This statement from the NCTM Principles and Standards for School
Mathematics reveals the emphasis on communication in mathematics
instruction, a decided change from when mathematics in the elementary
school focused solely on the mastery of arithmetic operations. Not only does
talk help students solidify their understanding, it also provides a window
into children’s thinking. In regard to their students who are struggling,
teachers have often been surprised by something their students express that
indicates understanding or a question a student asks that indicates confu-
sion. In either case, the information the teachers learn informs instruction.
When these students are given the opportunity to justify their answers, dis-
cuss similarities and differences among strategies, and ask questions, teach-
ers have found that they are more prepared to solve a variety of problems
(Behrend 2003).
The teachers who wrote these essays and appear in these videos share a
fundamental belief that their struggling students can learn mathematics
along with their peers and that promoting classroom talk aids their mathe-
matical understanding. Including all students in classroom discussion is
complex and requires careful planning (Hiebert et al. 1997; Boaler 2008).
Students who are struggling in mathematics need support to actively and
productively participate in whole-class discussions. These teachers strive to
make their classroom a safe place for all of their students, one where clear
routines and expectations for behavior are established, taking risks is
encouraged, and mistakes are viewed as opportunities for learning.
Meticulous preparation before discussions and documentation of stu-
dent thinking during and after the discussions characterize these teachers’
practice. They anticipate concepts or strategies that might be difficult for
their students who struggle, they plan accommodations, and they find ways
to take notes afterward to assess what students understood and what confu-
sions might have emerged. These teachers also provide multiple entry points
into discussions so that a variety of students can participate. For example,
some of the teachers post strategies the class has developed to be used as a
reference point for discussions. Others provide a variety of models and rep-
resentations that allow students to visualize the problem and organize their
thinking. When sharing strategies, the teachers begin with one that is acces-
sible for all class members, and the teachers record all students’ contribu-
tions, using notation that others can follow.
These teachers often structure small-group time with students who find
it difficult to participate in the whole-group discussion. This time might be
used to review an activity that they introduced in the whole group or to pre-
view a sharing discussion by helping the students rehearse one of their
BUILDINGUNDERSTANDINGTHROUGHTALK