that she should get the same answer to a problem no matter what way she solves
it. She knows she can take away the quantity in parts and uses 10 as an easy num-
ber to take away. She counts backward by 10s and not by 1s. It seems as though
Yamilka is still working on how to figure out whether she should add or subtract
particular chunks of numbers and making sure what she does with the numbers
matches what is actually happening in the problem. She is also still working on
figuring out whether her steps and her answer make sense and not just whether
her answer matches the answer she got using a different strategy.
In a part of the interview not seen in the video Ana says:
Yamilka said you never add when you’re taking away, I had to think “OK, this is
what she’s taking out of this situation.” But it was very interesting because we had
been adding up to solve subtraction problems. But the kids struggle with that be-
cause they could do it but they did not know why it was working, and that was
something that I wanted to continue exploring.Ana’s assessment of the students’ understanding of subtraction indicated to her
that she has more work to do to address the range of understandings within the
group. Some, like Carlos, had developed some useful strategies and were learning
to apply them flexibly. Some, like Kassandra, will need more help in using strate-
gies in which the value of the numbers are clear to them, and most likely all need
more practice in understanding the relationship between addition and subtrac-
tion. As she continued to work on subtraction with her students, Ana planned to
continue to use familiar contexts. For example, Yamilka’s family owned a store,
so Ana planned to introduce a “store” context so that children could practice
giving change. Working with prices and giving change would give them the
opportunity to use a variety of strategies, including adding up or counting back,
and reflect on the relationship between addition and subtraction. Ana planned
to continue to focus on understanding the operation of subtraction and developing
efficient strategies for solving subtraction problems in the next series of lessons.
LINKINGASSESSMENT ANDTEACHING