Now, I do not mean to suggest that counting-numbers were invented at the dinner table, but I am not so sure that they could have been invented for keeping track of his flock by the proverbial shepherd ! Not unless he had a very large flock - say, 20 or more - so that he could not keep track of them by some distinguishing features. Why, he might even have a name for each one of them, just as in a human family each member has a name.
The point is : what pretext - or context - could we use to get children acquainted with this activity. Today, in a country like the USA where you can still count your pennies, we could tell the children to look at the grocery store receipt and count the change returned if the payment was by cash. In India, years ago, we had 100 "naye paise" coins making up a rupee. Then came 5 paise, 10 paise 25 paise and 50 paise coins. But these have all disappeared and one will have to work with 1 Rupee , 2 Rupee, 5 Rupee and 10 Rupee coins. But that is still not a small amount of money to let children play with. One can, of course, use nursery rhymes or jingles - one, t wo, buckle my shoe,... !
Perhaps, we should think of contexts where counting is not done just to find out how many individual entities - "ones"- there are in a collection. These could begin with pouring out juice into mugs or paper-cups, but going beyond that, perhaps measuring a piece of string with a measuring tape. ( I was about to write "measuring the length", but what is "length" for a beginner ? ) One could go on to measure height of the child, girth, height of a wall, length of a wall, depth of a ditch. One will soon discover that counting numbers do not suffice. ( Perhaps, we could make and use a tape with only centimeter or inch marks. ) So one would be led to meet "fractions", not through slicing of a bread loaf, cutting an apple, slicing a pizza. Can one ever slice a bread loaf into perfectly equal slices ? The measuring tape comes very close to a perfect cutting or division.
The point is : what pretext - or context - could we use to get children acquainted with this activity. Today, in a country like the USA where you can still count your pennies, we could tell the children to look at the grocery store receipt and count the change returned if the payment was by cash. In India, years ago, we had 100 "naye paise" coins making up a rupee. Then came 5 paise, 10 paise 25 paise and 50 paise coins. But these have all disappeared and one will have to work with 1 Rupee , 2 Rupee, 5 Rupee and 10 Rupee coins. But that is still not a small amount of money to let children play with. One can, of course, use nursery rhymes or jingles - one, t wo, buckle my shoe,... !
Perhaps, we should think of contexts where counting is not done just to find out how many individual entities - "ones"- there are in a collection. These could begin with pouring out juice into mugs or paper-cups, but going beyond that, perhaps measuring a piece of string with a measuring tape. ( I was about to write "measuring the length", but what is "length" for a beginner ? ) One could go on to measure height of the child, girth, height of a wall, length of a wall, depth of a ditch. One will soon discover that counting numbers do not suffice. ( Perhaps, we could make and use a tape with only centimeter or inch marks. ) So one would be led to meet "fractions", not through slicing of a bread loaf, cutting an apple, slicing a pizza. Can one ever slice a bread loaf into perfectly equal slices ? The measuring tape comes very close to a perfect cutting or division.
Dear Sir,
ReplyDeleteFirstly, thank you very much for "re-educating myself". It is indeed great excitement and fun to learn from you.
I was about to attempt answering the question on the counting problem from your "Disturbing YOU" video. I could not find the reason why the count would always come to 11 objects/entities (as in the video), but try to prove mathematically that it cannot be different. However, after reading this blog, especially the post on 6 June 2020, I had to revisit the counting problem and believe that the counting problem you are referring to is probably more a measurement problem something I am unable to comprehend. Still thinking....
Looking forward to reading your next post.
Thank you.
Dear Prof. Agashe , I have actually seen frequently Shepards exiting from the confines of village limits and entering grazing lands in the forest that adjoins through a narrow ledge. At the entrance of the ledge the shepard actually moves stones one by pne as the sheeep enter the grazing ground. I do not know if he can count many (the herd numbered about 30-40) but when asked he said he does the process reverse in the evening and he can then feel certain that no sheep is missing. The attack by leapord is quite common and more common is sheep which misses out. he really cannot count large numbers but is very accurate to tell if 1-2 sheep are missong in the evening in which case he puts all these in the Pen and goes out looking with a milder weapon (Spear tied to the long pole plus sometimes a Lantern.
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