In what passages in James Joyce's "Araby" can one see how dialectical materialism corresponds with Bakhtinian theories of polyphony and carnivalesque?

"Araby" is a story about a boy’s first brush with desire. He has a crush on a girl. When she notices him and speaks to him, she asks if he is going to Araby, the local bazaar; the boy, seeking to impress her, says he is and promises to bring her something from the fair. His desperation to get to the fair has less to do with getting a present and everything to do with proving his devotion and maturity. He wants to be an adult, and love this girl like an adult. When he gets to the fair, it is not what he had expected; he is so put off by the manner of the one shopkeeper who is still open that he decides to buy nothing.
It might seem odd to try to pin grandiose terms like “dialectical materialism” and “dialogism” to such a slim slice of life, but it can be useful to think about the story in these ways to understand what forces are at play. Dialectical materialism—the assertion that thought or consciousness is the product of labor—underpins the boy's deterministic expectations. The girl is defined by her visible attributes, to which the boy is terrifically sensitive (even while she is talking to him, at the longed-for moment of acknowledgment, he is noticing how she looks, “The light from the lamp opposite our door caught the white curve of her neck, lit up her hair that rested there and, falling, lit up the hand upon the railing. It fell over one side of her dress and caught the white border of a petticoat, just visible as she stood at ease.” The bargain he happily makes with himself is simple: he will go to Araby on her behalf; he will “bring [her] something,” a present she has not asked for but which he thinks will be sufficient to secure another conversation with her, during which he can relive for her the experience of Araby and develop their relationship further. To crudely characterize this exchange in “dialectical materialistic” terms, by performing the “labor” of visiting the bazaar, he will in effect “produce” the opportunity to talk to the girl again, and own for himself her image that tantalizes him so.
Of course, this formulation is spoiled by his real experience getting to the bazaar. First, he is made late by his uncle, who does not return home until the bazaar is nearly closed; then, after rushing to it and arriving just before closing time, he is put off again by the manner of the shopkeeper, as shown below:

Observing me the young lady came over and asked me did I wish to buy anything. The tone of her voice was not encouraging; she seemed to have spoken to me out of a sense of duty. I looked humbly at the great jars that stood like eastern guards at either side of the dark entrance to the stall and murmured:
“No, thank you.”

Bakhtin’s idea of polyphony, or dialogism, can be seen as opposed to dialectical materialism in that, instead of labor as the determining element in understanding reality, language is paramount, in particular the way different forms of speech or discourse interact. In this case, part of his reaction to “the young lady” is that she is flirting with the two boys in a way that is not only inaccessible to him, but is counter, perhaps, to the way he thinks boys should talk to girls. Certainly her casual exchange is at odds with how he would like to talk to the girl he likes. Another Bakhtinian touch is his sensitivity to her change in tone when she addresses him: she is not flirting with him; she is speaking “out of a sense of duty.”
The end of the story, in which he says “Gazing up into the darkness I saw myself as a creature driven and derided by vanity; and my eyes burned with anguish and anger,” can be interpreted as a realization of the delusional nature of his desire for the girl and his mission in coming to the bazaar. It’s not just that he sees that she is perhaps not what he wanted, or that he is not brave enough to do what he thinks will get her; it’s that his suppositions about how the world works have been undermined. He realizes that his way of thinking about the world is only one insignificant piece of a much larger conversation, one in which he has yet to learn how to participate.