TO INTRODUCE ALGEBRA
A quote by Stefan Banach .
“Mathematics is the most beautiful and most powerful creation of the human spirit.”
Mathematics is a way of thinking, a way of reasoning. It is a creation of Human mind and gives us an insight into the power of Human mind. It is a language with concise symbolic representations. Mathematics can also be called as a study of pattern. It is also an Art. There is an order and harmony which produces the beauty.
AIMS:
To express verbal statements in terms of appropriate symbols.
To express abstract ideas.
To inculcate the habit of analysis.
To link to other science subjects and to generalize scientific truth.
To appreciate and attach meaning to verbal statements.
MAIN USES/FUNCTIONS/RELEVANCE OF LEARNING ALGEBRA:
i. It is very easy to decide what is to be done as there are symbols. It inculcates and helps us towards correct analysis.
ii. It helps us in generalizing facts.
iii. It helps us in calculations and to find solutions.
iv. It gives great scope for creative thinking.'
Before algebra is taught, one has to be in conversant in operations in arithmetic; should have a grip over the language (comprehensive ability) and also exposure to many life situations where arithmetic is involved. Letters can be introduced by asking the following questions:
I am aged 30 years. You are ‘X' years younger than me. What is your age?
I have Rs. X with me. You have Rs.5 more. How much do you have?
What is X% of Rs.500?
The length of a rectangle is 15 mts. Find the area and perimeter of the rectangle if breadth is Y mts.
The above-mentioned questions train the students (pupils) to use the literal letters, to represent, to recognise the importance of arithmetical procedures, to drill the four fundamental operations already learnt.
Note: Before introducing letters, one can use numerals and then proceed. Eg : am 65 yrs, my son is 40 yrs younger, what is his age?
Man is born with lots of curiosity.
As I had mentioned in the early paragraph, algebra is a language of patterns. By seeing the patterns one can learn algebra. I am not using the word ‘Variable’, instead I am using whether there is any change or no change. The explicit fashion is brought out (written). The questions are asked by giving the following pattern. What do the students observe?
33+33, 11+9, 13+15…... or an operation that is formed in the following manner:
In column A, there are two columns 1st column is the same number 7 and the second column the number is not the same, hence it can be generalized as 7+ a where a can be assigned any value (number).
In column B, there are two columns 1st column and the second column have the same number, this can be generalized as b + b.
In column C, here again there are two columns, both the numbers are different, can be generalized as c+ d.
That is to say we have used literal letters to formulate the given data of numbers.
NOTE: Instead of addition, you can even take subtraction.
We can take even two-digit numbers and find the pattern:
27 = 10*2+7
46 = 10*4+6
53 = 10*5+3
From these, one can understand how the numerical statement can be generalized.
---------- be continued
No comments:
Post a Comment