Question

how did miss sullivan understood helen and taught her according to her ability and needs?

Answer 1

Miss Sullivan was an extraordinary teacher. The world is full of ordinary teachers who just teach shallowly. Miss Sullivan touched the depths of Helen's soul and brought light to her darkened world. 

The day she arrived at Helen's house, Helen called that day the most important day of her life. Helen compared the arrival of her teacher to the shining of 'light of love' in her darkened life. Miss Sullivan took unprecedented pains to teach Helen manual alphabet. Since Helen was suffering from hearing as well as visual disabilities, Miss Sullivan really had to work very hard to teach Helen the alphabet. Initially Helen did not accept all her explanations, techniques and methodology, but after Miss Sullivan won Helen’s confidence, Helen had complete faith in her.  Miss Sullivan understood Helen thoroughly. She knew how to make things clear to her. Whether it was teaching her the difference between ‘w-a-t-e-r’ and ‘m-u-g’ or teaching her the word ‘d-o-l-l’ for both the dolls, Miss Sullivan knew the methodology.

 

 In the 7 chapter, Helen praises Miss Sullivan in the following words: "Thus I learned from life itself. At the beginning I was only a mass of possibilities. It was my teacher who unfolded and developed them. When she came, everything about me breathed of love and joy and was full of meaning." It was Miss Sullivan's genius, her sympathy, her loving tact which made the first years of Helen's education so beautiful. Miss Sullivan made learning easy and fun-filled for Helen.

 

Answer 2

Children learn by repetition, their basic knowledge of pronunciation and word association, hence depends upon it.
With deaf children, this is where the difficulty arises,since for them the pronunciation of words is difficult to understand and recreate.
In Helen's context her blindness, coupled with deafness, posed an almost extraordinary challenge for Miss Sullivan, which she overcame in innovative ways.
She taught Helen to spell by spelling out the words in the palm of her hand, then making her feel the object; in this way Helen was able to associate words to objects.
Even when it came to complex things like abstract things like emotions, Miss Sullivan was able to make her identify them, hence opening her eyes to a new world. 
After Helen learned how to spell, Miss Sullivan made her progress on to reading, wherein she devised a fun way to teach Helen how to form sentences, with the help of the objects around her.