- Education and Science
Why is mathematics difficult for vast majority of people?
What is mathematics?
We are already encountered with the first problem. The first allusion on mathematics for many is the notion of the number and computation. That would be a very narrow view of mathematics. Math is not dealt only with numbers, but also with other facilities throughout its history.
Mathematics – What do you first associate with this term when you hear it or see it?
For the vast majority of people this term is a major problem in their lives. Not everyone can be a great mathematician, but the human brain can serve as the best and most perfect calculator. If we calculate an operation over numbers, for example (6x5 or 2x7) and we get the exact required number (30, 14), our brain will remember this information and write it down in one of its memory. When we need to perform the same action over these numbers our brain will tell us: I've done this and it will show us the result from the database. Each of us has that knowledge written somewhere in the code and we carry that knowledge for lifetime. The first thing we need to know is that math is not perfect branch. It is not perfect because the numbers are not perfect. This will serve as a good example to those people who do not want to teach mathematics.
Take for example the number 3. Can we split an apple to 3 pieces and give every man an equal share? The answer is no. None of the three of them can get the same. Someone will always get more and someone less. Why is that so? Take a calculator and divide 1 to 3! What do you get? 0.3333333 .......... the repetition of the number 3 in the infinity. It is imperfection. Many numbers are imperfect.
Some people can calculate quite complicated operations with numbers. If you have the task of multiplying in your mind rather than on paper 25x24x68x21 what would you do? Nothing, I guess. There would be a complete mess in your head. Yet there are people who can come up with a solution of such problems quickly without the help of pen and paper. Such people have perfect knowledge that was previously upgraded many times. In fact they learn some legality of numbers. Furthermore they realize the repetition of these same laws and they skillfully use it. In my opinion, these people are not weird people. They know how to use their brains to solve the problems. They are genius.
Our brain is capable of many things, but it remains a big unknown secret. Scientists, I dare to say, will never be able to explore a brain to the very end, not even 50 percent of it. Some secrets go to the grave with us. It has been discovered perhaps 20 percent of brain functions. What about those 80 percent? What else we can do that we don't know about it yet.
Getting back to the topic. Why is mathematics difficult? From the beginning of our school days we learn how to use 4 main operations over numbers (Addition, Subtraction, Multiplication and Division). After our basic knowledge of mathematics, through the life, this knowledge is becoming more and more advanced and things that were difficult become easy. Yet some remain difficult. Why is that so? The answer is very simple. Insufficient use of our brain. It is important to use your brain. When you turn on your computer - what happens if it just remains on and you do nothing with it? The computer then does not process any data. It is useless. It only consumes energy. So the same is with the human brain. When we wake up, the brain wakes up too, which is not exactly true (rather we can say brain opens our eyes as the human turn on the lights on his car in the night to see where he is going.) The brain works when we sleep because if it doesn’t work there would be no dream. When we wake up, the brain looks for new solutions for all the problems that await us in that day. Some will say, we don't have problems? We just woke up. To get to the toilet and brush your teeth - what do you need to do in order to properly perform this action?
First you need to get up, then dress up, get to the bathroom, take a brush, put toothpaste .....
All of this are series of actions that the brain performs. The brain has found a solution for all these problems. Let us remember childhood. When we were small we couldn’t not even walk, nor brush our teeth.
And now it's all possible. How? The brain remembers useful actions, things that will be needed in our life.
If our brain fails to find a solution thanks to our laziness the first time when our problems become hard to be solved, it will see it as something difficult and useless.
It will connect the problem with anxiety and torture, with something that is difficult to be done. It would be able to calculate but we obviously don’t want to calculate that kind of problem. The brain in its database will not have a solution on this problem, and as time goes on, problems will become more and more difficult.
Are you thinking in mathematical way?
In 1970, British psychologist Peter Wason conducted a study with one, at first glance a simple task, but that most people don’t know how to solve it. Imagine four playing cards on the table in front of you. You were told that each card at one side has number, and at the second letter. You can see these symbols on cards: E K 4 7.
It's all up to you to determine which card must be turned in order to verify that the rule is respected. If vowel is at the one side of the card, an even number is at the other side of the card. Please stop reading and try to solve this problem. No matter which solution you choosed you’re probably still checking. This is normal. Now let me check your solution. Quite possibly you would turn over the card E to make sure the other side is even. And it certainly needs to be done. And then? Some of you will turn the card with the number 4, but it is not necessary, because the rule will be respected even if the other side is consonant. Right move is turning a card with the number 7. If at the other side is a vowel, we realize that the rule is not respected.
There is another very specific problem almost all people know how to solve. Suppose that you are organizing a party where you don't want to violate the rule that minors are not allowed to drink alcohol, and you ask all the guests to put identification card next to the cup. At one table there are four young men for which we don't know their age. For one of them we know that he is drinking beer, and for other we know that he is drinking soda.Their identification cards are laid out so we don't see their ages. The other two have open cards so we know that one is adult, and the other is not. But you don't know whether they drink a tonic or vodka. And it is clear to everyone what to do. For one who drinks beer we turn the ID card to see his age and for other who is underage we smell the glass. Is it possible that this is a completely analogous problem? Yes, actually, it is the same problem. If we look now at the Wason test, then we can easily conclude that the task of the party is a third level of abstract thinking, and the one with the cards is of the fourth, much more demanding level. Math is dealing with abstract concepts or objects that have little or nothing to do with objects in the real world. Every issue raised in the fourth level of abstract thought requires far greater intellectual effort then similar "tangible" problems.
So from the logical side we have two same problems. Why then the first one many consider extremely difficult, and the other is extremely simple?
It is because people more easily think about familiar objects and recognizable situations, rather than a completely abstract objects in unusual situations.
Long ago people used many ways to approach and solve the tasks. These methods were different but they led to the same solution. People eventually perfected the technique and made countless inventions that have helped in calculating, writing, drawing, modeling and so on. But does this technique blunt us and make us stupid? I think the answer is yes, unfortunately. We become dumber and dumber because we get all of that things served on the table. We no longer use our own brains to come up with solutions. We put into the calculator, for example: 20 * 35 and get a free solution. Now the calculator replaced our brain and it thinks for us. And that's not good. If we continue like this with accelerated pace in the development of technology we will become a blank sheet.
Many of you have never heard of Vedic mathematics. Ancient people used it and they were solving their problems with this type of mathematics. We are using their knowledge which are now inserted in the computers and calculators.
What is Vedic Mathematics?
Vedic Mathematics is the name given to the ancient system of Indian Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). According to his research all of mathematics is based on sixteen Sutras, or word - formulae. For example, 'Vertically and Crosswise` is one of these Sutras. These formulae describe the way the mind naturally works and are therefore a great help in directing the student to the appropriate method of solution.
In the Vedic system 'difficult' problems can often be solved immediately by the Vedic method. These beautiful methods are just a part of a complete system of mathematics which is far more systematic than the modern 'system'.
My favourite sutra is Nikhilam Navatashcaramam Dashatah. It means All from 9 and the last from 10.
Vertically and crosswise
Example: to multiply 9 by 8, hold your 8th finger down, and count "7" and "2", the answer is 72
Math is fun:
1 • 9 + 2 = 11
12 • 9 + 3 = 111
123 • 9 + 4 = 1 111
1 234 • 9 + 5 = 11 111
12 345 • 9 + 6 = 111 111
123 456 • 9 + 7 = 1 111 111
1089 x 9 = 9801
Mathematics becomes very simple when you realize some correlation and when you discover the logic of things and certain rules.
© 2015 Kristian Režić