One, Two, Many -- Can you count past three?

[Weird Harold]

An interesting article about how people count:

From: http://www.bib-arch.org/bswb_AO/bswbAOOrigins.html

It is a common misconception that we humans instinctively count to ten because we have ten fingers. Not all cultures even use a base-ten numerical system (or a numerical system of any base at all): Some Mesopotamians used a sexagesimal (base-60) system, a form of counting that survives on our watches; the French word for 80, quatre-vingts (or four twenties), may well be a survival from a base-20 system; and modern computers use a base-two system. There is no innate method of counting; one system is as good, and as artificial, as another.

Nor is developing a counting system, of any type, instinctual. Cognitive psychologists have demonstrated that pre-school children do not identify more than three sets: a set of one object, a set of two objects, and a set of three or more objects (also called "many"). Although toddlers do perform tasks involving numbers, such as setting the table, they use one-to-one correspondence: one plate for mommy, one plate for Mary, and so on—which is really just counting to one, over and over again. Human beings, it appears, are born with the ability to recognize only patterns of one thing, two things and many things and to count in one-to-one correspondence.

Do you agree or disagree that counting past three is unnatural and counter-instinctual?

I think I do agree with the conclusion -- witness how much trouble children have learning simple arithmetic or even counting.

 

[Ishmael]

Hmmmmmmmmm, never gave it much thought.

Math is learned to an extent. But children seem to catch on real quick once the concept of money is introduced. Also if you ask a child "How many" they will invariably show an interest in learning how to calculate and communicate the quantity.

Every ancient culture had a means of enumeration and a means of communicating same. The Inca's used knotted strings as a means of denoting quantity.

Now that I think about it though, I can find no instance of a number system based on odd numbers. No base 3 or 7 or 11 systems, although they are just as valid for enumeration as any other base.

Ishmael

 

[SINthysist]

Yeah, and us computer geeks have to add letters Like 1 + 9 + C = ?

 

[SINthysist]

Of course we instictively start going 2 to the first pluse 2 to the...

 

[SINthysist]

Of course, Ish is probably doing a series of L-shifts...

on on off on off on on on on off off ...

 

[Ishmael]

Of course, Ish is probably doing a series of L-shifts...

on on off on off on on on on off off ...

Yep, I'm multiplyin'. If I were doing the R-shift thing I'd be dividin'.

Ishmael

 

[SINthysist]

 

[lilminx]

An interesting article about how people count:



Do you agree or disagree that counting past three is unnatural and counter-instinctual?

I think I do agree with the conclusion -- witness how much trouble children have learning simple arithmetic or even counting.

Not all children have trouble learning arithmetic or counting. Most of my first-graders last year came into first grade knowing how to count to 20, could recognize those numbers written, and could do simple arithmetic with addends up to 12.

As Ishmael implied, it all depends on how you implement instruction. The children who were having difficulty with higher numbers and counting patterns (2s, 5s, 10s), learned it very quickly when it involved them earning money for good behavior and then using the earned money to buy little things in a school store.

 

[JazzManJim]

As we all know, the proper counting scheme is:

One, Two, Many, Lots!

 

[Guest]

Solo, Coupling, Three-Way, Orgy...


One-tracked mind this AM...

 

[Texan]

I think Ishmael really hit it on the head when he said he couldn't think of a number systems that was based on an odd number.

I remember an article from many years ago that said ALL numerical systems are based on 2. They are based on man's inate understanding of simple symetry. Everything is based on "balance." It doesn't take much to think of the countless areas of life that envolve 2.

Anyway, this "concept" would agree with Ishmael's idea, as well as, the premise that WH started the thread upon.

 

[Cheyenne]

An interesting article about how people count:

Do you agree or disagree that counting past three is unnatural and counter-instinctual?

Disagree. Those of us who make our living by dealing with numbers find it very natural to "count" large numbers. Most of us do it in our heads automatically. It is also a skill that comes in handy shopping at "xx % off" sales as well as while traveling in foreign countries where currency conversion is needed on the spot.

 

[Hamletmaschine]

I have no idea whether it is unnatural for us to count beyond three. But the number 3 figures prominently in mythology and folklore throughout the globe, and this number also figures heavily in world literature, too. It is the "magic" number insofar as we expect things to come in threes--and when the third element is introduced (in a story, for example), we feel a sense of psychological/emotional completion, fulfillment, and satisfaction.

A quick example: stories have beginnings, middles, and ends. Ya gotta have all three, or it ain't a story. Imagine reading/hearing/watching a story with just a beginning and a middle. . . .

 

[morninggirl5]

I think we're dealing with two separate issues here. Natural behaviors and mathematical knowledge as a result of teaching.

Natural behaviors are those things such as setting the table, sharing a pack of crackers, putting the groceries away, etc. All of these involve mathematical concepts. Children AND adults use numbers up to 3 or perhaps 4 when they complete these tasks. Think to yourself about the last time you counted a large group of objects, you probably did so in groups of 3 or 4. One-to-one correspondence is something that children develop through natural interactions in most cases before they ever enter school. As such, it's extremely difficult to teach in anything other than a natural setting.


Mathematical knowledge is a separate issue. Young children can be taught a lot about Mathematics. Contrary to what Ishmael believes, money is one of the hardest mathematical concepts to teach young children. It involves too many patterns in one system. Count by 25's, then change gears and add 10's, change gears again and add 5's, one final gear change and add 1's.

Counting money was the single objective in the Kindergarten Math series that all of my students had problems with last year. I'm teaching it completely differently this year in hopes that i can slowly build their knowledge.


WH, the article is a pretty close reflection of an article i read during grad school, if i can find it again, i'll send it to you.

 

[Spinaroonie]

I count
1 2 3 4 5 6 7 8 9 A B C D E F 0

 

[Guest]

I count
1 2 3 4 5 6 7 8 9 A B C D E F 0

______

So, your a hexadecimalist!

That explains a lot of things.

 

[Spinaroonie]

______

So, your a hexadecimalist!

That explains a lot of things.

Yeah, Blame it on ResEdit.

 

[Ishmael]

I think we're dealing with two separate issues here. Natural behaviors and mathematical knowledge as a result of teaching.

Natural behaviors are those things such as setting the table, sharing a pack of crackers, putting the groceries away, etc. All of these involve mathematical concepts. Children AND adults use numbers up to 3 or perhaps 4 when they complete these tasks. Think to yourself about the last time you counted a large group of objects, you probably did so in groups of 3 or 4. One-to-one correspondence is something that children develop through natural interactions in most cases before they ever enter school. As such, it's extremely difficult to teach in anything other than a natural setting.


Mathematical knowledge is a separate issue. Young children can be taught a lot about Mathematics. Contrary to what Ishmael believes, money is one of the hardest mathematical concepts to teach young children. It involves too many patterns in one system. Count by 25's, then change gears and add 10's, change gears again and add 5's, one final gear change and add 1's.

Counting money was the single objective in the Kindergarten Math series that all of my students had problems with last year. I'm teaching it completely differently this year in hopes that i can slowly build their knowledge.


WH, the article is a pretty close reflection of an article i read during grad school, if i can find it again, i'll send it to you.

Well that kinda tells me your an education major and you DON'T have any kids of your own.

You don't TEACH a child how to count money. You give them some money and take them shopping. The little rascals figure it all out real quick. Lilminx's school got that one figured out and didn't even need PhD to do it.

Ishmael

 

[alexandraaah]

Solo, Coupling, Three-Way, Orgy...


One-tracked mind this AM...

That's good..

 

[dreamer]

What gets REALLY interesting isn't the 'base' you're calculating or counting in but when you change the algebra itself.

For all intents and purposes hex, binary, or decimal systems are all the same...just different ways of scratching what you mean on the wall. I've always found it interesting that we as a civilization have accepted base 10, and I lean towards believing it has SOMETHING to do with our fingers....and the whole french base 20 hypothesis follows nicely if people counted on their toes...

But, change the meaning of the operators we have all grown to know and love (+,-,x, /) and look out...there are more algebraic systems that hold up equally well as what we know to be TRUE than one can imagine.

DAMN, I miss these types of conversations...maybe I should go back to school.


Oh and Hamletmaschine as a HUGE fan of Norse mythology and well..all mythology I know exactly what you're talking about but by all accounts they never wrote '3' they most likely used a more Roman III or a primal three scratches to represent three. Not to mention most of those beliefs were oral tradition (in the north anyhow) till relatively recent times. Maybe not Beginning and Middle...but how about First and Last...halves that is?

 

[SimGuy]

An interesting article about how people count:

Do you agree or disagree that counting past three is unnatural and counter-instinctual?

I think I do agree with the conclusion -- witness how much trouble children have learning simple arithmetic or even counting.

I believe math and counting is learned, but I don't think counting past three is unnatural.

Gotta remember, it was only a few months before, that these toddlers believe Mommy and Daddy ceased to exist when they couldn't see them anymore.

The ability to count is a necessary ability that mankind has had to develop.

 

[morninggirl5]

Well that kinda tells me your an education major and you DON'T have any kids of your own.

You don't TEACH a child how to count money. You give them some money and take them shopping. The little rascals figure it all out real quick. Lilminx's school got that one figured out and didn't even need PhD to do it.

Ishmael

I'm a TEACHER. And while i don't have kids of my own, i've been second Mommy to four kids for the past nine years.

When they are students in your class, you DO teach them to count money. Particularly when NONE of them have ever had ANY experience shopping with money on their own.

I'm a damned good teacher, and i resent your implication otherwise, joking or not.

 

[Ishmael]

I'm a TEACHER. And while i don't have kids of my own, i've been second Mommy to four kids for the past nine years.

When they are students in your class, you DO teach them to count money. Particularly when NONE of them have ever had ANY experience shopping with money on their own.

I'm a damned good teacher, and i resent your implication otherwise, joking or not.

OK, be that way. See if I care.

Ishmael

 

[Weird Harold]

Re: Re: One, Two, Many -- Can you count past three?

I believe math and counting is learned, but I don't think counting past three is unnatural.
...
The ability to count is a necessary ability that mankind has had to develop.

I'm not so sure that mankind really needs the abilility to count -- society might need it, but not mankind.

For example, I can't think of very many situations in my reclusive everday life whenI need to count beyong three -- setting the microwave to cook dinner is the notable excepion, and that's not really "counting" it's memorizing a one-to-one corespondence that two burritos need "3, 3, 3, start" to cook the way I like them.

The only time I really need math and counting is on "mother's day" when I have to figure out how much I owe each "mother" that wants his money on the first of the month.

In fact, I really don't need to count past three until I interact with society -- as long as I stay home I can get along just fine with "one, two, many."

 

[Pyper]

I saw an interesting documentary in Spain (I think it was dubbed BBC) that talked about tracing families of languages. There was a linguist who had a theory that the most important words in a language (mama, food, etc) changed very little over time and could be used to determine how closely languages were related.

The program stated that among these primitive, unchanging words were the numbers one, two, and many. They inferred from this that early societies had no need to count beyond this, and thus this is the natural numerical system of all humans.