by Kornelia Thul
In a conversation with Felix (5;1) I want to find out if he can already do arithmetic and if so, if he can explain to me what it is. He thinks for a moment and says that he can already do arithmetic, which he immediately proves to me by explaining that 2+2=4 and 3+3=6. He explains to me that you need numbers to calculate and that there are lots of them, up to infinity.
I now ask him to write down the problem 2+2=4. He knows the numbers, but the symbols of the problem are still unknown to him.
Now I ask him to write down the numbers from 1 to 10 on the sheet, and I also write these numbers on a sheet. Felix is now supposed to compare his and my numbers with each other. He quickly notices that some of his numbers look different, which is true because he wrote them down mirror-inverted. He also thinks that my numbers look much neater.
Felix wants to learn more about the numbers, he wants to learn how to write them correctly and nicely. I suggest that I write the numbers in his notebook and indicate the direction of writing with arrows. Felix now writes all the numbers from 1 to 10 once more.
Afterwards we look at our written numbers again and I ask him if he can write down the next numbers after 10. He still knows 11 and 12 and writes them on his sheet.
I ask him to look at the numbers again and tell me his observations. Felix can’t discover anything new and I tell him to take a closer look at 11 and 12 to see which numbers they are made up of. Now Felix can tell me immediately that these numbers are made up of 1 and 1 again or 1 and 2.
Now I write the following numbers up to 20 on my piece of paper so that Felix can tell me what they are made of. Then Felix is challenged to dictate numbers to me, which I write down. He really enjoys this and his numbers get longer and longer. But each of the numbers consists of the numbers we wrote on our slips of paper at the beginning.
Felix is fascinated, suddenly he says that with the 10, the 1 was already on the piece of paper, but the 0 wasn’t yet. He answers my question about the value of the 0 with „nothing at all“. Now he is asked to place the 0 in our written sequence of numbers, he immediately puts it at the beginning before the 1.
Now I explain to him that all the other numbers, no matter how long they are, can be made from the numbers 0 to 9. We look again at the numbers he dictated and Felix is impressed.
Next, Felix is asked to go in search of numbers in the group room. Many things quickly accumulate: Clock, games, number cubes, tape measure, thermometer, ruler….
Now I want him to tell me whether numbers can be represented in other ways, and if so, how. Again the search starts in the group room, Felix finds a dots cube. Felix: „The dots show the numbers.“ That’s all he can find in the group.
Felix should think about whether there are other ways of representing the numbers, but which clearly show which number is meant. A little „finger pointing“ from me helps him along, he shows me the numbers with his fingers. Now we have already gathered three different ways of representing numbers, I ask him to look everywhere for more possibilities (in the outside area of the kindergarten; on the way home; at home).
The next morning, Felix brings me a sheet with lines on it. He explains to me that his friend Carlo has a book about the Stone Age, in which there are cave paintings. On them, Stone Age people drew animals, for example gazelles or deer, and made lines behind them. Carlo explained to him that this shows how many animals a Stone Age hunter killed; the one with the most strokes was the best hunter and had a high position in his tribe.
So the strokes
become the fourth type of representation.
But Felix saw something really funny on the way to kindergarten: „There was a sign on a house where the house numbers are.“
I ask him to draw the sign for me. An IX appears on the paper. Felix has no idea what it means, but he has already heard of the Romans. He knows that there is a city called Rome, which is in Italy, where his father’s parents live. The Romans came from there about 2000 years ago and were also in Cologne, where there is still a Roman museum.
I explain to him that his observation is about a Roman number, namely 9. The ancient Romans didn’t have any extra signs for numbers, they simply used letters to form numbers.
I wrote down the other Roman numerals up to X (10) for Felix.
So all in all, he has found
five ways of representing numbers.
Felix wants to know if our numbers are called German numbers because we use them in Germany.
I explain to him: „These numbers are called Arabic numerals, but they actually originated in India and then came to our region via Arabia about 1000 years ago. So today we mainly use the Arabic numbers, but the Roman numbers are still in use, as you can see from the house number IX.“
You can get Felix so enthusiastic about something with little effort that he keeps working on it and involves the people in his social environment to come to new conclusions.
He is not immediately satisfied with what he has achieved, but remains attentive and open to the task at hand.
But what now should be done with the collected observations?
I suggested to Felix to create something for the group, maybe a number wall with the different ways of representing numbers. Felix agreed, but wanted to work alone with me and then give it to all the children and adults in the group.
The number wall is created
For the number wall we needed cardboard in DinA6 format. Felix wants to write Arabic and Roman numerals, paint on the cube numbers, make the line numbers out of paper – and I should photograph the finger numbers. We get pens, paper, craft scissors, pencil and ruler as well as a nice cloth as a background for the finger number photos.
Felix starts with the Roman numerals. He asks me to help him with the preliminary drawing, as he wants the numbers to be large and clear so that the other children can see them easily. He now paints the numbers with great dedication.
Now the Arabic numbers follow, which Felix can draw on his own and then colour in. While he paints, I set him small addition tasks, first in the tens space, then up to 20. He enjoys it and quickly learns to master the 10 hurdle in arithmetic. I explain to him how to subtract, and up to 10 he can quickly solve the tasks set.
He enjoys doing mental arithmetic so much,
that he comes to me again and again
to do his arithmetic.
The cube numbers are a problem for Felix: if he just draws a square, you can’t tell that it’s supposed to be a cube.
We look at a large cube together, talk about faces, edges and corners. Felix notices that you always see more than one face of the cube; he doesn’t know how to draw that. I draw a cube with pencil and ruler that Felix likes. He wants the cubes for the number wall to look the same.
I get some graph paper so Felix can mark the corners of the cubes exactly before we connect them together with the help of the ruler. He learns that you have to work very precisely so that the edge lines are really straight. When he finally looks at the result, Felix notices that the pencil lines are not very easy to see and he draws them on his own with a felt-tip pen and ruler. In the process, he realises how difficult it is to trace the lines exactly. Again and again the ruler slips and he is a bit disappointed because the cubes don’t have straight edges. I can console him a little with the explanation that the dots on the cubes are more important for our number wall.
Taking photos of the finger numbers is quite quick. We look at the individual photos and then I run through them quickly. Felix can’t stop laughing, he finds the quick run-through so funny, with his individual fingers appearing quickly or disappearing on the return run.
Now it’s the turn of the „line numbers“. Felix cuts strips out of clay paper and sticks them onto the cards according to the respective number. He chooses a different colour for each number because it looks nicer, according to Felix.
The width of the strip should be 1 cm and the strip should be 9 cm long so that there is still a margin at the top and bottom of the 10 cm wide cardboard. We measure the strips together with a ruler and pencil and draw them on. Felix then cuts them out and glues them on. He takes great care that the strips are straight and in a line next to each other. When he glues on the strips for the number four, he ponders for a moment and finally says: „With the big numbers, we have to cut the strips thinner because otherwise they wouldn’t fit on the cardboard, which would then be too small.“ To explain, he takes a strip already cut out for the five and adds it to the four. The whole cardboard is now full, there are no more edges on the left and right. I am amazed that he has recognised this so early and immediately offers the solution, namely „thinner“ strips.
We paint on thinner strips – and it works, even the number ten has enough space on the cardboard thanks to Felix’s attention.
Now that all the rows of numbers are finished, we think together about where the number wall should find its final place. This is not so easy because we are currently redesigning our group room. Felix has an idea: „We can put it above the clock, there are numbers on the clock too.“ But he realises that there wouldn’t be enough space where the clock is hanging now.
As an alternative, he suggests: „We could hang it up in the painting studio (next room), then the children could always look at how the numbers are written correctly.“
In the painting studio we have attached a picture line on which the children can hang their pictures with clothes pegs. Felix thinks it’s funny because it looks like laundry and he also wants to hang the rows of numbers on the line.
Since the wall is still to be painted, we have to wait a little longer before finally placing the number wall.
But since I don’t think Felix’s idea of the clock is bad either, I suggest that we ask our kindergarten director, Mr M., if he can get us a clock for the number wall. Felix goes straight away to clarify the matter and Mr M. comes to the group together with Felix to get an idea. Felix shows and explains everything to him in detail and also says that the number wall would be even nicer with a clock, and waits anxiously for the answer. Mr M. promises that he will buy a clock for Felix’s wall after the holidays. Felix is visibly happy that he will soon be able to surprise the other children with his gift to the group.
It is amazing how self-confident Felix has become. A few months ago, he certainly wouldn’t have gone to Mr M. on his own to clarify the matter of the clock.
Date of publication in German: November 21
Copyright © Hanna Vock
Translated with www.DeepL.com/Translator (free version)