parentheses because this was a step Stephen did in his head. She asks him to fully
describe each step he took, for example, she asks him to continue his counting by
25s when, initially, he only repeated the beginning of the count. She asks him how
he figured out 6 25 so quickly to highlight the understanding he was using to
solve the problem. She asks other students if they solved it in the same way: “You
broke up the 46 right away.” Her questions and comments help clarify the mathe-
matics of how Stephen solved the problem, help Stephen articulate his thinking,
and make connections to the strategies other students were using.
Sam’s Strategy
Sam’s strategy was one Heather thought was mathematically powerful but might
be less accessible to many of the students in the class, so she decided to have Sam
share his strategy after Stephen. Her questions and recording of Sam’s strategy
help other students understand his strategy. She has him explain each of his steps
and she records each step, even the steps he “just knew” and therefore probably
didn’t write down for himself. By writing the steps he “just knew” in parentheses,
she is trying to make his reasoning apparent for students who might not “just
know” those steps. For example, she asks Sam questions such as “How did you do
50 25 so quickly?” which encourages him to think about and explain what he
knew that helped him solve that step of the problem.
Stephen’s Mistake
When Stephen says that his second strategy was similar to Nashaya’s, but that he
didn’t get the correct answer, Heather uses his mistake as a learning opportunity not
only for Stephen, but for the whole class. She uses his mistake to highlight the im-
portant mathematical ideas that students need to consider as they solve the problem.
She asks another student to listen carefully as Stephen explains his mistake
because she thinks the student had made a similar mistake. This emphasizes that
everyone can learn from a mistake and highlights that the students use similar
strategies. When the class tries to figure out Stephen’s mistake, Heather asks the
students to look at the strategies that were successful and compare them to
Stephen’s strategy. She tries to help them see what components the other strate-
gies include that Stephen’s did not. She uses what Nashaya did correctly to help
the students figure out what Stephen did incorrectly. She focuses on one step that
Nashaya did that connected to Stephen’s mistake: “Why did [Nashaya] add 10 25
four times? Because that’s key. Why is that so important?” Through this question,
she highlights that there is an important idea here to pay attention to when mul-
tiplying these numbers. She summarizes the mistake for everyone in the end, “It
Solving Multiplication Problems