What is an example of a research article related to discourse analysis? How does it reveal the link between the research and any real classroom...

I assume you are referring to critical classroom discourse analysis (CCDA). A classic article in the field is Kumaravadivelu's article on CCDA. (Kumaravadivelu, B. “Critical Classroom Discourse Analysis” TESOL Quarterly 33.3 (1999): 453–484.).

In this article, Kumaravadivelu argues that in order to fully understand the relationship between classroom interactions and learning outcomes, educators must understand their student's situatedness with larger discourses, e.g., gender, race, class, colonial status. Writing from the perspective of a classroom observer,...

I assume you are referring to critical classroom discourse analysis (CCDA). A classic article in the field is Kumaravadivelu's article on CCDA. (Kumaravadivelu, B. “Critical Classroom Discourse Analysis” TESOL Quarterly 33.3 (1999): 453–484.).

In this article, Kumaravadivelu argues that in order to fully understand the relationship between classroom interactions and learning outcomes, educators must understand their student's situatedness with larger discourses, e.g., gender, race, class, colonial status. Writing from the perspective of a classroom observer, K. Suggests that traditional qualitative methods of recording classroom interactions (e.g., COLT), as well as more qualitative ways of understanding teacher-student, or observer-class, interactions do not fully capture classroom dynamics. After defining "discourse" as it is used in the work of Foucault and Said, Kumaravadivelu argues that the classroom discourse "like all other discourses, is socially constructed, politically motivated, and historically determined; that is, social, political, and historical conditions develop and distribute the cultural capital that shapes and reshapes the lives of teachers and learners." (472) Teachers who are able to analyze their classrooms in these terms may be able to better understand how what they say to their students is actually interpreted, and be better equipped to evaluate why their students respond the way they do. The presumption is that such understanding can lead to better learning outcomes.

Kumaravadivelu's article is an attempt to decenter teacher-centric methods of classroom evaluation. Rather than simply measuring what the teacher says or does, CCDA attempts to describe and analyze the entire "discourse" of the class, including student responses, and the cultural or social motivations for those reponses. By understanding that classroom discourse is collaborative, the argument goes, we have the opportunity to mobilize student experience to improve learning.