently)

"y" (day=daily, angry=angrily)

Double vowel (true=truly)

Exceptions (haste=hastily, whole=wholly)

 

[CelticRose]

I use the same approach, but my brain latched onto other criteria. For multiplying with 9, instead of just learning the table by heart in second grade like the rest of my class did, and which would have been much more practical, I noticed that anything multiplied by 9 could always be added down to make 9. In second grade, I never did this beyond "times 10" as it wasn't required, but as I got older I noticed it actually held:

Simple example: 9*7=63
6+3=9
Bigger example: 9*82=738
7+3+8=18
1+8=9
Bigger yet : 9*2640=23760
2+3+7+6+0=18
1+8=9

and so on. Of course, I have no proof - or any chance of understanding the math required to find a proof - for this, but it worked for everyday purposes and though I grew up to be a math doofus, at least there was this glorious moment in second grade when I actually came up with a simple theorem. The strain must have shut the math part of my brain down forever.

This meant that whenever I came across a small, multiplication (which is the only one you do in second grade) with 9 I would go one down and add up whatever made it nine. I.e for 6*9 my brain would go: one from six is five, five plus what is nine? Four. Five four. Fifty four. 6 times 9 is 54.

Other tricks I utilised to save myself the work of just learning the bally tables was to note that single even numbers multiplied by 6 tended to end in themselves: 6*2=12, 6*4=24, 6*6=36, 6*8=48, so when multiplying odd numbers by six my brain would find the higher nearest even number and then subtract six: 6*7=6*8-6=42.

The only table I couldn't find a trick for was 7 - but since I had tricks for all the other ones, I just did 7s the other way around. (Still talking kiddie school math, you understand, so not many big numbers flying about)

This meant that I calculated instead of rattling off, which actually made me slower than my classmates.

I never ever thought to share this with a math teacher and chose an all humanities package for my upper secondary because my teachers and I agreed that I did not have a math brain, since I was always lagging behind.

Those sound a lot like the tricks that I was taught in grade school when we were learning the multiplication tables. I'm actually very impressed that you figured them out on your own.

The process wasn't speeded up by the fact that I for some reason ascribed the single digits - only the single digits not larger numbers- personalities and disliked some of them causing me to feel some digits fared better to the expense of others, an injustice I was determined to correct. I detested the number 5, which I thought of as a disgusting goody two-shoes, teachers pet and total prigg, and would sometimes change answers if today's assignments had contained - in my opinion - too many fives, in order to let the four come out and play more often. (Four being honest, dependable and a good friend) My teacher at the time found it really weird that I would so often be exactly one off the correct answer. We came to the joint conclusion that I basically sucked at math and left it at that.

With a brain that messed up, no wonder math wasn't for me. I don't think there is a teaching method in the world that could straighten out that mess. (Although I did grow out of the "numbers have personalities" thing. These days, they are just numbers)

I have an unrequited love for math. I love to read about it - especially number theory - but I don't understand any of it. I experience it like I would dadaistic poetry and leave it at that.

Have you ever heard of synesthesia? Synesthetes often perceive numbers as having personalities, etc.

 

[Unlike a Bull]

I'm talking simple calculations.

I mean that when I buy something at a store with cash, I let the clerk do the calculating and look like I'm too. But I'm actually acting like I am.

Do you mean that you can't add up the items that you bought? like, .99 for bread, 1.29 for a snickers and 87.32 for a redbull? because that would take me a little bit of time to calculate also. Or do you mean you can't count out the money? like I owe 89.60 for my foodstuffs, I have four twenties, a five and five ones ... how much is that?

If the former is the case, I wouldn't do that math in the store (and I consider myself to be pretty good at doing math in my head), I would just round everything up and assume that tax will cover the error. Sometimes I'm a little over, sometimes a little under, but it's just an estimate.

If the latter is the case I would think that you might have a disability. Keep in mind that I am in no way qualified to make this claim, have done no research on the subject, and for all intensive purposes, have no idea what I'm talking about.

I have an idea for you though. You could just start carrying around more 20's 50's and hundred's (if you're American. If not, change the denominations to be appropriate for your currency) and just give the next largest denomination of bill. so if you owe 89 dollars just give 100. if you owe 36 give a 50. the problem is that you will end up accumulating small bills form the change you receive. These can be paper clipped into appropriate stacks (20 5's, 20 1's, 10 10's) and either given in place of larger bills or traded to the bank for large bills.