Characterizing Responsiveness in Middle-Grades Mathematics Classrooms

• In Event: 54.044 - Exploring Varied Approaches to Supporting Responsive Teaching in Science and Mathematics

Abstract

Discourse, by its nature, is responsive and relational (Bahktin, 1986; Halliday, 1978). We describe classroom interactions that build on students’ thinking and in which students help to determine the direction of lessons as highly responsive. Despite widespread support for this type of instruction in the larger educational community, responsive interactions are not the norm (see Lemke’s (1990) description of triadic dialogue in science; Mehan’s (1979) IRE exchanges in primary classrooms; and Pimm’s (1987) clozed questioning gambit in mathematics). An important part of the development of responsive teaching is describing and operationalizing responsive interactions in action so that these characterizations can inform work with teachers. In this poster we contribute to the conversation about responsive teaching by describing a framework for responsiveness during whole-class discussions and using this framework to document variation in responsiveness across middle grades mathematics classrooms.

Our perspective on responsive teaching is grounded in sociocultural theories of teaching, learning, and interacting. In his discussion of speech genres Bakhtin (1986) says, “Utterances are not indifferent to one another, and are not self-sufficient … Every utterance must be regarded primarily as a response to preceding utterances” (p. 91). Our stance is that participating in mathematical discourse is inherently a responsive act for listeners and speakers. In that vein, we define responsiveness to students’ mathematical thinking as a characteristic of interactions that describes the extent to which students’ mathematical ideas are present, valued, attended to, and taken up as the basis for instruction.

The responsiveness framework below was developed using the constant-comparative method (Strauss & Corbin, 1998) to analyze video recordings of 183 mathematics lessons across 12 grades 5–7 classrooms. The unit of analysis was a segment, which we define as a series of turns of talk with a common focus (e.g., activity or strategy). In our framework, responsiveness occurs in varying degrees on two dimensions. In order for teachers to be responsive, students’ mathematical ideas must be expressed. As such, characterizing students’ mathematical thinking is a necessary component of describing responsiveness. Thus, we holistically categorize segments in terms of two interrelated features of whole-class discussions: (a) students’ mathematical contributions, and (b) moves teachers enact in response to these contributions (Figure 2).

Figure 2. Responsiveness Framework for Whole-class Discussions

Categories for student contributions express increasingly sophisticated contributions ranging from no contributions (none); to recalling facts and performing calculations (minimal); to sharing mathematical information, explanations, or strategies (considerable); to providing justification or participating in mathematical argumentation (substantial). Categories of teacher moves reflect the extent to which students’ mathematical ideas are made public and the basis for instruction: low (ignoring, brushing-off, evaluating student contributions), medium (revoicing student ideas, asking probing questions), and high (directing students to engage with others’ ideas). We used this framework to analyze the responsiveness of whole-class discussions in middle grades mathematics classrooms and found that there are multiple ways to be responsive to student thinking. During the session we will describe variation in responsiveness by comparing responsiveness profiles for multiple classrooms.

Authors

• Jessica Pierson Bishop, Texas State University

• Julia Przybyla-Kuchek, University of Georgia - Athens

• Hamilton Hardison, University of Georgia - Athens