Reference and Education Article Category

Using calculators is a part of our modern way of life. Today it is not a problem for kids to get a calculator and put it into practice. Really, why must they toddle if they may ride a bike? On the face of it using calculators at school allows keeping away from many troubles.

By the help of a calculator we can carry out complicated mathematical operations quickly and accurately. Calculator proponents claim that calculators simplify tasks and allow students to spend less time on monotonous calculations and more time on understanding problems and determining the best methods for solving them; calculators allow students who would normally be turned off to math because of dissatisfaction or boredom to increase their mathematical understanding. Furthermore, every teacher of mathematics knows that there are graduating pupils in primary school who had not mastered the multiplication table, have difficulties with subtraction within the limits of 20 and so on. Give all of them calculators and they will obtain desirable result without sweating, puffing and having a dread of mistakes and therefore will become more confident about their math abilities.

But this good-looking picture is too charming to be a realistic one. There are several circumstances which make using calculators at school not so attractive. Firstly even a brand new modern calculator which has amazing computational power is a device only. Each calculator is as good and as accurate as its operator. To use it in proper way a pupil must know its manual well. Calculators of different kinds use different orders for carrying out mathematical operations, pressing keys, and their manuals have a bad habit to get lost. It is very easy to make simple mistakes when using one. You must think of the rough size of answers, so that you can see if an answer is sensible or not. To avoid mistakes you must repeat all calculations. If you get two different answers, then you must repeat all calculations for the third time.

Very often even advanced students make mistakes - pressing wrong buttons, forgetting to change a mode, rounding values too soon, forgetting to use brackets rightly ... And what about bad achieving pupils? Can you imagine that a pupil who does not know what brackets are for can use them correctly? How can a kid who cannot mentally multiply 8 by 7 weighs up a result?

For advanced students a calculator is a comfortable vehicle, which helps him to reach their aim more rapidly and more easily, but in case of need they can go out of it and move themselves. And what is more they very often perform better without a calculator since in many cases mental computations are quicker, easier and more errorless then computations with calculator.

Whereas for bad achieving pupils a calculator is a motored wheel chair for cripples, without which they cannot move. They are afraid to carry out mentally simple arithmetical operations and waste precious time when pressing keys.

Besides that there is another significant hazard. A person who all the time uses a calculator gradually loses his/her mental computational skills. Very often even advanced pupils take calculators when they need to make simple computations which can be easily implemented in head. Their brains slowly but surely get accustomed to walking on crutches and became indolent to use mental computational abilities, whereas skills, which are not used, became forgotten very soon. In certain cases it leads to difficulties in math's learning.

Both my experience (32 years in the classroom) and my investigations (20 years of studies) shows that pupils with unsteady elementary mental computational skills (addition and subtraction within the limits of 20, multiplication and division within the limits of 100) have great difficulties while learning the other basic topics of arithmetic and algebra. In other words they are doomed to poor progress in school math. Even calculators cannot help them. If you want to see some figures and diagrams you can read my article "Influence of a Level of Elementary Mental Computation Skills upon Success in School Mathematics" at my web site Prevention of Failure in School Mathematics (reference - My Articles).

Do not think that I am trying to stop progress and calling to finish with any computing stuff at school. It is obvious that we can not manage without calculators today, but we must remember about simple mental computations and their significance for success or failure in math. I consider that it is necessary to lay emphasis once more - extensive using of calculators (especially at the first six or seven grades) leads to degeneration of pupils' mental computational skills and afterward to deterioration of their learning ability. This is the main hazard of using calculators at school.

The Power Of The Unconscious Mind - The Secret To Student Success

One of the best ways I know of to give a massive boost to your ability to learn and to enhance your grades beyond all recognition is to leverage the immense power of your unconscious mind.

'The thinking process is unconscious. We become aware of the results consciously. All change takes place at the unconscious level. We become aware of the change consciously when we are ready.' Joseph O'Connor

What on earth does this mean???

Well, read on ......

Roughly two million bits of information per second come into the human nervous system. We are literally bombarded with information. To maintain sanity, our conscious mind filters out most of the stimuli and Miller (1956) discovered we can consciously handle only seven plus or minus two bits of information at a time.

The unconscious mind deals with everything else over and above the seven (plus or minus two) bits of information that you are not consciously paying attention to at a particular time. As soon as we switch our attention to something, then it becomes conscious. Some parts of your physiology will always be unconscious. This should not surprise us really. Our unconscious mind takes care of us all the time! We do not run our heart, lungs, kidneys, immune system etc... consciously do we?

I want to show you how to bypass the conscious mind in order to access the immense powers of your unconscious mind. The unconscious mind is around 90% of your total mind power as opposed to the 10% of the mind that you usually use in your normal daily waking state. The unconscious mind is a source of great treasure - of skill, of memory and experience.

The power of positive thinking can be significantly enhanced and reinforced by the use of affirmations. An affirmation is a short statement in the present tense repeated frequently to impress itself onto and be accepted by the unconscious mind. The ideal affirmation must be short and totally unambiguous. This is important, as the unconscious mind cannot easily assimilate long or complex statements. The unconscious mind is much more easily influenced by short, appropriately worded statements.

The majority of people however, are in the habit of negative thinking - of dwelling on problem areas in their life by repeating exactly what they do not wish to happen. This often ends up compounding the original problems and making them even worse. For example, a student might keep on saying to themselves:

"I will never be successful in my examinations".

Or: "I always get sidetracked when I am studying".

Or: "I simply can't concentrate".

The student who constantly repeats these negative affirmations, either consciously or unconsciously, will be much less likely to succeed in their examinations, and may never be able to concentrate or get their studying done.

Underlying almost every negative emotion is a thought or belief, and most often these are unhealthy thoughts or beliefs. By unhealthy I mean they are not effective in getting you what you want in your life. They don't serve you.

The belief (often unconscious) is like a trigger. It sets you up to fail in certain situations.

Remember this! If you do not THINK and fill your head with positive thoughts and beliefs, then negative ones will always come in to fill the gaps.

Please NEVER, ever, ever, ever underestimate your own abilities. It is never a question of can you do something. The real question is will you?

In the examples above, the student was repeating the negative affirmations in their head. They should instead replace them with the equivalent positive affirmations. Such as:

"I know I will be successful in my examinations ".

Or: "I am focussed when I sit down to study".

Or: "my concentration is improving".

This might well seem difficult to do, particularly in what may seem to be difficult circumstances or where the reality appears to be totally the opposite. However, believe me, like most things, it is just a question of practice.

Where attention goes, energy flows! You become what you think about most of the time.

The more often an affirmation is repeated, consciously or otherwise, the more quickly and effectively it will become real. But take care because this works just as effectively for both positive and negative affirmations. A great time to repeat positive affirmations is just before drifting off to sleep at night or just after waking in the morning before you get up. At these times your conscious mind communicates best with your unconscious mind. If you can repeat the affirmations throughout the day and even write them down and place copies around your home, so much the better.

An even more powerful possibility exists as an alternative to affirmations that are stated aloud or within the mind. This is the power of "Subliminal messages".

The power of subliminal messages has been proven over many years to be a highly effective way of programming the unconscious mind by using either audio or visual methods. In fact,subliminal messages are so powerful in the way they work on the unconscious mind, that in 1974 the US government banned all forms of subliminal message advertising on radio and television.

Subliminal messages reach the unconscious mind by working at a level that cannot be detected by the conscious mind. The conscious mind therefore never has an opportunity to reject them and the unconscious mind can receive and act upon them.

There are two main ways of using subliminal messages in a most powerful way - visual and audio.

Visual subliminal messages are affirmations that are flashed before the eyes so quickly that the conscious mind cannot perceive them. The affirmations therefore go directly to the unconscious mind, which perceives and acts upon them immediately.

Audio subliminal messages work in a similar way by being played at a frequency that is just above the normal threshold of human hearing. Again, as with visual subliminal messages, although the conscious mind cannot perceive these affirmations, the all-powerful unconscious mind can perceive them, and will therefore immediately act upon them.