MAKINGMATHEMATICSEXPLICITunderlies an activity, making mathematical connections between different activ-
ities they have done, or figuring out what to look for as they solve a problem.
Examining the Video Footage
MichaelFlynn chose to work with this group of students because they seemed
to be missing or not understanding important aspects of the mathematics of the
activity, and most were trying to count all the dots during the three seconds he
was showing the image. It may be that they did not realize that the ways the dots
are arranged could help them figure out how many there are particularly in rela-
tion to 5 or 10. They also might not have realized they can figure out smaller
subsets of the quantity first and then combine the subsets to find the total.
In the second interview, Michael said of the group of students seen in the
video, “What they need [are] strategies for doing this activity because it’s all about
paying attention to the right thing and not trying to count.” Throughout the
video, you see him helping the students by making the strategies students are us-
ing explicit, nudging them a little further in the strategies they are using, and
making the mathematics in the activity explicit. He does this not by telling them
the strategies to use, but instead by asking them questions and making comments
about their strategies and thinking. He asks them to explain in detail what they
are seeing or doing, and then he repeats what they say and asks them if his restate-
ment is correct. This helps the students think through their strategies and at the
same time makes them clear for others. In asking the students whether they agree
with the strategy being presented, Michael gets everyone involved in examining the
strategies. His emphasis with the students is on how they got the answer; however,
through this discussion, students with an incorrect answer often correct themselves.
The following are some examples of the Michael’s questions and comments
that helped make explicit for everyone the strategies students were using and helped
the students further develop their strategies for doing the Quick Image activity.
After doing a couple of easier images with the students and asking them to share
their strategies, Michael asks, “So when I show you the image, what are you paying
attention to? What are you trying to remember in that three seconds I give you?”
Asking these questions highlights that there are certain things that are useful to pay
attention to in general as students do this activity. It also helps them focus on the
strategies they are already using.One student shares that she knows there are 10 boxes in 1 frame and that if
1 row is filled, there are 5 dots, and if 2 rows are filled, there are 10 dots.
Michael focuses on this strategy and asks, “When you’re looking at the rows,
how does it help you when I’m showing you something for three seconds and
then covering it up?” Through this question and follow-up questions about the