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Classroom Discourse and Teacher Change
Education reform practices encourage student-led discourse and student-to-student discourse about curricular content. Such ‘socially mediated’ construction of knowledge is considered to promote deep and sustained learning.
Many teachers recognize the potential for such interactions but they also wrestle with how to provide that environment while ensuring that the ideas presented relate to the curricular agenda.
Students’ original contributions are important to productive classroom discourse. But teachers need to monitor where the discourse is going, and should develop some criteria for deciding when the class has reached the goal. Teachers need to learn the ‘stepping in and out’ that’s so important to promoting productive discourse. Mathematical talk is a skill unto itself that deserves instructional attention, according to UW-Madison education professors Mitch Nathan and Eric Knuth.
Teacher education programs and professional development programs should provide preservice teachers and practicing teachers with experience participating in, and facilitating, productive mathematical discourse, they say.
Nathan and Knuth recently worked with a sixth grade mathematics teacher, Ann (a pseudonym), to analyze the nature of whole group discourse that occurred in her classroom. Over the course of a two-year collaboration, Ann changed her classroom practice to better reflect her vision of reform-based mathematics instruction.
Nathan and Knuth videotaped Ann’s classroom teaching. Then they all reviewed the tapes, observing how Ann used analytic scaffolding and social scaffolding. Examples of analytic scaffolding include a teacher describing student contributions to a discussion in more precise mathematical terms, or a teacher highlighting particular aspects of student contributions in light of their potential use in introducing more advanced mathematical ideas. Social scaffolding aims to encourage classroom interactions, for example, asking students to explain their solutions to problems or eliciting contributions to whole-class conversations from all students.
Ann wanted her students to value all of the opinions expressed in class. She also wanted her students to learn that mathematics problems could be solved by many methods. Ann was convinced that many students inappropriately looked for a solitary method when solving mathematics problems. Ann’s beliefs about student learning and development can be summarized by two statements: (a) students learn best from other students, and (b) students learn best through class participation. Ann solicited a wide range of opinions on mathematical ideas and asked students to state their agreement and disagreement with ideas presented by her and other classmates.
But despite her belief that students prefer to learn from their peers, and despite her favorable evaluation of the level of participation in many of her lessons, very little student-to-student talk was evident during Year 1. The majority of analytic information flowed vertically, either from the teacher to the class (71.4% of the time) or from students to the teacher (27.1%).
Ann’s actions did not successfully promote much horizontal information flow among the students. She was the central player in all class interactions. Students rarely participated in exchanges unless called on. They relied much more on the teacher for information rather than other students. They rarely used discourse to construct their own conceptions, test hypotheses, or question other students’ ideas.
During professional development sessions in the summer following Year 1, Ann and the researchers reviewed the classroom videos, evaluating information flow and scaffolding. Ann began to reconsider some of her classroom tactics as she realized that some of her most important goals for peer interaction and learning through participation were not being met.
Ann decided to remove herself from the role of conversational “hub” more often in Year 2, staying out of class discussions to leave more room for students to think, ask questions, and publicly express their own ideas. During Year 2 Ann frequently invited students to speak. Students responded positively to Ann’s overtures and held up the mathematical end of the discussion. In response to this shift in practice, Ann saw tremendous growth in student-to-student mathematical talk. She was aware of the greater amount of class time these interactions took. Still, from Ann’s perspective, students were learning that mathematics included forming and expressing one’s ideas, not simply asking the teacher or doing calculations.
In Year 2 Ann’s analytic scaffolding dropped to about 50% of all whole class exchanges. Social scaffolding remained relatively unchanged, however, at around 20%. Thus, Ann continued to guide student talk and manage the classroom, while stepping aside to let the math talk happen around her. Ann relied on students to compensate for her relative analytic absence. The proportion of analytic scaffolding students provided each other during classroom exchanges increased more than 15-fold over the 2-year period.
The increase in students’ social role suggests that, as students took over the discussion in the mathematical realm, they also recognized a need to help direct the classroom social interactions to conduct these conversations. Students who participate more frequently in discussions also realized the need to reinforce accepted rules and establish new norms.
In her role as class discussion facilitator, Ann kept discussions going, got students involved, solicited views, and reminded students of the classroom’s social norms. This shift succeeded in stimulating student-to-student talk.
Patterns of whole-classroom interactions changed substantially. Students frequently addressed one another directly or spoke to the class as a whole. Ann’s statements to the class during Year 2 were more often social in nature than in Year 1, emphasizing management issues and the social facilitation of student-driven discussions.
Although students interacted more frequently, discussions often lacked rigorous argumentation and evidence, and lacked convergence toward acceptable mathematical ideas and conventions. With no clear mathematical authority participating, student ideas were offered publicly for others to pick up, refute, or ignore, often with no basis for evaluation other than opinion.
On the surface, Ann realized her goals of discourse-based teaching. Yet under deeper inspection, she questioned whether students were learning the mathematical content. Even though students were more vocal, Ann felt less certain of where individual students stood in their understanding of new concepts. That may be due to two things. Ann’s large shift to emphasizing social scaffolding led to a shift in her attention away from the specific mathematical talk among students. Also, Ann no longer used prompted discourse to ascertain student knowledge.
Students showed they can fill the conversational void, but they may not, and often cannot, serve as the analytic authority necessary to promote correct understanding about all of the content matters.
Nathan and Knuth say discourse of this nature does not come about simply because the teacher creates space for it. There is still a need to mathematically support students’ learning of content during classroom interactions. Ideally, teachers provide such support as they strike a balance between the social and analytic demands, that is, when students’ own social constructions of mathematical ideas are also connected to the ideas and conventions of the mathematical community.