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During our session at NCTMNOLA, participants explored several games that offer opportunities to encounter mathematical content and processes associated with the Common Core State Standards for grades K-2.
As the teachers played the games, or observed as others played, we asked them to keep an eye out for meaningful mathematical moments that might be shared with the entire group.
One of the games introduced many of the teachers to a new manipulative - a rekenrek.
A teacher in this group anticipated that students might have a hard time following the directions for this game and treat each row as a separate roll. She wondered when to intervene if a student did this.
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I am sure I gave her a very unsatisfying answer, "It depends."
It depends on my goal for the lesson. If the lesson is about using the structure of the rekenrek to help students visualize groups of tens and fives in regards to place value understanding, then I might intervene. However, if I want the lesson to focus on decomposing numbers in order to make groups of ten, then I might wait until the whole class discussion (reflecting on the learning); this choice allows us to talk about it as a group.
It also depends on whether or not everyone is exhibiting the same issue. I hate putting out a lot of little fires. If I saw everyone doing this, then I might intervene with the entire group since there would be a lack of diversity in what students could share during the reflection. However, if it was a single student, then I could decide whether or not to select this approach for the reflection and where in the sequence (see Orchestrating Discussions).
So let's assume that my goal was about making tens and only Patsy played the game in this way. After having a few students who followed the directions as written share, I would move our attention to her "game board."
I want to share Patsy's work because she played a slightly different game. She answered a different question. If I wanted to know what Patsy rolled during each turn, I could find out from her rekenrek: 10 the first roll; 7 on the second; on the third a 3 (coincidence there, eh?); 9 on the fourth; 1 on the fifth; and 4 on the sixth roll. But the game wants us to say how many beads we have total and how many we need to get to 100. So with an elbow partner, I want you to devise a plan for finding these two numbers, the total and what's left to get to 100, but don't find them - yet. Ready? Go.
Although it is not what I expected (probably because it is not what I expected), I really like what Patsy's new game does for the lesson. In fact, I might tuck this example away for another time when we play the game. Then, if no one else plays it this way, I can still use it in our discussion because the game provides a shared context. This context, at least once, created an interesting problem for students to solve. And that was the main point of the session: