Theory:

Every tinkle on the shingles
Has an echo in the heart;
And a thousand dreamy fancies
Into busy being start,
And a thousand recollections
Weave their air-threads into woof,
As I listen to the patter
Of the rain upon the roof.
Explanation:
 
The poet helps the readers visualise a warm rainy day from the perspective of a child. The child stays indoors and admires the beauty of the rain outside, lying relaxed on his bed. The rainfall outside makes a beautiful patter sound which can be heard inside.  The sound rings in his ears like music. He does not mention it as simple as rainfall or the sound of rain.
 
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Rain hitting the roof
 
He rather calls it tinkle. A tinkle is usually associated with a pleasant sound, like that of an anklet or a small bell. He compares the sound of rain to a pleasant sound. The rain falls on the shingles, which can be interpreted as both falling on stones or on the tiles that are placed on the roof. As he lay below the roof on his bed, he can listen to the droplets falling above him. The sound creates a deep impact on him, such that it feels like an echo inside the heart, indicating that his heart had been hollow for so long that the rain provided relief by its sound.
 
The sound makes him dream of nearly a thousand fanciful things. Usually, when one is relaxed, he/she can have good dreams in sleep. He dreams of pleasant things that he has always wanted forever. He gets a positive attitude towards his dreams. Not only does it impact his dreams, but it also brings back all his repressed lovely memories. He compares it to a thread being weaved into a loom. He lays there in the bed listening to the sound of the rain, dreaming and bringing back pleasant memories.
 
Screenshot 2021-05-20 144013.png
Thread weaved into loom
 
Words with Difficult Meaning:
 
S.No
Words
Meaning
1
TinkleThe sound of a bell or anklet
2
ShingleStones or the tiles on the roof
3
RecollectionsRemembering previous incidents
4
FanciesDreams and imagination
5
EchoSound caused by hollow spaces
6
WoofWeft, thread woven across the loom
7
LoomThe tool or machine used for making clothes
Reference:
National Council of Educational Research and Training (2006). Beehive. Rain on the Roof -  Coates Kinney (pp 41-42). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.