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Rack Your Brains and Help/102

Cours gratuits > Forum > Exercices du forum || En bas

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Rack Your Brains and Help/102
Message de here4u posté le 12-09-2021 à 22:05:06 (S | E | F)
Hello dear Fellow-workers!

Mon élève a beaucoup travaillé sur ce nouveau texte et n'a laissé que 12 fautes. (Cependant, comme il le fait toujours, il a répété ses fautes plusieurs fois, vous le savez ... (sigh) ) Il a vraiment besoin de votre aide pour trouver ses erreurs ... et les corriger !
Cet exercice est un et sa correction sera en ligne le lundi 27 septembre 2021.

Please, Help my poor Student! He needs you... This text contains 12 mistakes. (to be corrected in CAPITAL LETTERS, please!)

Humans evolve with ten digits on their hands and that’s likely the reason we have ten digits in our number system. Counting on our fingers feels like such natural and obvious thing to do that you might assume everyone does it in the same way. But, if you’re in UK or Europe, there’s a good chance you start counting with your left thumb. While in US and the Canada they start with the index finger, and finish with the thumb. In parts of the Middle East like Iran, they start on the right hand, with the pinky. That system basically is so for every number, you add a new finger, what researchers call: a linear system. This linear way of fingers counting seems that it could be innate or universal. Researchers assumed that children basically need fingers counting as a tool to learn, to grasp the concept of number but also to learn counting. In Japan you start with the fingers extended, and curl them in as you count upwards. In other places, things diverge ever more. In Eastern Africa, they try to make symmetric representations as much as possible, which is very important to them culturally./// END OF PART ONE /// The big limitation with these methods is they quickly run down of fingers – but that’s not an issue everywhere. In India, instead of counting complete or entire fingers, you count the lines between the segments, which gives you four different numbers for each finger: so you’ll reach much further than with the Western system. These linear systems are called one-dimensional, but there are also two-dimensional systems: the left hand counts till five, and the right hand keeps track of how many sets of fives have been counted – so these fingers represent a different dimension, multiples of 5. It’s also possible to combine these methods together: using the Indian system in two-dimensions would enable you to keep track of 20 sets of 20 – or up to 400!
There’s a third category of fingers counting where things get really interesting – symbolic. In China, counting from one to five is the same that in the West. But after six, they keep counting on the same hand, and instead of using quantities to represent numbers, they use symbols. /// END OF PART TWO /// This system works perfectly well when you master it, but it takes time in order to learn it. The Ancient Romans used a symbolic system to count till the thousands. Three fingers on the left hands were used to count «units». The thumb and forefinger made different shapes to represent the «tens». Adding the right hand lets you to keep track of «hundreds» and thousands in the same way.
So what does all this mean for our relationship with numbers? Fingers counting clearly has a huge cultural dimension. Natural as it feels, it’s a behaviour we learn as children, rather than something we do instinctively. At some point in the past, our ancestors have started counting and started designing counting systems. Which role did fingers counting play in that process? It’s a challenging task but hopefully we get closer of an answer to it. /// END OF THE TEXT ///

May the FORCE be with you... Thanks for your help!


Réponse : Rack Your Brains and Help/102 de taiji43, postée le 17-09-2021 à 12:05:41 (S | E)
Hello Dear Here4U
Really interesting article, however is the text without mistakes?...Our here4u expert will tell us..

READY TO BE CORRECTED

Humans EVOLVED with ten digits on their hands and that’s likely the reason we have ten digits in our number system. Counting on our fingers feels like such A natural and obvious thing to do that you might assume everyone does it in the same way. But, if you’re in UK or Europe, there’s a good chance you start counting with your left thumb. While in THE US and CANADA ( pas d’article) they start with the index finger, and finish with the thumb. In parts of the Middle East like Iran, they start on the right hand, with the pinky. That system basically is so for every number, you add a new finger, what researchers call: a linear system. This linear way of FINGER- counting (nom de la méthode)seems that it could be innate or universal. Researchers assumed that children basically need FINGER- counting as a LEARNING TOOL , to grasp the concept of number but also to learn HOW TO COUNT In Japan you start with the fingers extended, and curl them in as you count upwards. In other places, things diverge EVEN more (encore plus) . In Eastern Africa, they try to make symmetric representations as QUICKLY as possible, which is very important to them culturally./// END OF PART ONE ///

The big limitation with these methods is (THAT° qu’elles) they quickly run down of fingers – but that’s not an issue everywhere. In India, instead of counting complete or entire fingers, you count the lines between the segments, which gives you four different numbers for each finger: so you’ll reach much further than with the Western system. These linear systems are called one-dimensional, but there are also two-dimensional systems: the left hand counts UP TO (till =jusqu’à mais ne se dit pas ici car till= as far as) five, and the right hand keeps track of how many sets of FIVE (série du nombre cinq) have been counted – so these fingers represent a different dimension, multiples of 5. It’s also possible to combine these methods together: using the Indian system in two-dimensions would enable you to keep track of 20 sets of 20 – or up to 400!
There’s a third category of FINGER- counting where things get really interesting – symbolic. In China, counting from one to five is the same AS in the West. But after six, they keep counting on the same hand, and instead of using quantities to represent numbers, they use symbols. /// END OF PART TWO ///

This system works perfectly well when you master it, but it takes time in order to learn it. The Ancient Romans used a symbolic system to count UP TO the thousands. Three fingers on the left hands were used to count «units». The thumb and forefinger made different shapes to represent the «tens». Adding the right hand lets you KEEP track of «hundreds» and thousands in the same way.
So what does all this mean for our relationship with numbers? FINGER- counting clearly has a huge cultural dimension. Natural as it feels, it’s a behaviour we learn as children, rather than something we do instinctively. our ancestors STARTED (passé) counting and started designing counting systems. Which role did FINGER- counting play in that process? It’s a challenging task but hopefully we get closer of an answer to it. /// END OF THE TEXT ///



Réponse : Rack Your Brains and Help/102 de maxwell, postée le 19-09-2021 à 08:21:50 (S | E)
Hello Here4U
I don't know if I did well but I can't find any other mistakes. This exercise is really worth 4 or 5 stars!

Help my student:

Humans evolve with ten digits on their hands and that’s likely the reason WHY we have ten digits in our number system. Counting on our fingers feels like such A natural and obvious thing to do that you might assume everyone does it in the same way. But, if you’re in THE UK or IN Europe, there’s a good chance you start counting with your left thumb. WHEREAS in THE US and IN Canada they start with the index finger, and finish with the thumb. In parts of the Middle East like Iran, they start on the right hand, with the pinky.
That system basically is AS FOLLOWS : for every number, you add a new finger : THAT'S what researchers call: a linear system. IT SEEMS THAT this linear way of FINGER counting [] could be innate or universal.
Researchers assumed that children basically need FINGER counting as a tool to learn, to grasp the concept of number but also to learn counting.
In Japan, you start with the fingers extended, and curl them in as you count upwards.
In other places, things diverge EVEN more. In Eastern Africa, they try to make AS MANY symmetric representations as possible, which is very important to them culturally./// END OF PART ONE ///
The big limitation with these methods is they quickly run OUT of fingers – but that’s not an issue ANYWHERE. In India, instead of counting complete or entire fingers, you count the lines between the segments, which gives you four different numbers for each finger: so you’ll reach much further than with the Western system. These linear systems are called one-dimensional, but there are also two-dimensional systems: the left hand counts till five, and the right hand keeps track of how many sets of fives have been counted – so these fingers represent a different dimension, multiples of 5. It’s also possible to combine these methods together: using the Indian system in two-dimensions would enable you to keep track of 20 sets of 20 – or up to 400!
There’s a third category of fingers counting where things get really interesting – symbolic. In China, counting from one to five is the same THAN in the West. But after six, they keep counting on the same hand, and instead of using quantities to represent numbers, they use symbols. /// END OF PART TWO /// This system works perfectly well when you master it, but it takes time [] to learn it. The Ancient Romans used a symbolic system to count UP TO thousands. Three fingers on the left HAND were used to count «units». The thumb and forefinger made different shapes to represent the «tens». Adding the right hand lets you [] keep track of «hundreds» and thousands in the same way.
So what does all this mean for our relationship with numbers? Fingers counting clearly has a huge cultural dimension. Natural as it feels, it’s a behaviour we learn as children, rather than something we do instinctively. At some point in the past, our ancestors HAD started counting and started designing counting systems. Which role did fingers counting play in that process? It’s a challenging task but hopefully weRE GETTING closer TO an answer to it. /// END OF THE TEXT ///



Réponse : Rack Your Brains and Help/102 de here4u, postée le 21-09-2021 à 06:36:59 (S | E)
Come on, guys!

we need your help!



Réponse : Rack Your Brains and Help/102 de swan85, postée le 25-09-2021 à 20:58:49 (S | E)
Hello Here4U

Here is what I suggest for this very difficult text.

Humans evolve with ten digits on their hands and that’s likely the reason WHY we have ten digits in our number system. Counting on our fingers feels like such A natural and obvious thing to do that you might assume everyone does it in the same way. But, if you’re in THE UK or Europe, there’s a good chance you start counting with your left thumb. While in THE US and Canada they start with the index finger, and finish with the thumb. In parts of the Middle East like Iran, they start on the right hand, with the pinky. That system IS basically so for every number, you add a new finger, what researchers call: a linear system. This linear way of fingers counting seems that it could be innate or universal. Researchers assumed that children basically need fingers counting as a tool to learn, to grasp the concept of number but also to learn counting. In Japan you start with the fingers extended, and curl them in as you count upwards. In other places, things diverge ever more. In Eastern Africa, they try to make symmetric SYMMETRICAL representations as much as possible, which is very important FOR them culturally./// END OF PART ONE ///

The big limitation with these methods is THAT they quickly run OUT of fingers but that’s not an issue everywhere. In India, instead of counting complete or entire fingers, you count the lines between the segments, which GIVE you four different numbers for each finger: so you’ll reach much further than with the Western system. These linear systems are called one-dimensional, but there are also two-dimensional systems: the left hand counts TO five, and the right hand keeps track of how many sets of fives have been counted – so these fingers represent a different dimension, multiples of 5. It’s also possible to combine these methods together: using the Indian system in two-dimensions would enable you to keep track of 20 sets of 20 – or up to 400!
There’s a third category of fingers counting where things get really interesting – symbolic. In China, counting from one to five is the same that in the West. But after six, they keep counting on the same hand, and instead of using quantities to represent numbers, they use symbols. /// END OF PART TWO ///

This system works perfectly well when you master it, but it takes time in order to learn it. The Ancient Romans used a symbolic system to count TO thousands. Three fingers on the left hands were used to count «units». The thumb and forefinger made different shapes to represent the «tens». Adding the right hand lets you to keep track of «hundreds» and thousands in the same way.
So what does all this mean for our relationship with numbers? Fingers counting clearly has a huge cultural dimension. Natural as it feels, it’s a behaviour we learn as children, rather than something we do instinctively. At some point in the past, our ancestors have started counting and started designing counting systems. Which role did fingers counting play in that process? It’s a challenging task but hopefully we get closer of an answer to it. /// END OF THE TEXT ///



Réponse : Rack Your Brains and Help/102 de here4u, postée le 27-09-2021 à 23:23:02 (S | E)
Hello, Dear Workers!

I had thought the text was "interesting", and you found it "difficult"... Let's hope it was both... and let's hope that your EXCELLENT WORK and this correction will help you realise that it wasn't that difficult after all...

Humans evolve with ten digits on their hands and that’s likely the reason we have ten digits in our number system. Counting on our fingers, feels like such a natural and obvious thing (1) to do that you might assume everyone does it in the same way. But, if you’re in the UK (2)or Europe, there’s a good chance you start counting with your left thumb. While in the US(2) and Canada (2) they start with the index finger, and finish with the thumb. In parts of the Middle East like Iran, they start on the right hand, with the pinky. That system basically is so: for every number, you add a new finger, what researchers call: a linear system. This linear way of finger counting (3) seems that it could be innate or universal. Researchers assumed that children basically need finger counting (3) as a tool to learn, to grasp the concept of number but also to learn counting. In Japan you start with the fingers extended, and curl them in as you count upwards. In other places, things diverge even more(4). In Eastern Africa, they try to make symmetric representations as much as possible, which is very important to them culturally.///END of PART ONE/// The big limitation with these methods is they quickly run out of fingers(5) – but that’s not an issue everywhere. In India, instead of counting complete or entire fingers, you count the lines between the segments, which gives you four different numbers for each finger: so you’ll reach much further than with the Western system. These linear systems are called one-dimensional, but there are also two-dimensional systems: the left hand counts up to five (6), and the right hand keeps track of how many sets of five (7) have been counted – so these fingers represent a different dimension, multiples of five. It’s also possible to combine these methods together: using the Indian system in two-dimensions would enable you to keep track of 20 sets of 20 – or up to 400!
There’s a third category of finger counting (3) where things get really interesting – symbolic. In China, counting from one to five is the same as (8) in the West. But after six, they keep counting on the same hand, and instead of using quantities to represent numbers, they use symbols.///END of PART TWO/// This system works perfectly well when you master it, but it takes time in order to learn it. The Ancient Romans used a symbolic system to count into the thousands(9). Three fingers on the left hands were used to count «units». The thumb and forefinger made different shapes to represent the «tens». Adding the right hand let you keep track(10) of «hundreds» and thousands in the same way.
So what does all this mean for our relationship with numbers? Finger counting(3) clearly has a huge cultural dimension. Natural as it feels, it’s a behaviour we learn as children, rather than something we do instinctively. At some point in the past, our ancestors started counting (11) and started designing counting systems. Which role did finger counting(3) play in that process? It’s a challenging task but hopefully we get closer to (12) an answer to it.
///END of the TEXT///

(1) like such a natural and obvious thing: toujours faire attention à l’ordre des mots avec SUCH : such + article indéfini singulier + NOM singulier/ such + nom au pluriel.
(2) The UK (the United Kingdom)/ The United States, but/ Canada. Article devant les pays formés de plusieurs Etats.
(3) finger counting: bien sûr, il faut compter plusieurs doigts, mais «finger» est ici en position d’adjectif et ne s’accorde pas.
(4) ever more: evermore serait en un seul mot et signifierait : Lien internet
/// even more: Lien internet

(5) run down of fingers: ne veut rien dire ! Lien internet
: run out of … Lien internet

(6)counts till five: till est employé pour exprimer un temps (till 5 o’clock) / pour exprimer un lieu, une distance : as far as// et pour une quantité : up to// count up to twenty.
(7) a set of five/ a set of ten/ a set of twelve: ce sont des adjectifs numéraux – ils restent invariables.
(8) Traîtrise suprême ! it’s the same AS (mon élève avait mis «the same than…» qui aurait pu, bien sûr, vous mener directement à «the same that» (vraie tentation pour les apprenants ! ) ! Sorry ! (En fait, je n’ai même pas à vous dire "SORRY!" parce que vous avez déjoué ce piège méchant !) BRAVO !
(9) to count into the thousands: into the thousands= up to the thousands.
(10) let you keep track: to let somebody DO something.
(11) our ancestors started counting ; du moment qu’il s’agit des ancêtres, l’action se passait forcément dans le passé révolu. => prétérit.
(12) close to= near ; adjectif; au superlatif : closer to.

Difficile ? pas plus que les précédents, si ? Alors, si vous le voulez bien, j'ai besoin de VOLONTAIRES pour le Follow Up Work! Tout le monde peut essayer de traduire une partie, maintenant ... Courage à vous et encore BRAVO! et



Réponse : Rack Your Brains and Help/102 de susu52, postée le 28-09-2021 à 11:21:16 (S | E)
Hi everyone !
Ready to be corrected ! (EDIT : I've just noticed I was one day late, , so I'm going to check the correction by my own , thanks again )
Thanks again for those interesting exercises, I've discovered them only a few weeks ago, and as I tried, it turned out I was pretty bad at it, but I'll keep training as much as possible !


Humans evolve with ten digits on their hands and that’s likely the reason WHY we have ten digits in our number system. Counting on our fingers feels like such natural and obvious thing to do that you might assume everyone does it in the same way. But, if you’re in THE UK or Europe, there’s a good chance you start counting with your left thumb. While in THE US and THE Canada they start with the index finger, and finish with the thumb. In parts of the Middle East like Iran, they start on the right hand, with the pinky. That system basically is so for every number, you add a new finger, what researchers call: a linear system. This linear way of fingers counting seems that it could be innate or universal. Researchers assumed that children basically need fingers counting as a tool to learn, to grasp the concept of number but also to learn counting. In Japan you start with the fingers extended, and curl them in as you count upwards. In other places, things diverge EVEN more. In Eastern Africa, they try to make symmetric representations as MANY as possible, which is very important to them culturally./// END OF PART ONE /// The big limitation with these methods is they quickly run OUT of fingers – but that’s not an issue everywhere. In India, instead of counting complete or entire fingers, you count the lines between the segments, which gives you four different numbers for each finger: so you’ll reach much further than with the Western system. These linear systems are called one-dimensional, but there are also two-dimensional systems: the left hand counts till five, and the right hand keeps track of how many sets of fives have been counted – so these fingers represent a different dimension, multiples of 5. It’s also possible to combine these methods together: using the Indian system in two-dimensions would enable you to keep track of 20 sets of TWENTIES – or up to 400!
There’s a third category of fingers counting where things get really interesting – symbolic. In China, counting from one to five is the same AS in the West. But after six, they keep counting on the same hand, and instead of using quantities to represent numbers, they use symbols. /// END OF PART TWO /// This system works perfectly well when you master it, but it takes time in order to learn it. The Ancient Romans used a symbolic system to count till the thousands. Three fingers on the left HAND were used to count «units». The thumb and forefinger made different shapes to represent the «tens». Adding the right hand lets you to keep track of «hundreds» and thousands in the same way.
So what does all this mean for our relationship with numbers? Fingers counting clearly has a huge cultural dimension. Natural as it feels, it’s a behaviour we learn as children, rather than something we do instinctively. At some point in the past, our ancestors HAD started counting and started designing counting systems. Which role did fingers counting play in that process? It’s a challenging task but hopefully we get closer TO an answer to it. /// END OF THE TEXT ///



Réponse : Rack Your Brains and Help/102 de here4u, postée le 28-09-2021 à 12:33:00 (S | E)
Hello susu!

Don't worry susu! I'll send your correction today... It will help you! for your work!

(... and I DON'T WANT YOU to say you're bad at anything! OK? Don't forget that "practice makes perfect!"



Réponse : Rack Your Brains and Help/102 de maxwell, postée le 29-09-2021 à 16:34:01 (S | E)
Hello!
Je traduirai la 1e partie

Humans evolve with ten digits on their hands and that’s likely the reason we have ten digits in our number system. Counting on our fingers, feels like such a natural and obvious thing to do that you might assume everyone does it in the same way. But, if you’re in the UK or Europe, there’s a good chance you start counting with your left thumb. While in the US and Canada they start with the index finger, and finish with the thumb. In parts of the Middle East like Iran, they start on the right hand, with the pinky. That system basically is so: for every number, you add a new finger, what researchers call: a linear system. This linear way of finger counting seems that it could be innate or universal. Researchers assumed that children basically need finger counting as a tool to learn, to grasp the concept of number but also to learn counting. In Japan you start with the fingers extended, and curl them in as you count upwards. In other places, things diverge even more. In Eastern Africa, they try to make symmetric representations as much as possible, which is very important to them culturally.


Les humains évoluent avec dix doigts dans les mains et c'est probablement la raison pour laquelle nous avons dix unités dans notre système de numérotation. Compter sur ses doigts semble quelque chose de si naturel et évident que vous pourriez supposer que tout le monde le fait de la même façon. Mais si vous êtes au Royaume-Uni ou en Europe, il y a de grandes chances que vous commenciez à compter sur votre pouce gauche. Alors qu'aux Etats-Unis et au Canada, ils commencent avec l'index et finissent avec le pouce. Dans certaines régions du Moyen-Orient comme en Iran, ils commencent par la main droite, avec le petit doigt. En gros, ce système est le suivant : pour chaque nombre, vous ajoutez un nouveau doigt. C'est ce que les chercheurs appellent : un système linéaire. Cette manière linéaire de compter semble pouvoir être innée ou universelle. Les chercheurs ont supposé que les enfants ont besoin du comptage de doigts comme outil d'apprentissage, pour saisir le concept de nombre mais aussi pour apprendre à compter. Au Japon, vous commencez avec les doigts étendus et les recroquevillez à mesure que vous faites un comptage ascendant. Dans d'autres lieux, les choses divergent encore plus. En Afrique orientale, ils essaient de faire des représentations symétriques le plus possible, ce qui est très important pour eux culturellement.



Réponse : Rack Your Brains and Help/102 de swan85, postée le 30-09-2021 à 14:20:34 (S | E)
Bonjour

Je propose de traduire la seconde partie.



Réponse : Rack Your Brains and Help/102 de magie8, postée le 30-09-2021 à 14:55:41 (S | E)
hello ; traduction de la dernière partie

Ce système fonctionne parfaitement bien, lorsqu'on le maîtrise, mais il faut du temps pour l'apprendre. Les Romains de l'Antiquité utilisaient un système symbolique pour compter jusqu'à des milliers. Trois doigts de la main gauche étaient utilisés pour compter les "unités" Le pouce de la main gauche et l'index faisaient des formes différentes pour représenter les "dizaines". L'ajout de la main droite permet de compter les "centaines" et les milliers de la même manière. Alors, que signifie tout cela pour notre relation avec les chiffres ? Le comptage sur les doigts a clairement une énorme dimension culturelle. Aussi naturel que cela puisse paraître, c'est un comportement que nous apprenons dès l'enfance, plutôt que quelque chose que nous faisons instinctivement. A un moment donné dans le passé, nos ancêtres ont commencé à compter et à concevoir des systèmes de comptage. Quel rôle le comptage sur les doigts a-t-il joué dans ce processus ? C'est une tâche difficile, mais nous gardons bon espoir de nous approcher d'une réponse à cette question.



Réponse : Rack Your Brains and Help/102 de swan85, postée le 02-10-2021 à 14:01:39 (S | E)
Hello

Ci-dessous la traduction de la seconde partie.

''
Ces méthodes sont limitées car ils sont rapidement à cours de doigts. - mais on ne rencontre pas ce problème partout. En Inde, au lieu de compter sur les doigts uniquement, vous comptez les lignes entre les segments, ce qui vous donne quatre nombres différents pour chaque doigt : Ainsi vous comptez beaucoup plus rapidement qu'avec le système occidental. Ces systèmes linéaires sont appelés unidimensionnels, mais il existe également des systèmes bidimensionnels : la main gauche compte jusqu'à cinq et la main droite calcule combien de séries de cinq ont été comptées - ainsi ces doigts représentent une dimension différente, des multiples de cinq. Il est également possible de combiner ces méthodes entre elles : l'utilisation du système indien en deux dimensions vous permettrait de suivre 20 séries de 20 – ou jusqu'à 400 ! Il existe une troisième catégorie de comptage des doigts où les choses deviennent vraiment intéressantes – le symbole. En Chine, compter de un à cinq est comme en Occident. Mais après six, ils continuent à compter sur la même main, et au lieu d'utiliser des quantités pour représenter des nombres, ils utilisent des symboles.''



Réponse : Rack Your Brains and Help/102 de here4u, postée le 02-10-2021 à 15:03:11 (S | E)
Hello Dears,

VOICI LA CORRECTION DU FOLLOW UP WORK! Merci de votre patience !


Humans evolve with ten digits on their hands and that’s likely the reason we have ten digits in our number system. Counting on our fingers, feels like such a natural and obvious thing to do that you might assume everyone does it in the same way. But, if you’re in the UK or Europe, there’s a good chance you start counting with your left thumb. While in the US and Canada they start with the index finger, and finish with the thumb. In parts of the Middle East like Iran, they start on the right hand, with the pinky. That system basically is so: for every number, you add a new finger, what researchers call: a linear system. This linear way of finger counting seems that it could be innate or universal. Researchers assumed that children basically need finger counting as a tool to learn, to grasp the concept of number but also to learn counting. In Japan you start with the fingers extended, and curl them in as you count upwards. In other places, things diverge even more. In Eastern Africa, they try to make symmetric representations as much as possible, which is very important to them culturally.

Les humains évoluent avec dix doigts dans les aux mains et c'est probablement la raison pour laquelle nous avons dix unités dans notre système de numérotation. Compter sur ses doigts semble quelque chose de si naturel et évident que vous pourriez supposer que tout le monde le fait de la même façon. Mais si vous êtes au Royaume-Uni ou en Europe, il y a de grandes chances que vous commenciez à compter sur votre pouce gauche. Alors qu'aux Etats-Unis et au Canada, ils commencent avec l'index et finissent avec le pouce. Dans certaines régions du Moyen-Orient comme en Iran, ils commencent par la main droite, avec le petit doigt. En gros, ce système est le suivant : pour chaque nombre, vous ajoutez un nouveau doigt. C'est ce que les chercheurs appellent : un système linéaire. Cette manière linéaire de compter semble pouvoir être innée ou universelle. Les chercheurs ont supposé que les enfants ont besoin du comptage de doigts comme outil d'apprentissage, pour saisir le concept de nombre mais aussi pour apprendre à compter. Au Japon, vous commencez avec les doigts étendus et les recroquevillez (repliez) à mesure que vous faites un comptage ascendant. Dans d'autres lieux, les choses divergent encore plus. En Afrique orientale, ils essaient de faire des représentations symétriques le plus possible, ce qui est très important pour eux culturellement. TTBien, Maxwell ! Le texte est parfaitement compris et bien traduit.

The big limitation with these methods is they quickly run out of fingers – but that’s not an issue everywhere. In India, instead of counting complete or entire fingers, you count the lines between the segments, which gives you four different numbers for each finger: so you’ll reach much further than with the Western system. These linear systems are called one-dimensional, but there are also two-dimensional systems: the left hand counts up to five, and the right hand keeps track of how many sets of five have been counted – so these fingers represent a different dimension, multiples of five. It’s also possible to combine these methods together: using the Indian system in two-dimensions would enable you to keep track of 20 sets of 20 – or up to 400!
There’s a third category of finger counting where things get really interesting – symbolic. In China, counting from one to five is the same as in the West. But after six, they keep counting on the same hand, and instead of using quantities to represent numbers, they use symbols.

Ces méthodes sont limitées car les apprenants sont rapidement à court de doigts. - mais on ne rencontre pas ce problème partout. En Inde, au lieu de compter sur les doigts entiers uniquement, vous comptez les lignes entre les phalanges, ce qui vous donne quatre nombres différents pour chaque doigt : ainsi vous comptez beaucoup plus rapidement qu'avec le système occidental. Ces systèmes linéaires sont appelés unidimensionnels, mais il existe également des systèmes bidimensionnels : la main gauche compte jusqu'à cinq et la main droite calcule combien de séries de cinq ont été comptées - ainsi ces doigts représentent une dimension différente, des multiples de cinq. Il est également possible de combiner ces méthodes entre elles : l'utilisation du système indien en deux dimensions vous permettrait de suivre 20 séries de 20 – donc jusqu'à 400 ! Il existe une troisième catégorie de comptage des doigts où les choses deviennent vraiment intéressantes – le symbole. En Chine, compter de un à cinq se fait comme en Occident. Mais après six, ils continuent à compter sur la même main, et au lieu d'utiliser des quantités pour représenter des nombres, ils utilisent des symboles. Très bon travail, Swan! Bravo ! C'est bien compris!

This system works perfectly well when you master it, but it takes time in order to learn it. The Ancient Romans used a symbolic system to count into the thousands. Three fingers on the left hands were used to count «units». The thumb and forefinger made different shapes to represent the «tens». Adding the right hand let you keep track of «hundreds» and thousands in the same way.
So what does all this mean for our relationship with numbers? Finger counting clearly has a huge cultural dimension. Natural as it feels, it’s a behaviour we learn as children, rather than something we do instinctively. At some point in the past, our ancestors started counting and started designing counting systems. Which role did finger counting play in that process? It’s a challenging task but hopefully we get closer to an answer to it.

Ce système fonctionne parfaitement bien, lorsqu'on le maîtrise, mais il faut du temps pour l'apprendre. Les Romains de l'Antiquité utilisaient un système symbolique pour compter jusqu'à des milliers. Trois doigts de la main gauche étaient utilisés pour compter les "unités" Le pouce de la main gauche et l'index prenaient des formes différentes pour représenter les "dizaines". L'ajout de la main droite permettait (la forme est la même au passé ! ) de compter les "centaines" et les milliers de la même manière. Alors, que signifie tout cela pour notre relation avec les chiffres ? Le comptage sur les doigts a clairement une énorme dimension culturelle. Aussi naturel que cela puisse paraître, c'est un comportement que nous apprenons dès l'enfance, plutôt que quelque chose que nous faisons instinctivement. A un moment donné dans le passé, nos ancêtres ont commencé à compter et à concevoir des systèmes de comptage. Quel rôle le comptage sur les doigts a-t-il joué dans ce processus ? C'est une tâche difficile, mais nous gardons bon espoir de nous approcher d'une réponse à cette question. Très très bien, Magie ! Bravo !

Un grand à vous, ô volontaires, pour cet excellent travail !




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