I think that the speaker of the poem, presumably Whitman, ends up breaking out on his own path rather than that of the "learn'd astronomer" represents a strong presence of Transcendentalism. The Transcendental idea of forging one's own path away from the conventional notion of the good is a heavy idea in Thoreau and Emerson. It is also something that Whitman embraces at the end of the poem. The idea of "formal" and "informal" as seen in emotions is another element that is present. The classroom instruction is seen as sterile and plastic. The Transcendental idea of embracing emotions and using an emotional frame of reference with which to appropriate the world is something that is seen in the closing of the poem. Along these lines, the use of emotions in understanding something as complex as the stars and astronomy is evident when Whitman decides to leave the formal and conforming classroom setting and find his own voice, his own sense of self. In this, Whitman defines himself as a Transcendental persona in the poem.