LAS MATEMÁTICAS NO SIRVEN PARA NADA

LAS MATEMÁTICAS NO SIRVEN PARA NADA

Alicia estaba sentada en un banco del parque que había al lado de su casa, con un libro y un cuaderno en el regazo y un bolígrafo en la mano. Lucía un sol espléndido y los pájaros alegraban la mañana con sus trinos, pero la niña estaba de mal humor. Tenía que hacer los deberes.

— ¡Malditas matemáticas! ¿Por qué tengo que perder el tiempo con estas ridículas cuentas en vez de jugar o leer un buen libro de aventuras? —Se quejó en voz alta—. ¡Las matemáticas no sirven para nada!

Como si su exclamación hubiera sido un conjuro mágico, de detrás de unos matorrales que había junto al banco en el que estaba sentada salió un curioso personaje: era un individuo larguirucho, de rostro melancólico y vestido a la antigua; parecía recién salido de una ilustración de un viejo libro de Dickens que había en casa de la abuela, pensó Alicia.

— ¿He oído bien, jovencita? ¿Acabas de decir que las matemáticas no sirven para nada? —preguntó entonces el hombre con expresión preocupada.

—Pues sí, eso he dicho. ¿Y tú quién eres? No serás uno de esos individuos que molestan a las niñas en los parques...

—Depende de lo que se entienda por molestar. Si las matemáticas te disgustan tanto como parecen indicar tus absurdas quejas, tal vez te moleste la presencia de un matemático,

— ¿Eres un matemático? Más bien pareces uno de esos poetas que van por ahí deshojando margaritas.

—Es que también soy poeta.

—A ver, recítame un poema.

—Luego, tal vez. Cuando uno se encuentra con una niña testaruda que dice que las matemáticas no sirven para nada, lo primero que tiene que hacer es sacarla de su error.

— ¡Yo no soy una niña testaruda! —Protestó Alicia—. ¡Y no voy a dejar que me hables de mates!

—Es una actitud absurda, teniendo en cuenta lo mucho que te interesan los números.

— ¿A mí? ¡Qué risa! No me interesan ni un poquito así—replicó ella juntando las yemas del índice y el pulgar hasta casi tocarse—. No sé nada de mates, ni ganas.

—Te equivocas. Sabes más de lo que crees. Por ejemplo, ¿cuántos años tienes?

—Once.

— ¿Y cuántos tenías el año pasado?

—Vaya pregunta más tonta: diez, evidentemente.

— ¿Lo ves? Sabes contar, y ése es el origen y la base de todas las matemáticas. Acabas de decir que no sirven para nada; pero ¿te has parado alguna vez a pensar cómo sería el mundo si no tuviéramos los números, si no pudiéramos contar?

—Sería más divertido, seguramente.

—Por ejemplo, tú no sabrías que tienes once años. Nadie lo sabría y, por lo tanto, en vez de estar tan tranquila ganduleando en el parque, a lo mejor te mandarían a trabajar como a una persona mayor.

— ¡Yo no estoy ganduleando, estoy estudiando matemáticas!

—Ah, estupendo. Es bueno que las niñas de once años estudien matemáticas. Por cierto, ¿sabes cómo se escribe el número once?

—Pues claro; así —contestó Alicia, y escribió 11 en su cuaderno.

—Muy bien. ¿Y por qué esos dos unos juntos representan el número once?

—Pues porque sí. Siempre ha sido así.

—Nada de eso. Para los antiguos romanos, por ejemplo, dos unos juntos no representaban el

Número once, sino el dos —replicó el hombre, y, tomando el bolígrafo de Alicia, escribió un gran II en el cuaderno.

—Es verdad —tuvo que admitir ella—. En casa de mi abuela hay un reloj del tiempo de los romanos y tiene un dos como ése.

—Y, bien mirado, parece lo más lógico, ¿no crees?

— ¿Por qué?

—Si pones una manzana al lado de otra manzana, tienes dos manzanas, ¿no es cierto?

—Claro.

—Y si pones un uno al lado de otro uno, tienes dos unos, y dos veces uno es dos.

—Pues es verdad, nunca me había fijado en eso. ¿Por qué 11 significa once y no dos?

— ¿Me estás haciendo una pregunta de matemáticas?

—Bueno, supongo que sí.

—Pues hace un momento has dicho que no querías que te hablara de matemáticas. Eres bastante caprichosa. Cambias constantemente de opinión.

— ¡Sólo he cambiado de opinión una vez! —Protestó Alicia—. Además, no quiero que me hables de matemáticas, sólo que me expliques lo del once.

—No puedo explicarte sólo lo del once, porque en matemáticas todas las cosas están

Relacionadas entre sí, se desprenden unas de otras de forma lógica. Para explicarte por qué el número once se escribe como se escribe, tendría que contarte la historia de los números desde el principio.

— ¿Es muy larga?

—Me temo que sí.

—No me gustan las historias muy largas; cuando llegas al final, ya te has olvidado del principio.

—Bueno, en vez de la historia de los números propiamente dicha, puedo contarte un cuento, que viene a ser lo mismo...

MISS BRACEGIRDLE'S NIGHT OF FEAR

MISS BRACEGIRDLE'S NIGHT OF FEAR

Stacey Aumonier

This was Miss Bracegirdle's first visit to France. She did not usually take holidays away from home.

Luckily she spoke a little French. 'It is not so difficult to live in France,' she thought. 'The thing to understand is that it is quite different from Easingstoke.'

She took her things one by one out of her bag and put them away carefully. She thought about her home in Easingstoke, with flowers in all the rooms and photographs of the family. She thought about her poor brother, working so hard. She felt a little sad, but only for a minute.

Her time in France was to be quite short. She was going to be home again soon. Now she must get a good night's sleep. But first that hot bath...

She took off her day things and put on her nightdress. Then she picked up her washing things and went to the bathroom, closing her bedroom door quietly. She lay in the hot water and thought about the nice young girl in the hotel getting her bath ready. People in this hotel were very friendly – always ready to help. There was so much she wanted to tell her brother when she got home.

She got out of the bath and put on her nightdress again. She cleaned the bath very carefully. She did not want French people to think that the English were dirty. Then she left the bathroom and went back to her bedroom. She went in quickly, put on the light and shut the door.

Then, one of those unlucky things happened: the door-handle came off in her hand. She tried to put the handle back on the door but she could not. 'How do I do it?' she thought. 'It is going to be very difficult to open the door now. Do I ask that nice girl to come and help me? Perhaps by now she is in bed.'

She turned away from the door, and suddenly, she saw something much, much worse than the door-handle. There was a man in her bed! She took one look at his thick black hair and his big black moustache and immediately felt quite ill with fear. For a minute or two, she could not think. Then her first thought was: 'I must not scream!' She stood there but she could not move. She just looked at the man's dark head and the big line of his back under the bedthings. She began to think very quickly.

Her next thought was: 'I am in the wrong room. It is the man's room.' She could see his jacket and trousers lying on a chair and his big black shoes on the floor. She must get out quickly. But how? She tried again to open the door with her fingers but she could not.

Here she was, shut in a hotel room with an unknown man – a Frenchman! She must think, she must think! She turned off the light.

'Perhaps with the light off, he is not going to wake up,' she thought.

'That gives me more time to do something. But if he does wake up, what do I do? He is not going to believe my story. Nobody is going to believe me.

In England perhaps but not here. How can they understand? So, I must get out of this room. By waking him? By screaming? By calling the young girl?

No, it is no good. If I scream or call out, people are going to come running immediately. And what do they find? Miss Bracegirdle from Easingstoke in a man's bedroom after twelve o'clock at night. Just think of all the talk back home when my friends hear about that!

And if I climb out of the window?' She thought of the big hairy man pulling her back by the legs as she tried to get out. He could wake up at any minute. She thought that she heard somebody going past outside the door. But it was too late to scream now.

Suddenly, she had an idea. It was now nearly one o'clock in the morning. Perhaps the sleeping man was not dangerous. At seven or eight o'clock, he must get up and go out to work. 'I can get under the bed and wait there until he goes. Men never look under the bed. When he sees the door-handle on the floor, he is going to open the door with something or call the girl to come. Later, I can come out from under the bed and go quietly back to my room. Nobody is going to know.'

She lay down on the floor and got under the bed. No sound came from the man above her, but from down here it was difficult to hear anything. She tried to think of her nice little bedroom in Easingstoke with its nice white bed but the floor was getting harder every minute. She tried to think what her room number was. One hundred and fifteen? Or was it one hundred and sixteen? She was always bad at remembering numbers.

She began to think of her schooldays and the interesting things she learned then. Suddenly, she felt that she was going to sneeze. She could not stop it. The sneeze came – a long, hard one. 'This is the end of me,' Miss Bracegirdle thought. 'Now this Frenchman is going to jump out of bed and turn on the light. Then he is going to look under the bed and pull me out.

And then...And then? What can I do then? I can scream if he puts his hands on me. Perhaps it is better to scream first, before that happens. If not, he can put his hand over my mouth and stop me from screaming.'

But no shout came out of her mouth. Her fear was much too strong. She stayed very quiet and listened. Was he going to hit her – with one of those heavy shoes, perhaps? But nothing happened. Miss Bracegirdle suddenly knew that she could not stay under that bed a minute longer. It was better to come out, wake up the man and tell him everything. With difficulty she got out from under the bed and stood up. She went over to the door and put on on the light. She turned to the bed and said, as strongly as she could, 'Monsieur!'

Nothing happened. She looked at the man and said again, 'Monsieur! Monsieur!'

But again there was no answer. She went closer to the bed. His hair and moustache were very black but his face had no colour in it. His mouth was open but his eyes were shut.

Then for the third time that night, Miss Bracegirdle nearly died of fear. Suddenly, her legs felt as weak as water. She nearly fell down. Because the man in the bed was dead! It was the first time that she stood face to face with a dead person, but there was no mistake. The man was dead. Miss Bracegirdle could only say, 'He's dead! He's dead!'

Her difficulties now were not important. She began to feel sorry for him, lying here dead in a hotel room. But a sudden sound broke into her thoughts. Somebody outside the door put down some shoes: the shoe-cleaning boy. She heard the sound of his feet die away and remembered where she was.

To be in an unknown man's bedroom was bad, but to be in a room with a dead man was much, much worse! If they found her here, people were going to think she killed him! A picture came into her head: the police taking her off to the police station, asking her questions, shutting her away... And her sister arriving in just a few hours' time too! She must get out of the room immediately. 'I cannot call for help now,' she thought, fighting back her fear. 'Do something, Millicent. It is now or never!'

But what? She went round the room, looking for something to open the door with. She could find nothing. Finally, she picked up the man's jacket. Inside it she found a small knife. She took the knife and put it in the side of the door. Very slowly she turned the knife and the door opened. She wanted to run out of the room immediately but she stopped first and listened. Nobody was there. Feeling very afraid, Miss Bracegirdle shut the door quickly behind her and ran as fast as she could to her bedroom.

She lay down on the bed and the fear slowly began to leave her. All was well!

But then she had another unhappy thought. The living fear came back.

Her washing things were in there. They were lying there in the dead man's room! And her name was on them. To go back again now was far worse than the first time but she had no choice. She could not leave her things lying there. 'If they find them, they are going to ask me how they got there,' she thought. She had to go back.

She went. She did not look at the bed. She quickly took her washing things and ran back again to her bedroom. Now that the danger was over, she suddenly felt very, very tired. She got into bed and put out the light. She lay in the dark, trying to forget her fears. Finally, she went to sleep.

It was eleven o'clock when she woke up. The sun was high in the sky and the fears of the night were far away. In the light of the day, it was all very difficult to believe. Miss Bracegirdle tried to think about other things.

Finally, the young girl arrived to wake her up. Her eyes showed that she was excited. 'Oh madame!' she said, 'a very bad thing happened here last night. The man in room one hundred and seventeen – he is dead!

Please do not say that I told you but the police were here, the doctor, everybody.'

Miss Bracegirdle said nothing. There was nothing to say. But the young woman was too excited to stop. 'And do you know who this dead man was, madame? They say that he was Boldhu, the famous killer, wanted by the police. Last year, he killed a woman and cut her up and threw her into the river. And last night, he died here in our hotel – in the room next door! We do not know how. Did you say coffee, madame?'

'No thank you, just a cup of tea – strong tea, please.'

'Very well, madame.'

Source: Simply Suspense (Penguin Readers)

READING ACTIVITY

THE FOLLOWING DAY, MISS BRACEGIRDLE WROTE A LETTER TO HIS BROTHER TELLING HIM ABOUT HER TERRIBLE NIGHT IN FRANCE. CHOOSE THE BEST ALTERNATIVES IN ORDER TO COMPLETE HER LETTER.

WORD BANK Dead, Believe, Under, Scream, Sneezed, Tension, Wake up, Bath, Handle, Escape, Scream, People, Thinking,  Wrong, Behave, Immediately.

My dear brother,

I am going to tell you a story that you will not   ______________________. Are you sitting

down? I spent yesterday night   ______________________________ a Frenchman's bed! 

I came back to my room after a   ______________. But when I saw a   _______________

man in the bed, I knew I was in the   ______________  room. I   ____________________

tried to leave the room, but then the door  ____________________  came off in my hand!

There was no   ________________. ‘What can I do? What will   ________________  think

of me? What will the man do to me?  I mustn’t   _________________________,’ I thought.

I didn't know how to   ________________________  in a situation like this, so I lay quietly

under the bed   ________________, when suddenly I   ___________________. The man

did not  ________________________. I couldn't stand the   _________________. Finally, 

I jumped up and put the light on, only to find that the man was   _____________________.

Oh God, it was really a terrible experience, wasn't it?

A big kiss.

SISTEMA CIRCULATORIO

Sistema Circulatorio Humano

Nuestro sistema circulatorio transporta la sangre, con oxígeno y nutrientes, hacia todos los tejidos del organismo y lleva los productos de desecho que ellos producen, hacia los pulmones y los riñones, donde son eliminados.
El sistema circulatorio realiza además dos funciones importantes, que son la coagulación y la defensa del organismo.
El sistema circulatorio consta de:
La sangre: Es un liquido de color rojo, compuesto por plasma y celulas sanguineas.
El plasma constituye la parte liquida de la sangre. En el se encuentra disueltas muchas sustancias como carbohidratos, proteínas, vitaminas, hormonas y lípidos.

Las células sanguíneas se encuentran suspendidas en el plasma y son de tres ti pos:

                                                                                                 
Glóbulos rojos son células sin núcleo que contienen una sustancia llamada hemoglobina, la cual le da el color rojo a la sangre. La hemoglobina es la encargada de transportar el oxígeno de los pulmones a las células y el dióxido de carbono en el sentido contrario.
Glóbulos blancos son de tamaño mucho mayor que los glóbulos rojos, poseen núcleo y su función consiste en defender el organismo contra el ataque de microorganismos dañinos.
Plaquetas son las células mas pequeñas de la sangre. Su función es la coagulación. es decir, taponan las heridas para que la persona no se desangre.Las plaquetas, los glóbulos blancos y los glóbulos blancos se forman en la médula de los huesos.

Las venas son vasos sanguíneos que transportan sangre con dióxido de carbono y productos de desecho, desde los tejidos hacia el corazón. Las paredes de las venas son mas delgadas y menos elásticas que de las arterias.
Las arterias son vasos sanguíneos que llevan la sangre rica en oxígeno y nutrientes desde el corazón hasta cada órgano del cuerpo. Las arterias son elásticas y se pueden contraer.

Los capilares son vasos microscópicos cuyas paredes apenas tienen una célula de espesor. Se encuentra cerca de casi todas las células del cuerpo. Su funciòn principal es permitir el intercambio de nutrientes y desechos entre la sangre y las células de los tejidos.

El corazón es la bomba muscular que impulsa la sangre por todo el cuerpo y posee un tabique que los separa en dos mitades; de esta manera, la sangre que fluye por el lado izquierdo no se mezcla con la que fluye con el lado derecho del corazón. Cada lado está dividido en dos cámaras. Las cámaras superiores se llaman aurículas y las inferiores, ventrículos.

Entre las aurículas y los ventrículos existen unas válvulas que controlan la entrada de la sangre e impiden que ésta se devuelvan. Esto asegura que la circulación se realice siempre en el mismo sentido.
Las venas recogen la sangre con dióxido de carbono de todos los órganos y la llevan al corazón. El corazón la bombea a los pulmones y allí se oxigena y elimina el dióxido de carbono. De los pulmones la sangre retorna al corazón cargada de oxígeno para ser impulsada a través de las arterias a todos los órganos del cuerpo.

Title: Curing A Cold

Title:     Curing A ColdAuthor: Mark Twain [More Titles by Twain]

It is a good thing, perhaps, to write for the amusement of the public, but it is a far higher and nobler thing to write for their instruction, their profit, their actual and tangible benefit. The latter is the sole object of this article. If it prove the means of restoring to health one solitary sufferer among my race, of lighting up once more the fire of hope and joy in his faded eyes, or bringing back to his dead heart again the quick, generous impulses of other days, I shall be amply rewarded for my labor; my soul will be permeated with the sacred delight a Christian. feels when he has done a good, unselfish deed.

Having led a pure and blameless life, I am justified in believing that no man who knows me will reject the suggestions I am about to make, out of fear that I am trying to deceive him. Let the public do itself the honor to read my experience in doctoring a cold, as herein set forth, and then follow in my footsteps.

When the White House was burned in Virginia City, I lost my home, my happiness, my constitution, and my trunk. The loss of the two first named articles was a matter of no great consequence, since a home without a mother, or a sister, or a distant young female relative in it, to remind you, by putting your soiled linen out of sight and taking your boots down off the mantelpiece, that there are those who think about you and care for you, is easily obtained. And I cared nothing for the loss of my happiness, because, not being a poet, it could not be possible that melancholy would abide with me long. But to lose a good constitution and a better trunk were serious misfortunes. On the day of the fire my constitution succumbed to a severe cold, caused by undue exertion in getting ready to do something. I suffered to no purpose, too, because the plan I was figuring at for the extinguishing of the fire was so elaborate that I never got it completed until the middle of the following week.

The first time I began to sneeze, a friend told me to go and bathe my feet in hot water and go to bed. I did so. Shortly afterward, another friend advised me to get up and take a cold shower-bath. I did that also. Within the hour, another friend assured me that it was policy to "feed a cold and starve a fever." I had both. So I thought it best to fill myself up for the cold, and then keep dark and let the fever starve awhile.

In a case of, this kind, I seldom do things by halves; I ate pretty heartily; I conferred my custom upon a stranger who had just opened his restaurant that morning; he waited near me in respectful silence until I had finished feeding my cold, when he inquired if the people about Virginia City were much afflicted with colds? I told him I thought they were. He then went out and took in his sign.

I started down toward the office, and on the way encountered another bosom friend, who told me that a quart of salt-water, taken warm, would come as near curing a cold as anything in the world. I hardly thought I had room for it, but I tried it anyhow. The result was surprising. I believed I had thrown up my immortal soul.

Now, as I am giving my experience only for the benefit of those who are troubled with the distemper I am writing about, I feel that they will see the propriety of my cautioning them against following such portions of it as proved inefficient with me, and acting upon this conviction, I warn them against warm salt-water. It may be a good enough remedy, but I think it is too severe. If I had another cold in the head, and there were no course left me but to take either an earthquake or a quart of warm saltwater, I would take my chances on the earthquake.

After the storm which had been raging in my stomach had subsided, and no more good Samaritans happening along, I went on borrowing handkerchiefs again and blowing them to atoms, as had been my custom in the early stages of my cold, until I came across a lady who had just arrived from over the plains, and who said she had lived in a part of the country where doctors were scarce, and had from necessity acquired considerable skill in the treatment of simple "family complaints." I knew she must have had much experience, for she appeared to be a hundred and fifty years old.

She mixed a decoction composed of molasses, aquafortis, turpentine, and various other drugs, and instructed me to take a wine-glass full of it every fifteen minutes. I never took but one dose; that was enough; it robbed me of all moral principle, and awoke every unworthy impulse of my nature. Under its malign influence my brain conceived miracles of meanness, but my hands were too feeble to execute them; at that time, had it not been that my strength had surrendered to a succession of assaults from infallible remedies for my cold, I am satisfied that I would have tried to rob the graveyard. Like most other people, I often feel mean, and act accordingly; but until I took that medicine I had never reveled in such supernatural depravity, and felt proud of it. At the end of two days I was ready to go to doctoring again. I took a few more unfailing remedies, and finally drove my cold from my head to my lungs.

I got to coughing incessantly, and my voice fell below zero; I conversed in a thundering bass, two octaves below my natural tone; I could only compass my regular nightly repose by coughing myself down to a state of utter exhaustion, and then the moment I began to talk in my sleep, my discordant voice woke me up again.

My case grew more and more serious every day. A Plain gin was recommended; I took it. Then gin and molasses; I took that also. Then gin and onions; I added the onions, and took all three. I detected no particular result, however, except that I had acquired a breath like a buzzard's.

I found I had to travel for my health. I went to Lake Bigler with my reportorial comrade, Wilson. It is gratifying to me to reflect that we traveled in considerable style; we went in the Pioneer coach, and my friend took all his baggage with him, consisting of two excellent silk handkerchiefs and a daguerreotype of his grandmother. We sailed and hunted and fished and danced all day, and I doctored my cough all night. By managing in this way, I made out to improve every hour in the twenty- four. But my disease continued to grow worse.

A sheet-bath was recommended. I had never refused a remedy yet, and it seemed poor policy to commence then; therefore I determined to take a sheet-bath, notwithstanding I had no idea what sort of arrangement it was. It was administered at midnight, and the weather was very frosty. My breast and back were bared, and a sheet (there appeared to be a thousand yards of it) soaked in ice-water, was wound around me until I resembled a swab for a Columbiad.

It is a cruel expedient. When the chilly rag touches one's warm flesh, it makes him start with sudden violence, and gasp for breath just as men do in the death-agony. It froze the marrow in my bones and stopped the beating of my heart. I thought my time had come.

Young Wilson said the circumstance reminded him of an anecdote about a negro who was being baptized, and who slipped from the parson's grasp, and came near being drowned. He floundered around, though, and finally rose up out of the water considerably strangled and furiously angry, and started ashore at once, spouting water like a whale, and remarking, with great asperity, that "one o' dese days some gen'l'man's nigger gwyne to get killed wid jis' such damn foolishness as dis!"

Never take a sheet-bath-never. Next to meeting a lady acquaintance who, for reasons best known to herself, don't see you when she looks at you, and don't know you when she does see you, it is the most uncomfortable thing in the world.

But, as I was saying, when the sheet-bath failed to cure my cough, a lady friend recommended the application of a mustard plaster to my breast. I believe that would have cured me effectually, if it had not been for young Wilson. When I went to bed, I put my mustard plaster-- which was a very gorgeous one, eighteen inches square--where I could reach it when I was ready for it. But young Wilson got hungry in the night, and here is food for the imagination.

After sojourning a week at Lake Bigler, I went to Steamboat Springs, and, besides the steam-baths, I took a lot of the vilest medicines that were ever concocted. They would have cured me, but I had to go back to Virginia City, where, notwithstanding the variety of new remedies I absorbed every day, I managed to aggravate my disease by carelessness and undue exposure.

I finally concluded to visit San Francisco, and the, first day I got there a lady at the hotel told me to drink a quart of whisky every twenty-four hours, and a friend up-town recommended precisely the same course. Each advised me to take a quart; that made half a gallon. I did it, and still live.

Now, with the kindest motives in the world, I offer for the consideration of consumptive patients the variegated course of treatment I have lately gone through. Let them try it; if it don't cure, it can't more than kill them.

-THE END-
Clemens] Mark Twain's short story: Curing A Cold

LA LECTURA Y LAS MATEMATICAS

La lectura y las matemáticas

Mucha gente tiende a ver las matemáticas como opuestas al lenguaje y la literatura, pero en realidad hay mucha interrelación entre ellas. De hecho, trabajan de la mano: las matemáticas ayudan a los niños a construir habilidades lingüísticas, y el lenguaje sustenta el aprendizaje de las matemáticas. Ambos construyen habilidades de pensamiento. Las últimas investigaciones revelan que la magnitud en que un niño es expuesto a conceptos matemáticos durante sus primeros años de vida predice qué tan bueno será en matemáticas durante la primaria. Incluso más sorprendente, también predice qué tan bueno será en la lectura. Para ir más lejos, los niños que pueden contar una historia conocida o inventar una nueva cuando están pequeños, tienden a ser mejores en matemáticas. La buena noticia es que esta relación números-letras puede desarrollarse simultáneamente.

Todo a nuestro alrededor puede entenderse mejor gracias a las matemáticas; puede ayudar a los niños a encontrar más sentido al mundo. Ayudando a nuestros niños a ver las conexiones entre su mundo y las matemáticas, estamos enriqueciendo su total aprendizaje y desarrollo.

Todo a nuestro alrededor puede entenderse mejor gracias a las matemáticas; puede ayudar a los niños a encontrar más sentido al mundo. Ayudando a nuestros niños a ver las conexiones entre su mundo y las matemáticas, estamos enriqueciendo su total aprendizaje y desarrollo.

El lenguaje de las matemáticas

Las matemáticas requieren que la gente piense sobre lo que significan las palabras. Cuando hablamos sobre "matemáticas", tenemos que ser precisos en nuestro pensamiento y lenguaje. Tenemos que explicar nuestro razonamiento. Pensemos en un rectángulo. Tiene cuatro lados y cuatro ángulos, pero sólo porque la mayoría de las formas que llamamos rectángulos tienen dos lados largos y dos cortos, eso no significa que todas las figuras con dos lados largos y dos cortos más cuatro ángulos sean rectángulos. Las matemáticas constituyen un contexto ideal para discutir el concepto exacto de las palabras –y para demostrar que las palabras tienen diferentes significados. Por ejemplo, algunas veces la gente dice "derecho" por decir horizontal o vertical, como en el caso del cuadro colgado en la pared: "está derecho o ladeado". Otras veces, derecho significa no curvo, en el caso de una línea recta en una figura.

Aprender cómo usar el lenguaje para expresar pensamientos matemáticos beneficia a los niños en muchas maneras que podrían no ser inmediatamente evidentes. Si el niño no entiende por qué el carrito no baja por la rampa, por ejemplo. Usando conceptos matemáticos, tales como altura o ángulo (qué tan inclinada es la rampa), puede ayudarle a ver la situación de una manera nueva. Cuando dos niños están tratando de encontrar una forma de compartir un juguete, las matemáticas pueden ayudar: sugerirle usar un cronómetro por un tiempo determinado para cada niño a su turno. Compartir juguetes puede involucrar "negociar" un número de bloques para cada uno.

Las matemáticas conectan con todo. Saltar, marchar, subir escaleras, por ejemplo, son formas de contar. Cuando los niños reconocen, dibujan, juegan y combinan figuras no están sólo aprendiendo geometría, están también experimentando con arte visual, arquitectura y ciencia. Cuando los niños escuchan una historia, están creando imágenes mentales de las escenas y de los personajes, usando frases como: "ojos tan grandes como platos", o el duende se esconde "debajo del puente".

Estas descripciones son ideas "espaciales", que literalmente dan forma a nuestra visión del mundo. De hecho, usamos conceptos espaciales en casi todos nuestros pensamientos. Cuando sean grandes, los niños usarán ideas espaciales para pensar sobre redes de comunicación, la estructura de las moléculas, geografía y muchas otras cosas. Pero el pensamiento espacial es también básico para un temprano desarrollo cognoscitivo de los niños. De hecho, las investigaciones demuestran que cuando los niños pequeños trabajan con figuras y las combinan de diferentes formas, están mejorando sus logros matemáticos para dos o tres años más tarde –además de mejorar su escritura e incluso su IQ--.

HISTORIA DE UN NIÑO MALO

Existía en otro tiempo un niño malo, que se llamaba Jim. Ya sé que hiciéramos una escrupulosa rebusca en los libros de lectura de las escuela dominicales, encontraríamos que casi todos que todos los niños malos se llaman Jaime. Es un hecho extraño, pero es cierto (…) Nuestro niño malo se llamaba Jim. Y su mamá no padecía de tisis ni cosa por el estilo. Antes, por el contario, era corpulenta y no tenia pesar ni daño que la atormentase. Otro rasgo distintivo de tal mamá era que se le daba una higa de lo que al muchacho pudiera ocurrirle, y en más de una ocasión se le oyó decir que si el chico se rompía la cabeza o se quebraba una pierna, maldita la cosa que se perdía. Lo mandaba a acostar, acompañando la orden con un cogotazo, y no hay noticia de que le besara ni una sola vez, ni que se tomara el trabajo de pedir a Dios que concediera buena noche al chiquitín.

Un día, el niño malo robo la llave de la despensa, se entró en ella bonitamente, se comió una ración más que mediana de confitura y para que su madre no descubriera la travesura, echó brea en el pote que había vaciado (…). Y en aquel momento no le cometió ningún terrible sentimiento de pesar. No oyó ninguna voz interior que le dijera: “¿has hecho bien en desobedeciendo a tu mamá? ¿Dónde van los niños malos que se comen glotonamente la confitura materna?”. (…) No. Eso es lo que hacen los otros niños traviesos de que hablan los libros de las escuelas.

Pero cosa extraña, con Jim pasaron las cosas de otra manera. Se comió la confitura y no se le ocurrió más que decir que estaba buena. Echó la brea en el pote, y la travesura le hizo mucha gracia tanta gracia, que reía a carcajadas pensando en la cara que pondrían sus papás cuando fueran victimas del criminal engaño infantil.

Cuando se descubrió la endiablada travesura, Jim juró y perjuró que no era suya aquel cambio; la mamá le pego con severidad y el chico lloró como una magdalena, y berreó como un becerro más de una hora. Como se ve en nuestra historia, no hay punto alguno de contacto con los cuentos de los niños malos de los libros infantiles.

(…) Otra vez birló mañosamente el cortaplumas al maestro de escuela, y para que no lo castigaran escondió el objeto en la gorra de Jorge Wilson, hijo de la pobre viuda de Wilson, el niño aplicado y bueno del lugar, un buen muchacho que obedecía siempre a su madre y que no mentía jamás.

Cuando cayó el cortaplumas de la gorra del buen Jorge, y este bajó la vista sorprendido y acosado al propio tiempo que el maestro descargaba la palmeta sobre las temblorosas espaldas del inocente, no se vio aparecer un inesperado juez de paz de noble actitud y peluca blanca que detuviera al iracundo maestro, diciéndole: “No castigue usted a ese generoso y aplicado niño. He aquí al culpable. Yo pasaba casualmente por la puerta, y por feliz coincidencia lo he visto todo”. (…) No. Esto hubiera sucedido así en los libros infantiles, pero no tratándose de Jim. No se presentó, ya lo he dicho ningún juez integrante y entremetido, para que lo echara a perder todo. Y el estudiante modelo, Jorge, fue vapuleado, y Jim tuvo una gran satisfacción, pues como era un niño malo, detestaba a los niños virtuosos.

Un domingo, aunque Jim fue a dar un paseo en bote, le ocurrió una cosa muy extraña. No se ahogó. Otra vez fue sorprendido por una tempestad, un día que estaba pescando y no le mato un rayo. ¡Es verdaderamente asombroso! Podéis consultar uno a uno todos los libros de lectura de las escuelas y no encontrareis cosa semejante.

Allí veréis que los niños malos que pasean en barco los domingos se ahogan irremisiblemente, y que todos los niños traviesos a quienes sorprende una tempestad cuando están pescando en domingo mueren infaliblemente carbonizados por un rayo. Todos los botes que llevan niños malos en domingo zozobran sin remisión. Y la tempestad estalla con furia en cuanto a un niño malo se pone a pescar en dicho día. El por qué y cómo se libró Jim de tan grave daño, es un misterio que no ha estado en mí descifrar. Indudablemente había algo mágico y oculto en la vida de Jim. De todo salía con bien (…). En la actualidad es el más temible bribón de su aldea natal: todos lo respetan, y forma parte de la intendencia.

Mark Twain, en Humoristas del mundo, Medellín, Colombia. Edilux Ediciones, 1993.E