Theory:

     His mother was an affectionate and thoughtful woman. It was proper, she thought, not to discourage the fanciful hopes of her little boy. So she said to him, "Perhaps you may.”
 
     And Ernest never forgot the story that his mother told him. It was always in his mind whenever he looked upon the Great Stone Face. He spent his childhood in the log-cottage where he was born, was dutiful to his mother and helpful to her in many things, assisting her much with his little hands, and more with his loving heart. In this manner, from a happy yet often pensive child he grew up to be a mild and quiet youth.

     Ernest had had no teacher, but the Great Stone Face became one to him. When the work of the day was over, he would gaze at it for hours, until he began to imagine that those vast features recognised him, and gave him a smile of kindness and encouragement.
Explanation:

Being a lovable, thoughtful person, Ernest's mother encouraged her son’s hope as she didn't want to discourage or intervene in his unrealistic thoughts. The very thought of Great Stone Face's arrival got registered in his mind. Also, he started helping his mother with a good amount of house-work as much as he could do at his age, which showed his love for her.
 
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Son helping Mother
 
His youth life was spent on this routine work and Great Stone Face. He spent time staring at the Great Stone Face regularly at the end of his day's work. In this way, though Ernest had no teacher, the Great Stone Face was one such to him. Every time he looked upon it for hours, it gave him a broad smile of kindness and encouragement.
 
Meanings of difficult words:
 
 S. No.
Words
Meaning
1.
Thoughtful
Think and caring about others
2.
Fanciful
Something that may not happen in real life
3.
Pensive
Involved in deep or serious thought
Reference:
National Council of Educational Research and Training (2008). Honeydew. The Great Stone Face I - Nathaniel Hawthorne (pp. 120-125). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.