focus on how they can help that to happen. “[Instead of asking] ‘What are my
students’ deficits?’ classroom teachers who include all learners tend to ask, ‘What
are their strengths?’ Beginning with what students can do changes the tone of
the classroom and builds confidence in reluctant learners” (Tomlinson 2003).
These teachers also recognize that understanding mathematics means
more than mastering a set of number facts or using a particular manipulative
to solve a problem. Students need to understand the mathematics deeply
enough to flexibly apply concepts in a variety of situations. A student may
do well solving addition problems with linking cubes, for example, but when
the same numbers appear in a story problem or a game, that student may be
unable to make connections to his prior work. These teachers use assess-
ment to identify where students are not making sense of a concept, then
help students see the connections among various representations and con-
texts and use what they know to integrate new knowledge.
Each of these examples of linking teaching and assessment begins with
the teacher’s understanding of the mathematical content, how mathemat-
ical ideas develop, and what teaching strategies are most likely to be effec-
tive in reaching struggling students. The teachers in these episodes bring
this vast array of knowledge to each decision that they make. Although the
content ranges from counting to fractions, the processes the teachers go
through have many similarities. They find ways to manage their classroom
routine so that they spend targeted one-on-one or small-group time with
students who are struggling and make adjustments as they monitor what
and how their students are learning. The information garnered from these
ongoing assessments allows the teachers to carefully consider the sequence
of activities and the variety of models and representations they offer their
students in order to build an understanding of key mathematical concepts.
In “Assessing and Supporting Students to Make Connections,” math spe-
cialist Ana Vaisenstein writes about her experience supporting a group of
students who are not fluent in counting by numbers other than one. She
provides a variety of activities, routines, and games designed to strengthen
students’ conceptual understanding by highlighting the relationships across
all of these learning opportunities.
In “The Pieces Get Skinnier and Skinner,” Marta Johnson writes about her
work with fourth-grade students to compare fractions based on numeric rea-
soning. She provides them with a variety of activities and models, all the
while adjusting her teaching based on what she discovers about what stu-
dents are learning and where they are confused.
LINKINGASSESSMENT ANDTEACHING