In the second half of his career, Yeats moved towards a style of poetry that sounded a bit more like spoken language. As a result, although he still uses alliteration in this poem, Yeats blends it into his speaker's seemingly causal monologue.
The early /k/ and /s/ alliteration provides a good example of how the speaker uses alliteration casually, rather lyrically—that is, as a means of holding the poem's images together rather than creating high-flown poetic beauty:
I walk through the long schoolroom questioning;
A kind old nun in a white hood replies;
The children learn to cipher and to sing,
To study reading-books and history,
The first alliterative pair of "questioning" and "kind," with those sharp /k/ sounds, subtly evokes the speaker's brief interruption as he questions this nun. The /s/ alliteration in "cipher," "sing," and "study," meanwhile, simply lends a sense of unity to this list of the children's school subjects.
Most of the poem's alliteration function much like the above. One noticeable exception is the final stanza, which is by far the poem's most lyrical. Here, /b/ alliteration flows throughout the stanza, as in these lines:
O chestnut tree, great rooted blossomer,
Are you the leaf, the blossom or the bole?
O body swayed to music, O brightening glance,
The shift to a more lyrical tone is clearly signaled by the speaker's repetition of "O," an old-fashioned form of the word "Oh," meant to capture a sudden burst of strong emotion. This burst of emotion is conveyed through the strong /b/ sound, which highlights poetic words like "blossom," "body," and "brightening." By repeating this strong sound with poetic words throughout the stanza, the speaker creates a lyrical summary of the poem's many concerns.