PAM: So what should I do with him then?
MICHAEL: I would do exactly what you were doing with Robert. That was
perfect. We’re doing a similar activity tomorrow.
PAM: But Steven is too quick to work with Robert.
MICHAEL: Steven needs to slow down. That’s half his problem. He just goes
on autopilot and does things without understanding. Do exactly what you
were doing with Robert and help Steven make those connections.
PAM: Should he build it to 10 floors?
MICHAEL: If he has to, then let him.
PAM: I don’t think he will. He really does know when to double.Pam was still missing the big mathematical point in the lesson. She really
wanted her students, particularly Steven, to work at the same pace as the rest of
the class. It was easy for her to worry that the boys were falling behind and natu-
ral for her to want them to “catch up.” However, I strongly believe that if we rush
students at the expense of their understanding, then we make it harder for them
to develop sound mathematical ideas. This math activity was about much more
than simply having the correct numbers in the table, and the next day’s lesson
would prove that.
MICHAEL: Well tomorrow’s activity is pretty much the same as today’s, but
the tables will go to 6 rows before jumping to 10. We’ll see if he really gets
it. I’m betting he’ll double the sixth floor to solve for the tenth. What do
you think?
PAM: OK, you made your point. He was just moving so fast with the pat-
terns. I thought he would get it.
MICHAEL: In terms of computation, he does get it, but working with the tables
is pretty abstract stuff. He’s going to need a lot of support to make sense of it.Implementing Accommodations
The following day, Steven did exactly what I predicted. Pam laughed and I jok-
ingly gave her an “I told you so.” For the rest of the period, she worked with Steven
much the same way she worked with Robert. She spent her time helping him con-
nect what was happening in his building to what was happening on the table.
This process was much slower, but Pam was beginning to realize that although
he was getting the correct answer very quickly, he didn’t understand what he was
doing. Students really have to understand what happens as the buildings grow to
understand why doubling the fifth floor would work. The students in my class who
noticed that doubling would work were able to justify in a few different ways dur-
ing our discussion at the end of the period.
Collaborative Planning