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Remember that Happiness is the outcome of Sharing, Caring and recognition.
Learning through perception helps us to concentrate on the work/job on hand.
You are bound to forget what you read sooner or later. What you perceive you remember for life.
About the author and co-author:
Co-author Dr. K.N. Sharma is having a good knowledge of languages, being himself a Sanskrit scholar first and then an engineer. He is having wide experience in teaching and handling various projects. Now he is working as associate Professor and principal investigator, Department of soil & water conservation engineering C.A.E.T., OUAT: Bhubaneswar. His contribution to the article is very valuable and (his grasp of power of using language without ambiguity is really admirable) evolved out of discussions between the author and the co-author.
The Author MCS Rao was a senior scientist in ministry of Defence. He worked on the projects meant for all three services. He is working on a self-financed project on Right Education for over 35 years. Right education should imbibe self-confidence and ability to verify and improve upon ones working methods on daily basis. He is promoting the concept that employment should be based on one's salable-skills for the prosperity of one-self and the nation.
Important things to remember:
Language is meant to make "others" understand "YOU" without ambiguity. Not following rules will lead to confusion and language-phobia. The result is poor IQ ratings.
Inability to understand languages leads to communication gaps and result in language-phobia and develops into subject-phobia (applicable to all subjects) in students. Shall we call it fear of the unknown?. It is applicable to all languages of perception, verification and assumption.
Yes you can do it and build a tension free learning atmosphere to your self. Learn through perception and practice to verify what has been done.
The most difficult thing in life is taking care of small things.
All big things are made out of small things. Take care of all small things.
The outcome will be really impressive.
All languages use rules of interpretation.
Rules are to be understood and used properly - scientific attitude. A lot of communication gap is due to inability to understand appropriate meanings of the words and the importance of the rules. Grammar of any language is nothing but science of that language and meanings the life.
Dealing with languages from scientific angle is all about learning through perception.
Languages are meant for communicating without ambiguity.
Main classification of languages used for communication: There are four main forms of languages we use to communicate. They are:
a) Spoken/written language. English, Hindi, etc,. All languages used for communications with spoken/written words - fall in this category. - Language of assumption.
b) Language of mathematics. Number system with positional values, alphabets used to represent constants & variables used in algebra and keeping track of give and take activities along with their rules - fall under this category. - Language of Verification.
c) Language of Drawings. Symbols we use to represent like triangles, circle, rhombus, pictures and figures etc. along with their rules - fall under this category. - Language of perception.
d) Language of physical expressions. Like Acting, mimicry etc. along with their rules - fall under this category. - Language of expression.
They are developed by human species to meet the requirements of human brain's working levels - perception, verification and assumption.
Note: All languages a, b & c are used in mathematics and one should practice, with special care, how to interpret them properly and independently with the help of spoken/written language.
The principles enunciated here after are equally applicable to all languages. Now on we concentrate on subject mathematics as it uses all three languages.
Note the difference between subject mathematics and language mathematics.
Why many of us develop equation phobia (fear of mathematical expressions given in the subject)?. I used the word phobia to stress the fact that it is an acquired quality and not natural. Use of all three languages and not adhering to the rules while reading the text is the general cause of mathematics phobia.
Try this and see the difference to yourself.
An attempt to learn through perception.
First make an attempt to understand what the heading of the subject/chapter is all about. Make sketches, name various parts of the sketches, reproduce charts and tables and let your brain wander about the possible relation of the to the meaning of the heading and use the language of assumption the text to understand what is the subject is all about.
An apple, tiger, aeroplane, rocket etc., make no sense if you have not perceived them by seeing them or some thing similar to them your self. The words apple, tiger etc., are the words of language of assumption and meant for invoking a mental image perceived by you and make you understand what the speaker is trying to convey to you. Now you know why communication gap arises all because of different perceptions by different listeners.
If you want to master nay understand your subject well avoid this pitfall of gap between you and the author by referring to dictionary-meanings to invoke a mental picture the author is trying to project.
More about language of Mathematics or shall we call the equations or mathematical modeling?.
Symbols of Mathematics language:
The language of mathematics is having a few symbols (0-9) to represent a count limited to the total count of the fingers of both hands less one. Operational symbols (+,- = and .) to indicate Take, give, equality and decimal expression. All other symbols are derived from above few symbols to express multiple operations (as such the child should be made to understand them properly).
Rules of language of Mathematics:
Symbols (0-9) are associated with positional values to represent the true magnitude of the symbol.
Magnitude of number should always be associated with a unit (like sheep, Kilo gram/s, Rupees etc.,) or number of operations to derive a communicable meaning.
All magnitudes should be associated with either give or take operation.
A take operation by one should have an equal magnitude-unit of give operation by another or vice versa.
I) Mathematical language is used to keep track of magnitudes of units one takes or gives.
II) The magnitude and units of both sides are equal in magnitude and units. The statements (I&II) taken together imply that mathematical language can be used by any one to keep track of magnitudes of units one takes or gives. He needs just keeping record of his activities to convey total activities that have taken place between him and others. The magnitudes and units are same, only symbols (+,-) or different. In all probability this aspect is what resulted in present method of teaching mathematics and associated mathematics-phobia.
Take and give operations are equal in magnitude and should be associated with symbols (+),
(-) to communicate their true meaning, when only one sided operation is represented, symbolically.
When many operations of similar type are involved, the true value of total operations can be obtained by adding or subtracting magnitude of single operational unit as many times as that of operations. If they are "take" operations by (+) adding and by (-) deducting if they are "give" operations repetitively to complete the number of operations involved.
Note: The stated rule implies that solving problems with multiple operations should be attempted by first reducing the problem to single operational unit.
When different languages like spoken/written, drawing, and mathematical languages are used to pose a problem, the problem should be first reduced to equations in spoken/written language before attempting to substitute the equivalent symbols of mathematics "assumed or otherwise".
Too many rules are they not? Naturally when we have very few symbols to express lot many operations with out ambiguity. Mathematics is a language used for keeping record of give and take activities, Action and reaction, cause and effect, debit and credit, assets and liabilities, LHS and RHS, etc., to name a few. Mathematics language is used to deal with both sides of the problem (=) by implication. They enable one to record transactions in a lucid way with out ambiguity. Rules are to be followed properly and simultaneously otherwise interpretations may be wrong even though magnitude of the result may be same. Anyway rules are simple and easy to master.
How to avoid equation-phobia:
Understand - make it a point to write down the meanings of each symbol as clearly as possible before making an attempt to understand the equation as a whole. You may have to resort to orderly translation from perception, verification and assumption languages.
The real intelligence lies in using the hands to write down meanings before reading. Language of assumption should follow perception but not other way round, as we are normally accustomed.
Learn how to split the problem/equation into logical & independent statements in given language/s.
Rewrite the given problem in written language as numbered equations.
Assume symbols to represent unknown values.
Substitute the magnitudes and symbols assumed along with units to convert the written language equations to equivalent numbered mathematical equations.
Understand /Solve the equations to find the unknown/what the author is trying to convey..
Note: ensure that you follow logical steps and one to one rule while converting any language to spoken/written language equations or equivalent numbered statements.
Follow the steps given below to avoid any ambiguity.
Remember that all problems are posed either in spoken/written language or a combination of spoken/written language, language of mathematics, and drawings.
Step1) drawings to language,
Step 2) Split the problem to spoken/written language numbered equation.
Step 3) Substitute the assumed/actual values following mathematical language to convert the above equations to mathematical equations,
Step 4) and finally solve the equations to find out the result/unknown.
Consider the following examples to understand what we mean:
If two bees sit on each flower one flower will be left out. Where as if one bee sits on each flowers one bee will be left out. Find out how many bees and flowers are there? E.g……..1
If 2 bees sit on each flower 1 flower will be left out. Where as if 1 bee sits on each flowers 1 bee will be left out. Find out how many bees and flowers are there? E.g……..2
In a right angle triangle the two adjacent sides are 3, 4 cm. Find out the hypotenuse. E.g……..3.
Find the roots of the equation ax2 +bx+c, where a=4, b=2 and c=1 E.g……..4.
Find the height of the cone made out of a 1200sector of a circle of radius 36 cms. E.g. ..5.
Mathematical equations are last but one-step in solving/expressing any problem/concept.
Remember the purposes of mathematical equations, are to find proper correct solutions but not some how.
The above procedures illustrated by us to enable you to understand and use all three languages properly but enables you trace back the steps and find out where you have gone wrong and correct them.
There is nothing like Power of verification to build confidence in one-self..
Make it a point to verify the result by substitution. And trace back the equations numbered to locate the fault in case of wrong results.
Few more tips.
Make it a point to follow consistently to name a drawing with letters a, b, c, d etc., in anti clock wise direction only to avoid confusion and trigonometry and drawings become much easier to follow.
After-all all drawings, Cartesian co-ordinates, polar co-ordinates, and vector co-ordinates are all to give the position of a point in space without ambiguity with respect to a reference. And equations formed using them are the mathematical representation of the picture formed by the point in space. What is important is to visualize the picture (perception) and find out the position of the point as per requirements.
Use the knowledge you gained to solve real life situation problems. Nothing will be more interesting than finding an application to the knowledge acquired.
An attempt is made in above article to help the readers understand the importance of perception and how to train one self to learn through perception. The present methods followed in education system are mainly through the language of assumption, other languages of perception and verification are no doubt used in textbooks but they take back seat when we were taught in classroom or when one reads. The authors want to emphasize this draw back and suggest use of language dictionary as a tool and source of perception to avoid ambiguity and communication gap.
The article contains key points to enable readers to change their methods of learning or at least explore the potential of the method, many got benefited why not you?.
Mathematics is a simple language no two people can interpret it differently, but translating other languages to language of mathematics needs systematic and logical approach. Following repetitive, consistent methods it becomes natural and easy. A whole lot can be expressed without ambiguity and power of verification through mathematical equations (mathematical modeling).
Practice makes man perfect.
If you like further guidance you can contact:
Co-author Dr. K.N.Sharma, Associate professor CAET., OUAT., Bhubaneswar. INDIA
firstname.lastname@example.org (R) Ph.2575559. 268/2 near Suman Press behind hotel Sidharth, Cuttack Puri Rd. BBSR. (O) A/52, Kalpana Area, OPP. to BDA Park, Kalpana Area, Bhubaneswar. INDIA.
You too can participate help build a peaceful world by promoting total personality development of individuals.!!! Why not participate in this noble cause?