Common Mistakes About Mathematics and Use of Mathematics in Everyday Life

8/11/2019 Common Mistakes About Mathematics and Use of Mathematics in Everyday Life

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Common mistakes about

mathematics and use ofmathematics in everyday life

By

Nitin OkeTeachers Workshop

at Swami Ramanand TeerthMarathwada Research Institute Nageshwarwadi,

Aurangabad For Ganit Yatra 2014organized by Jidnyasa Trust Thane andsponsored and catalyzed by NCSTC, DST Govt. of India


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Our own feelings - - - !

As a student or teacher of mathematicsmany a times we feel that why to teachproblems like A tank is filled in 3 hr by a tab andempties in 5 hours then if both tabs areopen in how much time tank will be filled?

Instead of calculating this time close theother tab why to keep it open?


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As a student or teacher of mathematicsmany a times, we feel that; why to teachproblems like A work is done in ten days by one workerif five workers are doing the same jobthe work will be done in how many days?

How many of us really think that afterincreasing number of workers the work willbe done with same speed?


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As a student or teacher of mathematicsmany a times, we feel that; why to teachproblems like A table and a four chairs cost 2000 Rsand two tables and four chairs will cost3000 then cost of a table is ?

Just imagine such conversation at a shopwhen you wish to buy a table and chair. Youwill decide to go to other shop immidiatly.


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As a student or teacher of mathematicsmany a times, we feel that; why to teachproblems like Sum of my age and my fathers age is 60years and my fathers age is double thatof my age then my age is ?

Just imagine such conversation when youasked age of your student and he answerslike this.


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As a student or teacher of mathematicsmany a times, we feel that; why to teachproblems like The last digit of is ?

At this moment we start thinking is itreally going to make any difference to my

life?

113107


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Status of Mathematics is

Even if we call mathematics as motherof all sciences it itself is NOT science.

Well the reason is it never tries to revelthe laws behind the facts in nature onthe other hand it provides the languageto do so, it provides methods to do so in

short mathematics can live withoutscience but science can not.


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What Mathematics is?

Well it is not just study of numbers. Neither it is study of figures. Mathematics; for science is

method of proof : Logic, a statement toprove, an implication to prove , note thedifference between statement and itsconverse

language of expression : F = m.a,a = (v u)/t or F = d(P)/dt or a = dv/dt


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Concept of rules of division

These are not hypothesis these are results soneed to have proof. You only need place valuesfor this for example

A number is divisible by 3 if sum of all digits isdivisible by 3 let the number be abc ( actually itcan be ( a1a2a3a4----an) so

abc = 100a + 10b +c = 99a+9b + a+ b + c

3 divides 99a and 9b under any case hence if3 divides a + b + c then will divide abc and hencethe result.


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Concept of rules of division

These are not hypothesis these are results soneed to have proof. You only need place valuesfor this for example

A number is divisible by 11 if sum of all digits ateven place and sum of all digits at odd placediffer by a number divisible by 11 let the numberbe abcd ( actually it can be ( a1a2a3a4----an) so

abcd = 1000a + 100b + 10c + d= 1001a- a+ 99b+ b + 11c c + d

Remaining part you can get on your own


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Euclidian geometry most easy to

understand most difficult to explain

Concept of point, some thing which has no length, nobreadth and nether height. Then what segment is ?segmentis projected as set of points but we alsoknow point added to point is again a point then any

figure cant be seen. But look at segment as set ofpoints ( not sum of points) then it works.

Means segment is set of points, go on splitting thesegment after infinite splits you will land on point but

addition of point is not segment. Sounds funny butmathematics of infinity is different than usual.


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Euclidian geometry most easy to

understand most difficult to explain

Examples of unscientific talks

Shirtboot

22/7 is irrational number Euclidean geometry is around

a = b ------ 1 = 2


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Rationalirrational and real number

2.3455553535346728254384625267374858959633743644646474848888888888888888888888888888888888888888888888888888888

8888888888888888888888866455555555555555555555555555555555555555555555555555555123456789012345678901234567890123456789012345678901234567890123456789

01234567890123456789012345678901234567890123456789012345678901234567890122


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Rationalirrational and real number

You can be confirm that number is rational if it isexpressed in form of

fraction of two integers ( with nonzero denominator)

Terminating or recurring decimal expansion

If the number is not in form of fraction and

decimal expansion is there and there and there

then because of finite life span we are not in

position to tell whether number is rational or not Be careful about difference in surd and or e


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Difference between countable and

uncountable infinity

Concept of infinity is very difficult ( not

possible) to explain.

Is it not really difficult to explain that youremove half the objects and remaining

number is same as before.

Please note that 0

a


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Trigonometry

We define trigonometric ratio with the help of

triangle but when it comes to sin (0o) or

cos(0o) (cant even think of cos(180o))then it is

meaningless by right angle triangle. You need

other approach, for the same, as polar co

ordinate system and Cartesian system.


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Trigonometry

We define trigonometric ratio with the help of

polar co ordinate system and Cartesian system

cos(polar

) =

sin(polar ) =

rpolar

xcartesian

rpolar

Ycartesian


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A(x,y)A(r,)

rpolar

xcartesian)cos(

rpolar

Ycartesian)sin(


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mathematics in our every day life

Two eyes and two years are for estimating

distance of source. Using trigonometry.


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Every expression of mathematics is having direct

relation in every day life as

Good purpose relations

amount of food prepared

Estimation of distance

Shift of centre of mass to get up from chair

The time management

The bad purpose relations

All for money management .A problem of traveler.


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Common Mistakes About Mathematics and Use of Mathematics in Everyday Life