Chapter 15 page 356
Problem 15.4 Understanding students’ thinking: Which core processes of effective
collaborative groups are present?Lorena: 8, 9, 9, and 8... how much it is ...
17, right?
Elisha: Yeah, that’s what I did.
Lorena: Yeah, then you carry the 1, that’s
9 and 9 is 18.
Kelsie: She wrote, “Oh, W..., I like you.
Lorena: Carry the 1, is 2...$2.89
Tatiana: You like her too?
Lorena: $5.00 it says there
Kelsie: No
Lorena: is 2 dollars 80...89 cents
Elisha: 89 cents?
Kelsie: You like, you like Andrea?
Lorena: Wait, and that’s a ... 4 minus 2
equals 2.
Kelsie: She lives downtown.Lorena: And 10 minus 7 is 3.
Elisha: OK.
Lorena: So, erase the answer, just
erase 8 and 7...that’s it.
Tatiana: I don’t want her phone
number. I hate...
Kelsie: You goin’ crazy. You’all
crazy.
Tatiana: Like this. Me and J...we the
only people that Andrea likes.
Lorena: And then write 13 cents.
Tatiana: She don’t like you.
Lorena: Wait, you don’t have to write
the cents.
Elisha: OK, I gotta go.
Kelsie: Then why’d she always look
at me?Response. Let’s examine each of the core processes.
Engagement. Two students (Lorena and Elisha) are generally engaged, despite the distraction
of Kelsie and Tatiana holding a separate, unrelated discussion. Kelsie and Tatiana are not
engaged and instead are off-task.
Positive interdependence. There is no positive interdependence. Kelsie and Tatiana feel no
need to engage with the group to produce the group produce. Instead, they are socially
loafing.
Mutual respect. Although Kelsie and Tatiana do not disparage each other, they are speaking
disrespectfully of other class members. Their interactions are negative.
Balanced interactions. If Lorena and Elisha were working as a pair, their interaction would be
balanced. But given that there are four group members, of whom two contribute nothing to
the mathematical discourse, the group’s interactions are highly unequal.
High-quality strategy use. Because Lorena and Elisha are the only ones engaged in any
strategy use, we must focus our attention on them. If you follow through Lorena’s
comments and Tatiana’s comments, you will see that Lorena provides procedural help in
almost every turn. There are no explanations. For example, she does not explain why she is
carrying out each step.
Uptake of ideas. Elisha adds nothing of substance to the discussion with Lorena. She does not
co-construct any ideas. She simply accepts most of what Lorena says, without discussion,
and with no re-explanation or uptake. As soon as they get the answer, Elisha abruptly
leaves, without having tried out any of the procedures on a new problem. Therefore, it is
unlikely that Elisha will learn much from this discussion.
Overall, this is a poor interaction all around. Two students were not only nonparticipants but
showed a lack of respect toward other class members. The other two students were talking
about the math problems, but Lorena’s talk was all at a procedural level, and there was no
uptake beyond acceptance by Elisha.