Semantic Relations and Student Participation in Middle School Mathematics Classrooms

• In Event: Using Systemic Functional Linguistics to Study Mathematics Classroom Discourse

Abstract

From a sociocultural perspective, coming to participate in a community, such as a mathematics classroom community, does not lead to learning but can instead be defined as learning itself (Lave & Wenger, 1991). In particular, Lemke (1990) argued that learning a subject is a process of coming to successfully participate in discourse that contains the terms and semantic relations that construe meaning in the subject. Semantic relations refer to the meanings that are made between signifiers, such as taxonomic or circumstantial relationships.

To what extent do students, rather than teachers or textbooks, express the semantic relations in mathematics classroom discourse? This study used video data of multiple lessons from 12 middle school mathematics classrooms from urban and suburban districts in two states. Analysis relied on Systemic Functional Linguistics (Halliday & Matthiessen, 2003) and, specifically, thematic discourse analysis (Author, YEAR), which was used on whole-class discourse to identify mathematical terms and map the semantic relations between terms. Students’ roles in expressing these relations were then considered.

Results included variation between classrooms with respect to students’ participation in forming the semantic relations. Categories of participation included (a) students predominantly uninvolved in expressing mathematical semantic relations, (b) students supplying mathematical terms into semantic relations expressed by the teacher, and (c) students expressing full mathematical semantic relations. The following interactions, from early algebra lessons on variable, illuminate distinctions between (b) and (c).

Ms. Wyncott: So we set up that the unknown is x. Our unknown is what in this situation? Brandon?
Brandon: The distance between our jumps.
Ms. Wyncott: The distance between our jumps? Okay, so how big a jump is. That’s our unknown. So x is how big the jump actually is.

Ms. Wyncott built links between linear expressions (5x+8) and the problem context, but the student turn supplies only a portion of the semantic relation. Brandon utters only a phrase about the jumps, whereas Ms. Wyncott first utters the beginning of the relation and then the full relation, “So x is how big the jump actually is.” This type of student participation differs from that below, in which relations between numerical operations and the problem context are uttered entirely by a student.

Ms. Albert: Alivia, would you mind sharing a little bit of that?
Alivia: For the first [frog], we did two times five because the jump could have been between two and six decimeters. And the five came from how many jumps she took, and then we get ten plus eight, which is where her starting point’s at, and you get eighteen.

This examination of student participation is significant because it traces the semantic relations carrying mathematical meaning and reveals what opportunities students have to voice those relations, which has deep implications for learning when learning is viewed as participation. One may also reinterpret well-known discourse patterns such as Initiate-Respond-Evaluate (Mehan, 1979) by recognizing that they involve teachers building a semantic relation into which students merely supply a term, contrasting with interactions where students formulate relation themselves.

Author

• Samuel Otten, University of Missouri - Columbia