By ENRIQUE FUERI, 10/10/2008, from elmundo.es
Se pasea por la sala en la que va a hacer la demostración como si la cosa no fuera con él. Callejea entre las sillas de su futuro auditorio con los despreocupados contoneos de un niño de su edad (cumplirá 8 años en tres días). Minutos después arrancará mares de susurros y resoplidos. Nakul se cepilla complejas operaciones matemáticas con la tranquilidad con la que otro crío de su edad se hurga en las narices. Su público, una treintena de madres ya deseosas de que sus vástagos sigan los pasos del joven hindú.
Todos los ejercicios son sometidos a comprobación por el público. Muchas de las operaciones cuentan con cifras elegidas al azar por los asistentes a la demostración, lo cual confiere más credibilidad si cabe al método de aprendizaje que Deepak y Neeraj (padre de Nakul) promocionan en el King College de Portals Nous. Vienen expresamente de la India para dar a conocer la técnica UCMAS, basada en la representación mental de la aritmética para desarrollar el intelecto de sus estudiantes.
Primero sumas, luego multiplicaciones y divisiones. Dos dígitos, tres, cuatro… Deepak pregunta por tres números de teléfono a las asistentes que une en una cifra de 27 dígitos en la pizarra. Nakul la multiplica por cinco en segundos. “This is no magic”, repite su padre a la masa bilingüe que cada vez murmura más alto. El sistema, mantiene, lo es todo. “No son sólo números”, insiste Deepak. “Trabajamos con las imágenes y les enseñamos a concentrarse; con este sistema sacan buenas notas en todas las asignaturas”. Nakul, según asegura, ni siquiera es el alumno estrella de su clase. Cualquiera de estos mocosos podría hacernos palidecer de vergüenza aún blandiendo una calculadora en nuestras manos.
La única ayuda de la que precisa el joven en los comienzos del curso (dura dos años, dos horas semanales) es un pequeño ábaco, un instrumento milenario inventando en la China para resolver sencillas operaciones matemáticas. Acompaña a los estudiantes durante sus primeras clases. Más tarde lo abandonan pero siempre que realicen algún cálculo lo harán mediante una representación mental de este instrumento. Memoria fotográfica.
Éxito de la presentación
Las aplicaciones desbordan las abstracciones matemáticas. Nakul toca el órgano desde hace dos meses con la precisión de un alumno experimentado. Su padre cuenta como en sólo unos días aquí, ya ha aprendido a contar en castellano. Y el niño lo demuestra ejecutando las operaciones oralmente.
Lleva año y medio con el programa y le restan seis meses para completarlo. Una vez finalizado, no es necesario preocuparse por refrescar periódicamente los conocimientos adquiridos. “Es como nadar o ir en bici”, promete Deepak. Suficiente para enfervorizar a las gradas. El escépticismo con el que llegaron a la sala ha dejado paso a una desbordante ilusión por el futuro de la prole. Esto no huele a crecepelo barato. Al acabar la demostración, las madres se apretujan para dejar sus firmas como interesadas, imaginando ya a sus retoños diseñando puentes o programando ordenadores.
El éxito suele ser una constante en sus presentaciones, asevera Deepak. Nakul, por su parte parece contento por perder un par de días de clase ¿Y de mayor qué? Lo tiene claro: científico de la NASA.
1) Do you use any mental strategy when doing mental math?
2) Being good at mental math can help being good at other subjects? Why?
a) I think that everybody have a method but we do it unconsciously so I don’t now what is my method but for example whem I was a child younger than now I use the fingers to count and know I operate with sums and subtractions from the tens for example 20-6=14, for this I don’t calculate like I express as I know that 10-6=4, I change. You could think that it’s a stupid method and it could be but for me is better. As I was saying in the last comment new the problems has got a lot of solutions ones are large than the other or in the other way.
b)I think that being good at mental math It’s ggod for all the subjects because a part from do exercise in mathematical part you are doing exercise also in the MENTAL part so you have got more agility to thing and to get conclusions and to get a solution faster, I think that there is a very big difference with persons that practice mental math and persons who don’t practice mental math and it’s not only for other subjects, also in your daily life too You get the solutions faster and you have the ideas more organise and it’s useful for every thing tou have in the brain, all the knowledge about all the life. But that’s only my phylosophical opinion, as Carlota says.
Thanks, see you soon!
a) Use a method to calculate something, it depends on the type of operation. When you are multipling, you will use other method that when you are mavy dividing. And it’s logical that the method you use in something, change with the time. We don’t use the same methods as before, when we were studing at primari school. But reviewing to the question… Well, I think I have answer it. Depending on the operation I use different methods. But I think it’s don’t necessari to explain, because I usually use the simply methods, the methods all the people usually use.
b) To answer this, I’m going to try to explain the same as Mariona in other words, because I’m completle agree with her. Being good at mental math it helps you a lot when you solve problems with more agility. Also, I have to say that the operations we do mentally, are those that are usually easy. We don’t use mental maths in long and difficult operations. But this type of ” strategy ” ( We can say it like that ), is losing it’s utility. Now there is a machine called calculator that help us a lot doing operations. But with it, some people do with it, all the operations, included the more easiest. It’s for that, that mental math is losing his utility, and that calculator is occupying it.
1) Do you use any mental strategy when doing mental math?
Well I think that yes I use one but at the moment I don’t know which. I mean, when I’m doing mental math, I usually use things that I know from primary for example that 2+2=4. I mean, of course not all the operations will be as easy as this, but some times the most difficult opperations can be solved with the easyest way, and, maybe, applying some properties. Well I don’t know if you understanded it, because it’s a bit difficult to explain.
2) Being good at mental math can help being good at other subjects? Why?
Yes, of curse. I think that mental maths keep your brain active, because you use it and you connect the things that you already know with the new things. For example when in phisics & chemistry the teacher teachaed us the cientific notation, it was easy, because I knew that 10 to the power of any number was adding (or subtracting) zeros. Also I’m agree with Mariona as I do with Joan. He said that nowadays, people use callculator to do the easiest operations in the world, and I’m agree with him because I have seen people using the calculator to do 3 times 9!!
Another thing I would like to comment of the new is that it says:<>. I think that we have to refresh our memory because, some summers, if i didn’t practiced, I remembered that I forget the multiplication table, so I think we NEED to refresh our memories.
1) Well, yeah, acually I do have a strategy: using calculator! Hehe, just kidding. I sometimes calculate with the basic strategies I learnt when I was a child. For example, if we have 40-9 which equals 31, I have something I use when I subtract anything to nine. I just subtract ten, and then I add one. Using this method, the operation above would be: 40-10=30+1=31. Maybe I complicate myself a bit, but I’m used to do this. In my oppinion it’s easier having mental methods than counting with fingers one by one (although I recognize that sometimes I do it, and sure other people do it too!). I also think that our generation is getting too used to new technologies, and by that I mean CALCULATOR.
2) Of course it’s also useful! If not, how are we supposed to do (as Noelia says) physics ans chemistry? And specially the exams we do not have the right do use calculator (right, Carlota?).
Another point that I would like to add, is that I completely agree with Noelia (again) in the last part, in which she says we have to refresh our memory in the summers, and I’m telling this FOR OWN EXPERIENCE. For example, this past summer, I hardly ever didn’t practice math (please Carlota, don’t be offended) and when I went back to school… errr… let’s say that to operate with fractions like 2/3 + 5/12 was more or less a bit (just a tiny tiny bit) complicated, as if to remember how to operate with fractions would take me almost one minute! To do this simple calculation! O.o (By the way, the result is 13/12)
1) Do you use any mental strategy when doing mental math?
Of course all of us have a mental strategy, but we do it without thinking, what I am saying is that we do it unconsciously (like Mariona says). In primary and secundary too, all of us, I supose, that sometimes we applied a method that we use the hands. This was the first method that in primary the teachers teach to us, and of course during this live we have used it. I remember one method that I some times use that is: when I have to add for example 7+5 I pass one of the number seven to the number five, and I have 6+6, so now it’s more easy to do, and the result is 6 plus 6 equals 12 or multiply 6 times 2, that the result is the same. There is a lot of methods in teh world but I think that every human use his method.
2) Being good at mental math can help being good at other subjects? Why?
Yes, being good at mental math can help being good at other subjects, because if you have an exam of one hour and the exam is about operations, you have to be quickly doing operations, because if you in one operation spend the half of the hour, you only will do two operations. Yes, we have the fantastic CALCULATOR (like Cristina says) but in some exams we can’t use it. For example in exams of operations, it’s stupid use a calulator becasue if you use a calculator why you are doing an exam of operations.
So the conclusion is that if someone aren’t good at mental math,starts to be good.
One more thing, I completely agree with Cristina and Noelia about the summers practice, because,I have to say that my first year here, in the CLIL project, the last summer I didn’t do practise, but this summer I have done practise and I have start better this year thanks the practise of the summer.
1) Do you use any mental strategy when doing mental math?
Yes, I do. One of the methods that I use more for multiply is this: rounding to the tenth, for example: 24×7= (20×7)+(4×7)=140+28= 168. Of course there are a lot of other methods, but one thing that we always have to do is simplify the most as you can, but knowing why you do it like that and the steps that are between.
In my opinion there are better ways for solving operations. And with the age This methods go being better than the others. I spouse that’s because you practice more with them and you see all the thing by a different way, you are a mature person.
2) Being good at mental math can help being good at other subjects? Why?
Yes! I’m completely agreed with my partners about that. If you are good at mental math you are also good in other subjects because you know how to be concentrate in something, you only see or listen what you want, you can pay a lot of attention on something, It’s incredible. That’s also useful in the daily life; you can solve the usual problems more quickly and by an easier way, with maths! You know that when we where little we always ask to people: What is maths for? Are they useful? What will we do with them in our work?
And it can be amazing how them can affect in our work.
For last I would like to say that you forget something if you haven’t got anything that remember it. For example you memories, do you know that you have all you memories in your brain but you can’t remember some of them if you haven’t got something that remember its? Moreover, sometimes your brain borrows some memories of your brain because they are painful for you. It’s a method of defence. With maths is the same, if you don’ practise them every day you forget it. But it’s true that are thing that are unforgettable like sum 2+2.
1) I think that all people that do maths use a method to do things more easy, for example for multiply, for sum … Like Mikel says when we are little the teachers teach to us that we had to use the fingers to sum, and now there are people that use it too. But I think that use this method is very slow because you have to count each finger, and if you had to do a very large sum you had a very big problem. For example for sum I use one method that it’s about that for example if you have 7+8, you have to transfors it to a number plus ten, in this case 10+5, and if the sum is larger for example 342+435 I sum 35+42 and after 300+400, and after I sum all, and I think that like this is easier. With this two methods I think that it’s easier do sums for me. But I think that every person use the methods that he invents for he, and the ethod that are better for he.
2)Yes of course, if you are good at mental maths you are good at other things, not only in exams of maths, in exams of other subjects too, because in exams of technology, phisics, geography… it can ask to you that calculate something, for example in geography they can ask to you that calculate the people that lives in one country and if you can do it with mental maths you do it quickler, because in exams of geography you can’t use the calculator. I think that if you don’t practice mental maths you are not good at this. For example in primary when we do exams of mental maths in two minutes I’m good at it, because we practised every week, but now I didn’t practise and it’s a little more difficult, because I hardly ever practise mental maths, because now we have the calculator, and then when we arrived to maths exams and we can’t use the calculator we have a problem, because we are slower to do operations. In CONCLUSION, Mental Maths are important for us, for do exams and other lot of things.
1.Well, I think everybody use strategies, for example rounding number, if you have 31 -10, as you know that 30-10=20 so 20+1=21. Or when I was younger that I used fingers to do sum, or when the teacher was doing an exam of oral mental mayhs I imagined my hands with the number of fingers or the number of pencils. For example; 7+6=13 I imagined 7 fingers and an other person with six, and I calgulate, or I imagined 7 blue pens and 6 green pens and I sumed them.
and this strategies were useful I mean, you use this mentally “sense voler” ‘cause you know it sinse you were in primary school. But well, I think that nowadays our strategie is called calculator.
2) I think that they’re useful in scientific subjects like chemistry, tecnology, fisic,… Because, How can I use mental maths in Catalan, English, French or Spanish? In chemistry yes, ‘cause you need to do lots of operations, and if everytime you have one you have to ask for a calculator, you can’t finish at time. Having a good mental maths level can help you a lot.
And I’ve seen that Noelia said that we need to refresh our mental maths, and I agree, ‘cause in primary we couldn’t use calculator, and we had a good math’s level, but at secondary school using calculators, we foregt all we had learn. I think I don’t use mental maths since first of ESO.
1)I think that all the people has a method to do mental math and there are a lots of methods.
I have to say that I count with the fingers yet, but during the years I learn a lot of methods different to do this. The method that I use more is rounding the number to the tenth like 52+42=94 to do this i calculate first 50+40 and then I calculate 2+2, I think that this method is the easiest. But, I remember a method that we learn in primary, it’s a little silly but I liked it when I learn it. The method is like all of we know take 5 pencils and 10 rubbers and we sum it. This method has an inconvenient that when you want to sum 365+142 it’s so difficult to take 365 pencils… but in primary we only do easy operations this method was good.
2)Yes, I think that being good at mental math can help you in other subjects. For example in phisical and quimical you has to do a lot of operations too, so if you do quickly the operations and the problems is easier for you to do better the problems. In tecnology it can help too because in some parts you have to calculate a lot of measures and it’s better that you calculate ir mental that not if you has to take the calculator and waste your time. But in Catalan and in general in all the language subjects it isn’t help because you don’t need to calculate anything and you don’t need maths. Maybe mental maths can help you in the speed that you do the things but it isn’t important in some subjects. I think that in P.E. help being good at mental math because, well I remember that this year we did a game that you has to calculate some operations quickly and went to the correct side depending of the result and in this class we use mental math a lot but not in all the subjects.
1) I don’t think that I have a method that I always do when I do mental math but when I was a child (and sometimes now I do too) I sum and substract with the fingers. It isn’t a bad method, but it’s a little bit slow to make mental math. Also I round the numbers (like Clàudia Maravalle says).
There are a lot of strategies but I think that the esaiest way to calculate is using the calculator.
2) Yes, of course. If you are good at mental math you are good at some subjects like chemistry, fisics…. You have more agility to calculate problems in chemistry or to calculate a scale in tecnology. Also you are more concetraited in class. But now, as some people said, we have the calculator that helps us to calculate more quickly and it’s more easier and because of that I think we are forget to calculate metaly. And sometimes we can’t use in the exams. And, as Júlia say, metal math help you in the life, for example when you go to the backery to buy the bread and the saleswoman give to you the change, you use mantal math to calculate if she gives to you the correct change.
So, if you are good in mental math can help you a lot in other subjects and also in the real life.
1) I think that I don’t have a “special” method to do mental maths I only try to find the easiest way to sum, divide or multiply numbers. Sometimes I use some of the methos that my partners says before ( Claudia’s Maravalle method for example, is a method that usually use) but sometimes I use others methods that help me to find the result.
2) Of course that mental maths is useful for other subjects that aren’t maths. For example it’s useful for calculate problems or exercises in chemistry, technology … (like Anna Adrover, Claudia Perona… says) I’m agree with them. But I also think that menthal maths is useful when you go to the supermarket and there are a offer ( for example 2X3) it’s useful to know if buy this think is profitable of not and of course you need to think in this mentally you don’t go to the supermarket with a calculator it will be very strange. I would say that I agree with all to my partners opinion.
1) Do you use any mental strategy when doing mental math?
I also think that I don’t have any special method to do mental maths. As most of people have said, a very useful method that we learned in primary is to use the hands (I confess that you also can use it in some difficult operations…) Another method to do mental maths is por example you have 12+12 or maybe another more difficult operation, is more easy to calculate it with a multiplication (in this case 12 x 2).
But also as Joan have said, it depends of the operation that you are doing. Is not the same if you are dividing, multiplying or calculating a square root.
2) Being good at mental math can help being good at other subjects? Why?
I think that being good at mental math can help you being at other subjects. As also a lot of my partners have said, at chemistry, technology and other subjects we also use operations, and it’s always good, that you can think easier and better. For example in exams. I know that in most of the exams we can’t use calculator, and we have to use our brain… But in some cases, you let your brain… well it’s what I think.
Finally I am agree with the Maria Merino’s example of the supermarket but maybe you can also use it when you are shopping. I also think that if you bring a calculator with you while you are shopping, the people can look at you strangely…