the mathematics content they are responsible for teaching and how students learn
it. They identify the central mathematical concepts, recognize how concepts are
related to each other, and understand how these concepts build from content
covered in earlier grades. They situate these concepts in a variety of representa-
tions and contexts familiar to students from their daily lives. They assess the cor-
rectness of students’ reasoning as students explain their solutions to a problem;
furthermore, if a solution is incorrect, the teachers analyze that reasoning to
determine what is correct about the students’ process and where the thinking has
gone awry. All of this knowledge—together with a deep sense of care and respect
for their students—is applied to the goal of having each student make sense of the
mathematics.
A reader might ask, “How can I put so much effort into one or two or a hand-
ful of students when I am responsible for so many?” The answer: The knowledge
exhibited by the teachers in this volume and many of the techniques they speci-
fy and elucidate enhance the learning of allof their students. When a teacher is
explicit about the mathematics of a lesson, provides additional representations,
and helps students figure out how to participate in whole-group discussion, it
serveseverystudent in the classroom.
Indeed, the challenge of reaching the range of learners in a classroom isgreat.
There is much to learn and much to do. But, as illustrated by My Kids Can, the
rewards are even greater.
Deborah Schifter
Education Development Center, Inc.ixFOREWORD