her work with them in a small guided math group to develop their under-
standing of the concept. She discussed what doublingmeant, asking them to
come up with their own definitions. She used cubes so that the students had
the experience of actually seeing objects being doubled and then posed a
problem in a familiar context about double scoops of ice cream.
In “Focused Instruction on Quick Images,” Michael Flynn works with a
small group of second-grade students on an activity called Quick Images
(Russell et al. 2008g). He decided to pull this group of students together be-
cause he thought they needed more work with this activity. During the
session, he helps students develop strategies that help them visualize the
dots in the image so they can accurately record them. For example, he asks
them questions about and comments on their own observations. He asks
them to explain in detail what they are seeing or doing, and then he repeats
what they said and asks them if his restatement was correct.
In “Solving Multiplication Problems,” Heather Straughter works with her
fifth graders on a set of cluster problems (Kliman et al. 2004). Heather works
hard to make explicit the mathematics of the problems her students are solv-
ing. She does so through her structuring of the lesson, through the directions
she gives, through the questions she asks, and through the decisions she
makes about whom to ask to share a strategy.
These essays and episodes about teachers’ practice provide insight into what
it means to be explicit when teaching mathematics—not to “tell” or “pre-
scribe” but to guide and support with purpose and forethought.
Questions to Think About
What do these essays and videos bring to light about what it means to be ex-
plicit with students who struggle?
What strategies do these teachers use to make the mathematics explicit?
What evidence do you see that students understand concepts that the teachers
are highlighting in their instruction?
MAKINGMATHEMATICSEXPLICIT