Levels of Discourse in a Mathematics Classroom

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The translation model for instructions suggests
that learning is enhanced if students can use
multiple ways to investigate the same
mathematical concept and make translations
between and within different modes of
representation. Students can use manipulatives,
pictures, written symbols, verbal symbols and
real-life contexts to explore and represent the
concept (Lesh, 1979).
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Deep learners in any discipline must possess the
ability to interact with ideas, offer evidence
for ones propositions, and react thoughtfully
and constructively to others propositions. The
skills that students develop in
teacher-orchestrated classroom arguments reflect
those characteristics of disciplinary learning
and help them develop rigorous and sophisticated
uses of mathematical language.
Choppin, J. M. Teacher-orchestrated Classroom
Arguments Mathematics Teacher 101, no. 4 (2007)
306-310
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Learning how to orchestrate classroom discussions
looks much like learning in any demanding
profession and, coincidentally, quite different
from traditional professional development. To
change teaching practices, teachers need to
collaborate and reflect in the context of a
professional community as they gain experience in
the new practice.
Choppin, J. M. Teacher-orchestrated Classroom
Arguments Mathematics Teacher 101, no. 4 (2007)
306-310
40
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The strong teacher role articulated in the vision
of discourse is at odds with some conceptions of
student-centered discussion. It represent a
fundamental change from traditional practices for
both teachers and students. Initially, at least,
teachers need to provide explicit support and
modeling to help students learn to reflect on and
build on their peers explanations.
Choppin, J. M. Teacher-orchestrated Classroom
Arguments Mathematics Teacher 101, no. 4 (2007)
306-310