approach is supported by research, such as the Cognitively Guided
Instruction Project (Carpenter, Fennema, and Franke 1996). This primary-
grade mathematics project integrated research findings on how children
think about mathematics with findings on how teachers use this knowledge
when making instructional decisions. The teachers in the CGI project
found that when their students with learning disabilities solved problems
with representations and contexts that were familiar to them and with
manipulatives and tools that made sense to them, they were able to under-
stand numerical operations conceptually and solve problems (Hankes
1996). Other studies have demonstrated that instead of remediating
deficits, encouraging children to develop computation strategies based on
their own knowledge increases understanding of operations as well as
knowledge of number facts for at-risk students and students with mild dis-
abilities (Thornton, Langrall, and Jones 1997; Karp and Voltz 2000;
Behrend 2003).
The teachers who wrote these essays help students establish routines so
that they can function independently by taking advantage of resources such
as charts and posters in the classroom; developing a series of questions to ask
themselves about a problem; and building on each success so that it becomes
a reference point in the future. Students learn to ask themselves questions
such as, “How did you know that?” and “What did you think about next?”
through carefully scaffolded instruction.
The themes in this section tie in closely with other sections of the book,
in particular the Linking Assessment and Teaching section. One teacher,
for example, had expressed interest in writing about the responsibility
theme, only to realize through close assessment that her student was a pas-
sive learner because she had major gaps in her understanding of math con-
cepts. As a result, she shifted her focus to the teaching and assessment cycle.
You will also recognize aspects of the Making Mathematics Explicit essays
here as teachers build their students’ abilities to reflect and take responsi-
bility for their learning by highlighting mathematics concepts in activities
and making them accessible for their students.
Kristi Dickey teaches first and second grade, looping or keeping the same class
for two years. In “Becoming a Self-Reliant Learner,” she describes her work
with a first-grade student who was a bystander, not engaging in the work of
the classroom. Kristi describes how she developed a routine with the student,
repeating the problem that the class was solving to make sure the student under-
stood what the problem was asking and checking that she had what she needed
to solve the problem. Kristi also asked her questions, such as, “Now,you have
TAKINGRESPONSIBILITY FORLEARNING