Making the mathematics of a lesson explicit is an essential part of support-
ing students who struggle with the mathematics of that lesson. Students who
struggle to grasp a particular mathematical idea or develop strategies they can use
to solve mathematical problems efficiently, often need help seeing the mathematics
that underlies an activity, making mathematical connections between different ac-
tivities they have done, or figuring out what to look for as they solve a problem.
In this video, you see the teacher, Heather Straughter, making the mathe-
matics of the problems her students are solving explicit. 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.
Examining the Video Footage
In the first interview, Heather talks about some of her goals for her students. As
she introduces the task, she clearly states her expectations for how students will do
the work. For example, she tells the students they can use one of the cluster prob-
lems, a few of them, or even a problem that is not on the list. Before they start,
Heather asks how many people know where they are going to start. These direc-
tions fit with her goals of having them figure out for themselves how to approach
a problem and solve a problem efficiently in a way that makes sense to them.
After Heather is sure all of the students have an entry point, the students
solve the problem individually. As students solve the problem, she pays close at-
tention to the strategies students are using and decides on the specific strategies
(and the order of the strategies) she wants to be shared with the whole group. As
students share their solutions, Heather asks them questions designed to make the
strategies clear to others and to herself and to highlight the mathematical ideas
within their strategies. She records their solutions on chart paper as they share
them, carefully writing down each step, including those they just did in their
head. By writing their solutions on chart paper for all the students to see, Heather
models a way to record a solution and to write a clear and organized explanation.
Her recording of the strategies also allows the others to see the steps the students
used in the strategy written out fully.
Stephen’s Strategy
In the second interview, Heather says she chose to have Stephen share first because
“His strategy was one that many other students used and would probably be acces-
sible to most students.” As Stephen shares his solution, Heather asks questions and
makes comments. For example, she explains that she is going to put 4 25 in
MAKINGMATHEMATICSEXPLICIT