THE SECRETS OF LEARNING MATH

THE SECRETS OF LEARNING MATH

THE SECRETS OF LEARNING MATH

There are essentially two secrets to learning mathematics; the first is concerned with the content and the other with teaching. There is far too much content at each grade level, and every few years the amount of content is increased. Under these conditions, students are urged to memorize concepts without understanding in order to maintain an acceptable grade level on tests. Research has determined that, for most math students, the memorization of concepts without understanding is stored in the short-term memory and soon forgotten. The first secret to student success in math is to reduce the amount of content at each level so that there is time to learn and understand the concepts.


The second secret is one concerned with teaching. I have often heard that in the history of education, the "best" education took place in the one-room schoolhouse. If this is true, then it is because in a one-room schoolhouse education often came about as a result of older students teaching younger ones; both students gain from this experience. When a student is able to explain in his or her own words a math concept, that student understands the concept. The second secret to student success in learning math is to have students understand math concepts and demonstrate their understanding the concept by correctly explaining it in their own words to someone else.

THE SECRETS OF LEARNING MATH

The predominate guideline for mathematics curriculum the past few decades has been acceleration and this has resulted in all math courses having too much content. This means that most students must memorize math to pass the course. Unfortunately memorizing is short-term and not related to understanding mathematics.

Conclusions from the Research

              Conclusions from the Research

There seems to be two main factors that could be corrected in our teaching of math courses that would go a long way toward eliminating the current problem. These two factors are memorization and acceleration.

Memorization:

                      Memorization

Students are trying to memorize all necessary facts that are needed to pass the course. Unfortunately, this is not possible for most students and such a course of action has no long-term benefits; hence causing the basic problem in mathematics.

Acceleration:

THE SECRETS OF LEARNING MATH

We are attempting to teach too much too fast in math courses. This, in turn, causes students to rely on memorization as their best hope to pass the course. We do not give them the proper amount of time to understand concepts, which reduces the need for memory.

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Number system in math

Numbers in mathematics

Number system

Number system in math

                               

Numbers in math

·       Natural number:- The numbers which start from 1 and goes upto to ∞ are called natural numbers.It represented by N.

                    N = 1, 2, 3, 4, 5, …………………∞

·       Whole numbers:- The numbers which start from zero(0) and goes up to ∞. It is represented by W(capital W).

              

 W= 0, 1, 2, 3, 4, ……………∞

·       Integers:- All the number between -∞ and ∞.It is represented by Z.

                   Z= -∞……….. -2, -1, 0, 1, 2,……………..∞.

Two type of integers are

A.    Positive Integers:- 1, 2, 3, 4,……………∞.

B.    Negative Integers:- -1, -2, -3,…………… -∞.

·       Even Numbers:- The numbers which are divisible by 2 or multiple of 2. i.e. 2, 4, 6, 8,……………….∞.

·       Odd Numbers:- The numbers which are not divisible by 2 or not multiple of 2. i. e. 1, 3, 5,…………………∞.

·       Prime Numbers :- Natural numbers which are divisible by itself             and unity . i. e. 2, 3, 5, 7, 11,………..

                The 15 prime numbers between 1 to 50.

               The 10 prime numbers between 51 to 100.

                The 25 prime numbers between 1 to 100.

       Only 2 is least prime number and also  only 2 is even prime      number.

·       Composite Numbers:-  The numbers which other divisors besides 1 and itself i.e. 4, 6, 8, 9 etc.

·       1 is neither  prime nor composite.

·       Rational  numbers:- The numbers which written in form p/q where q≠0, and p,q are the integers. i.e. ¾,  4/5, 1/3, etc.

       

         Every rational number can expressed in decimal form. There are         infinitely many rational numbers between two rational numbers.

·       Irrational Numbers:- The numbers which cannot written in form of p/q . i.e. √2, √5,  etc.

                                          

Number system in math
Irrational numbers

   π is an irrational number yet its values appears in rational numbers (π = 3.14). Because these are it approximate values.

·       difference of the rational number and irrational number is always irrational number.

       Sum and difference of rational number and irrational number is always irrational number.

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All differentiation Formula

All Differentiation basic formula:-

General Differentiation formula:-
     

                    1.   

Differentiation Formula-1

                   2.

                                 

differentiation formula-2

                  3. 

                               

differentiation formula-3

                 4.

                                   

differentiation formula-4

                   5.

                                 

differentiation formula-5

                     6.

                                         

differentiation formula-6

                      7.

                                       

differentiation formula-7

    

Ø Differentiation formula for trignometric function:-

               

                  8. 

differentiation formula-8

               9. 

                                 

differentiation formula-9

                10.  

                               

differentiation formula-10

                  11.

                               

differentiation formula-11

                  12.

                                

differentiation formula-12

                   13.

                              

differentiation formula-13

Ø Formula for inverse trignometric function :-

                    14. 

                           

differentiation formula-14

               15.

                          

differentiation formula-15

              16.

                         

differentiation formula-16

              17.

                       

differentiation formula-17

               18. 

                         

differentiation formula-18

              19.

differentiation formula-19

  Ø Formula for Exponential and logarithmic function:-

                   20.

differentiation formula-20

              21.
                   

differentiation formula-21

              22.
                   

differentiation formula-22

             

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differentiation /differentiation rules/differentiation formula.

Ø What is Differentiation?🚩

Differentiation is used to find the rates of change of one quantity as compared to another .

There are number of rules of differentiation  in mathematics to find the differentiation of any function easily.

Differentiation generally represent by the expression dy/dx or f’(x).

dy/dx means if y= function of x(in other world ,y is equal to an equation that containing number of x),then the derivative of y is written as dy/dx means rate of change in y w.r.t. x.  

                              dy/dx =Differentiation of y w.r.tx

Ø Basic Rule of Differentiation :

·       General rule of differentiation :

If y=x^n   dy/dx= nx^n-1 where nεR , n≠0

           

Differentiation

·       The derivative of any constant is always zero .

If y=k, k= constant , then dk/dx=0 always

              

differentiation rule-1

  

·       In any equation a constant multiplied by a function then the derivative of this equation is equal to the constant multiplied by the derivative of function.

                        

differentiation rule -2

·       The derivative of sum of two function is equal to the sum of derivative.

                             

differentiation rule-3

   

  

·       The derivative of difference of two function is equal to the difference of derivative.

                         

differentiation rule-4

 

·       Derivative of two multiplied function :if y=f(x).g(x) ,then

                       

differentiation rule-5

·       Derivative when y=f(x)/g(x) ,then

                   

differentiation rule-6

       

Differentiation Example:-

Question-1

Find derivative of following function by applying basic rule of differentiation.

Differentiation

                   

       Solution:-

             

Differentiation

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