All children's names have been changed.
Example Pete (anonymous)
Pete at the age of 1;3 is playing with a little wooden pot with a lid and he has 3 little stones and 3 little semi-precious stones.
He keeps putting the 6 items inside and then takes them out again. The semi-precious stones are shaped like eggs, they keep rolling away, sometimes he keeps hold of them by sitting on them. Yet he never stops before he has all 6 of them back in the pot, he always gathers all of them. No earlier than that does he begin to take them out again.
Date of publication in German: June 17th, 2010
Example by Heike Brandt, Remscheid
Towards the end of the morning circle it was time for the count up. Carl (3;10) immediately named three children who were missing that day.
On another day towards the end of the afternoon Carl declares that there are now 18 children in the group. I asked him how he got that number. He said that one child had been picked up for home.
Other than that Carl found the count up in the morning circle boring and declined to participate in it.
In a quiz game, when asked about the number of doors in our kindergarten, he almost gets it right and even remarks that the door to the next room is missing. His answer is at first misunderstood by the game host. Upon enquiry he explains himself: “I'm only 3.”
Date of publication: June 17th, 2010
Example Mara (2;6), anonymous observation in the family
For the past few weeks Mara has been showing a marked interest in numbers. Just reading the numbers from 0 to 9 isn't enough anymore, now she enquires about the meaning of two numbers side by side as in 10 or 12 and so forth …
When we were sorting chestnuts from one bowl to another yesterday, counting them, she instantaneously understood that the 'one'-digits are always the same and are simply attached to the 'ten'-digits.
She easily counts up to 20, and when I counted from 21 to 30 for her, she continued from 31 upwards to 50, she did stumble over the ten-numbers (30,40,50).
The inscriptions on our washing machine always get her interested, she wants to know what the numbers under 'spin cycle' mean (there the numbers 400/600/900/1200 can be seen), and then she asks me how to say it when the 4 and the 0 and another 0 are set together. Next thing she makes up numbers herself and asks me how to say them, like when the 1 and the 2 are together, and when the 1 and the 2 and the 3 go as one. Then she still continues and wants to know about the 1 with the 2, the 3 and the 4.
Date of publication in German: June 17th, 2010
Example by Monika Meeus, Bornheim
Enno (3;11) was able to recognize numbers very early on. He counts fluently up to 100. When he makes a mistake, he is able to correct himself. He stops shortly, thinks, and is then rather quickly able to say what comes next.
He can read and write numbers. When I write down a bigger number (51, 76 …) he can say it correctly right away.
He can also perform minor calculations. When I praised him for his great skills he replied: “Nobody taught me, I just knew how to do it.”
… We have a sorter toy at our kindergarten. This one consists of a square wooden board with 10 sticks of different length, glued to it and pointing upwards. Then there are 10 square boards with 1 to 10 holes in the same positions as the sticks. The children can slide the boards, one on top of the other, over the sticks to layer the boards. The one with the ten holes goes first. Then one of the sticks doesn't stick out any longer because it's too short, and on like that: next the board with 9 holes, in which the second shortest stick disappears. Enno could, at first glance, tell how many sticks and holes there were left, and how many were gone. Great!
Date of publication in German: September 9th, 2009
Example by Inge Förster, Aachen
Felix (4;8) has a good command of the numbers up to 100 and can read two-digit numbers. In exercises to enhance the understanding of basic mathematical concepts and calculations, which we do with our pre-school children, he needs to be given tasks of a higher degree of difficulty. For example, when dealing with the proportions of amounts and sizes by the use of natural objects, we ask the children to hide 10 acorns evenly among 5 places, but we have Felix hide 20 acorns evenly in 4 places.
In a playing situation five children agree to meet at midnight to go on a long night-hike. As his mother is picking him up that afternoon, Felix tells her about it and she reminds him, that he has arranged to see his grandmother the next morning at 8 o'clock. Felix considers this shortly and goes: If I only join them for one hour, I can sleep 6 hours, that's enough time. I get up at seven and have breakfast until grandma comes.
Felix' interest in numbers is increasing rapidly and he keeps demanding higher levels of difficulty, for example the addition of length or weight measures. Or he ponders the question: How many times would our church fit into the Dome of Aachen? A question which has not yet been answered satisfactorily.
Date of publication in German: September 9th, 2009
Example by Hanna Vock, Bonn
Eva was able to read all numbers from 0 to 100 at the age of 3;6.
She understood the concept of decimal positional notation (1-numbers, 10-numbers, 100-numbers) immediately upon this explanation: “At the very back you have the smallest ones, that's where 4 really stands for 4. On the place next to it you have the next bigger ones, that's where a 4 is 'automatically' a 40. Yet one more place to the left you have the even bigger ones; that's where a 4 is really a 400.
So 444 is really 'four hundred – forty – four'.”
She thought it was funny, that it this spoken 'in reverse' (the four before the forty!).
[In German two-digit numbers are actually spoken 'backwards', 44 is spoken 'vier-und vierzig' which is literally 'four-and forty'. Translator's note ]
The given explanation was sufficient for her and she went right ahead, trying all kinds of three-digit numbers.
Even the number 305 made her stop and think only shortly, and then she said: “Well, there isn't one in the middle, so I don't have to say anything there.”
Michael Hollenbach gives another example in the sleevenotes of his book (Recommended Reading) :
“Helen Wagner is riding her bike across a cemetery together with her 5 years old son. She hears him saying numbers again and again: 86, 22, 64, 80, 3, 77 – finally she realizes that the little know-it-all is calculating the ages at which the deceased had died.”
Date of publication in German: November 20th, 2008
Copyright © Hanna Vock 2008, see Imprint .