What is William Wordsworth's view on children and nature in his writings?

"The Child is the Father of the Man."

The positive and life nurturing impressions that get deeply etched in our minds when we are small children remain with us for the rest of our adult life. These early spiritual life sustaining childhood memories form the foundation of our adulthood and determine our personality. Hence, a happy childhood filled with pleasant life giving positive spiritual influences -here symbolized by the pleasant associations linked to the beautiful rainbow - is the 'father' or the creator or the architect of a mature adult, the 'man.'

William Wordsworth was a Nature poet who worshipped Nature as his God and it was his main source of spirtual comfort  and escape from all the cares of this world. His association with life giving and life sustaining Nature began even when he was only a child and remained with him till his death.

In this short lyric, the 'rainbow' symbolizes the life sustaining and life nourishing goodness of Nature. The sight of the beautiful rainbow which he saw when he was only a child is deeply etched in his memory and the same joy that he experienced when he saw it as a child contiunes to remain with him through his adulthood. He desires that this same childhoood joy should continue to sustain him even in his old age. Wordsworth says that he would rather die than not being able to experience the same joy that he experienced when he saw the rainbow when he was a small boy after he becomes an old man.

The memory of the beautiful rainbow and its pleasant associations form the link between his childhood, adulthood and his old age:past, present and future. Wordsworth concludes the poem by expressing the desire that each day of his existence be linked with the next by beautiful and simple natural sights like the rainbow.

For Wordsworth the life nourishing and life sustaining memories of beautiful natural sights like the rainbow are very precious and he deeply desires that they link each day of his life on this earth and remain with him till his death.