I always had trouble handling numbers. It began with the multiplication table. We were forced to memorise the multiplication table. The teacher would ask us to stand up and recite the multiplication table as if it were a poem. How sick a concept.
The next set of major troubles started with the decimal numbers. It was quite an exercise to multiply them. Then came the statistics with lots and lots of number crunching and huge formulae to learn. All of this was done using pen and paper without a calculator.
How relevant is number crunching skills in the days of calculators and super computers. ?
My grand mother had only very little education. But she could do quite a lot of complicated money calculations in her head, stuff that was useful to her in her daily life. Those skills helped her to live without a calculator.
My dad is a mathematics professor. But he doesn’t have the skills of his mother. He needs a pen and paper to do calculations. But he has an Mphil degree that my grand mother didn’t have. I have a B-tech degree and I don’t have the skills of my dad. I need a calculator. I hate using pen and paper for doing calculations. During my high school days, I used to write small C programs to cross check my statistics pen and paper calculations.
I am of the opinion that calculators and computers should be introduced early into the school. As long as the student understands what is happening when he multiplies 2 numbers, then the process of finding that answer is irrelevant. We all know how to use the shift and add mechanism to multiply. But how many of us truly understands how it works ? I know you are thinking… keep thinking.
One counter argument that I used to hear from my friends or people whom I discuss this with is that, the number crunching develops the brain. But scientists say intelligence is not something that can be developed. It has to be there when you are born. But you may develop some skills by practising. But are those skills relevant ?
Mathematics is something beyond number crunching and statistics. But our education system creates a really bad impression about mathematics by forcing the multiplication table and other irrelevant stuff down the child’s throat.
Its like the cat who fell into hot water. Once you are scared of something or had a bad experience with something, its very difficult to get it terms with it.
i dont agree 2 introducing calculaters early @ school.I think the shift nd add mechanism is used for the machine.nd inorder 2 do some natural multiplication we dont need that.
for eg:
Inorder 2 find the number of chairs arranged in rows nd columns in a room.it just need manual calculation.but if the students are given calculaters early at school he will run for a calculater 2 do this simple arithmetic..
Comment by sujith — June 5, 2008 @ 9:49 am
even with the current system, children today arent able to do what we were able to do at that time. yeah we did calculations in the old fashioned way, accept the fact that we have developed unknowingly according to that. our “aptitude” when we see some problem is developed due the early calculations we did.
i have heard that, now at school children do multiplications by repetitive additions. i think it would do nothing but spoil the aptitude of the child. and then you say introduce calculators at primary or upper level of schooling ???
Comment by cyriac — June 5, 2008 @ 11:53 am
@Sujith
If I ask you to multiply 2345 X 5678, Im sure you will run for a pen and paper and will do the shift and add method. So instead of running for a paper, why not run for a calculator.
Before pen and paper become popular, people like my grand mother used to do this in their mind. What if they didnt allow us to use pen and paper ? Our grand parents used their mind, we use pen and paper, let our kids use calculators and computers. Thats how we progress.
Comment by Kenney Jacob — June 5, 2008 @ 12:23 pm
I dnt completely agree to your view point on intelligence. See the follwing article and the links pointed by it:
http://www.m-cc.nl/The_True_Nature_of_Intelligence.pdf
Experiential and Reflective intelligence are developable. And skill in mathematics, in my opinion, fall into the second catagory
Comment by abdunni — June 5, 2008 @ 12:24 pm
@Abdunni
What I was trying to ask is that, is the mental arithmetic skills relevent in the current world. Why dont we learn the theory and then leave the rest to the calculator. Why waste time doing repetitive stuff.
Comment by Kenney Jacob — June 5, 2008 @ 12:29 pm
@Cyriac
I dont think we developed any useful skill because we did some arithmetic problems. Arithmetic problems should be done to help understnd the process, and not to polish the arithmetic skills.
Would anyone suggest that we abolish word processors and use a pen always so that we improve our hand writing.
We are always mislead by the media hype. Do you think Shakuntala devi is a good mathematician ? Is her skill useful for mathematics or its future ? She is just a human calculator.
Typing replaced writing, voice recognition will replace typing, and brain sensors will replace speech. The world is progressing amd every redundant or obselete thing will get replaced.
Doing mental arithmetic is a waste of productive time. It might help you become a shakuntala devi, but her skills are not needed in this world.
How good is a sword, when you have an AK 47.
Comment by Kenney Jacob — June 5, 2008 @ 1:18 pm
I agree with Kenney, whats the point in doing mental arithmetic when u have a calculator in your hand. …just as i feel its unncessary to mug up all the formulae and vomit them during exams. I feel the use of textbooks atleast in subjects such as mathematics should be allowed……..
Comment by sur@j — June 5, 2008 @ 1:54 pm
I think the factor ‘Time’ is getting outdated now, because, all are running because of nothing and for something which actually ends in nothing. I shall explain in detail.
Q: What do you think a lower class kid has got to do after his school? Does he have any in house duty to be done before sleep? Does he have a world to lift before learning to heal?
Does he make money all before he know what its value is?
A: NO!!
If the answer is YES in the present day world, the factor ‘Time’ is as less important as it should not be.
If kids have got no much time at least to learn things using their brains and heart, then what are they supposed to use them for?
Childhood is the bare base, if you don’t learn to stand up and walk, it is natural and proved, he/she will never run to victory. Perhaps he/she may run, but will keep running until he/she realize the distance covered is ZERO inches , not a step to say a FOOT. What you loose will be a lifetime.
Using calculators in the schools are like sleeping the whole day doing no job. A single day use of calculator by a small student decreases his/her mental ability by 4 times whereas the other way round increases the ability by 2 times.
For Kenney G’s comment:
A bare hand is worth a Sword or an AK 47 most of the times, provided his/her calculations are confident enough. Calculator give confidence?
Comment by SAF — June 5, 2008 @ 3:41 pm
@SAF
Given a problem to a student, its his ability to find the solution method that is important, rather than the minute calculation details.
Why do we use tools ? Why do we use a ruler to draw a straight line rather than asking the student to learn to steady his hand.
As we progress we find tools/processes to simplyfy the boring and often repetitive work. Human intelligence and creativity should be focused to solving larger problems at hand rather than trying to be a super computer.
Chinease may know 100 different Kunfu styles. But the american has the atom bomb with him. Finally who will win ?
Comment by Kenney Jacob — June 5, 2008 @ 5:05 pm
Hahaha… I am the answer i am the answer.
Q1: Why do we use tools?
A1: Because we are Lazy enough to realize our own abilities.
Q2: Why do we use a ruler to draw a straight line rather than asking the student to learn to steady his hand?
A2: Because he/she think the world is going to end in few seconds. One who says ‘I have no time’ is the worst lier and a dump too.
Q3: Human intelligence and creativity should be focused to solving larger problems at hand rather than trying to be a super computer.
A3: Who is going to make a larger problem from scratch? Actually how did larger problems start and how did people learned to solve? Should all people forget its cause and treatment and go for the larger problems fight? No one is gonna move an inch ahead. One day users of calculator will reach the limit, remember that. Its a machine, not a human. Dont kill human brains for a calculator ease.
Q4:Chinease may know 100 different Kunfu styles. But the american has the atom bomb with him. Finally who will win ?
A4: Did you mean a war or simply butchering? If its a war be brave to face it, not like atom bombs. If you meant butchering, american is simply setting a new pit hole for their own destruction. So finally who looses?
Question for KenneyG
1) Why do you read this full article? Can your calculator do your work?
2) How sure are you with the calculator outputs? You cross check with your C programs? Or you use another calculator for this?
3) How well you agree the fact that, a human brain calculation will always beat the speed and perfection with a calculator calculation?
4) If you don’t agree the above question, calculate 1×1 using your brain and using a calculator. Who wins?? This is a simile for your china usa question.
Comment by SAF — June 5, 2008 @ 5:26 pm
Now you sound like a philosopher.
The answers to the questions you asked.
1. When I become rich enough to afford a PA, I wont be reading this. Instead Ill be getting a summary from him.
2. I trust the computer more than I trust me, when it comes to computation.
3. I wont agreee. Human brain cant beat the speed of a calculator when it comes to number crunching.
4. Thats sooooo stupid. You are arguing for argument sake.
Comment by Kenney Jacob — June 5, 2008 @ 5:38 pm
1) Secondary summaries are as dangerous as a man with partial knowledge.
2) All up to you (person).
3) Argue this after testing.
4) Hahaha… 1×1 =1, you did’nt have to seek your calculator buddy??
Comment by SAF — June 5, 2008 @ 5:44 pm
Well Guys Interesting…..
I can see kenney on one end saying that we should ban the Ice with the Ice Box cause Refrigerators are here and on the other side SAF saying that we need to keep the Ice Box & the ice….I dont want to get into their fight…
The primary reason why man invented tools was to improve on quality and productivity. Technology was built to improve the lives of human beings – not to replace human beings with Machines.
Coming back to the calculator – a calculator should be only used in a case where the the person actually knows what he is doing and how it is actually done by hand. It does not make sense for some one to learn how to multiply 23582784596 x 3859208757 – using a pen and a paper. But at the same time it does not make sense to go and pick up a calculator to multiply 10 by 2…
I am of the opinion that basic maths should be thought without the help of any electronic devices. Once the student throughly understands the concept then he can use all the tools available to try and solve the mystery of life…
Nothing can replace the human intelligence and instincts and sometimes our stupidity also…
Comment by JMJ — June 5, 2008 @ 6:52 pm
I second Jyothi’s opinion. And to multiply the number he has given in the comment, I would use logarithm he heeeeee……..
I miss mathematics now…
Comment by Derick — June 8, 2008 @ 6:26 pm
Doing maths for fun is different from learning maths for a purpose. I miss my c programming days. I miss my chemistry labs. But those were fun activities. Now im doing serious stuff and output is more important that improving my coding skills or enjoying chemistry.
Comment by Kenney Jacob — June 15, 2008 @ 10:23 am
Calculators are one of the three main reasons American students are so dumb. High profile testing is the another reason. The article by this user states that it’s okay to use a calculator “As long as the student understands what is happening when he multiplies 2 numbers, then the process of finding that answer is irrelevant” (sic).
1. How can a student understand? The process of finding the answer is what demonstrates understanding!
2. Students of Mathematics should learn mathematics, not statistics. Statistics is a science in its own right. It is laughable that math teachers are expected to teach statistics – most are not remotely qualified to teach even the most basic concepts. Statistics requires not only intelligence but maturity. This means that students need to first reach a stage where they are proficient in mathematics and then begin to explore the deep concepts of statistics. The idiots who run the math curriculum in the United States have done tragic damage to many a student.
Finally, unless control is restored to the teacher, the American system of education will remain broken beyond repair.
Comment by John Gabriel — February 5, 2009 @ 11:02 pm
American students are dump ?
I thought America is still the most scientifically advanced country.
In India we have been learning this BS for quite some time. We boast ours is the most old and reputed system of education, but we are not going anywhere with it.
Comment by Kenney Jacob — February 6, 2009 @ 4:10 am
America is advanced.
However, few, very fiew kids go into the field of science or tech. Of course, the universities are doing ok, because they tend to attract the best talent from across the world. And many of them let students do a masters for almost no expense if they are qualified. For PHDs, most are free.
When I did my masters, in my whole department, there was only one (out of 100?) American (read white) kid doing Masters/PHD. He used to feel like a minority. Most of the PHD students came from China, India, Europe, Middle East etc. The other American born kids doing advanced studies were from ethnic minorities like Indian, Chinese etc.
So the point John is trying to make is that, the system does not have a healthy output of students into science/tech domestically.
Comment by Domestic Avalanche — February 6, 2009 @ 5:37 am
In terms of accuracy, Kenney’s probably correct. But I feel if not for advanced math calculations, you SHOULD be trained to do perform math of medium complexity on your own. My own experience is that now that I reach for the calculator or the computer for some calculation, I personally feel dull. At the same time, when I was about to take GMAT, my response time was very very good. IMHO, it makes you SHARP. And that’s probably the reason why Indians tend to score better than their American counterparts in math. I’m really of the opinion that being sharp does matter and pay off at the end of day.
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Comment by ashley — April 3, 2009 @ 11:06 pm