Chapter 15 page 344
Problem #7. 1/2 + 3/4
A: How did you do #6?
B: Hey, what’s #7?
C: 5/4.
B: Oh. 5/4?
C: Yeah.
B: OK.
Problem #10. 2/5 + 4/9
B: #10 is a hard one. What did you get?
D: OK. Five times 9 is 45, and there’s nothing
smaller that they both go into. So that’s 18/45
and 20/45. And add 18 and 20, and you get
38/45. I don’t think you can reduce that.
B: All right. I see. This set’s done. We’re done.Problem #8. 1/8 + 5/16
A: I think #8 is one half.
B: No. 2/16 plus 5/16. So that’s seven 16ths.
A: Let me see. ... 7/16. OK.
Problem #11. 3/11 + 1/22.
D: How about #11?
C: 7/22.
D: 7/22....
Problem #14. 5/6 + 1/4
A: Do you use 24?
D: No. 12.
(pause)
D: But I got 1 and one sixth.
C: Five sixths is 10 twelfths, and one fourth is 3
twelfths. Ten plus 3 is 13. That’s 13 twelfths.
One and one twelfth.
D: Oh. I made 1 fourth into 4 twelfths. But that
would be one third. I need to be careful when I
multiply those out.Explain the results. Classify the students’ comments in a way that can explain why some students in this
group learned more than others. Consider both what students say to others and what others say to them.
The case you have just read explores how students learn as a result of collaborative learning. In
collaborative learning, small groups of students learn by working together productively on an academic
task. The groups that work together on collaborative learning tasks are collaborative groups. A central
goal of collaborative learning is to enhance individual students’ conceptual and strategic knowledge. Other
goals including improving social skills, promoting prosocial attitudes, and fostering positive attitudes
toward peers of differing backgrounds.
This case highlights a very important feature of collaborative learning: the quality of talk within the
groups. When students engage in productive talk during groups—when they use effective cognitive
strategies such as explanation, elaboration, and monitoring as they speak—they learn more than when
they engage in less productive strategy use. This idea will be a main focus of the present chapter. Many of
the problems that you will work with in this chapter focus on the quality of talk in the groups.
Educational researchers have carried out many studies investigating the effectiveness of collaborative
groups, and the results have generally been positive. In well-designed collaborative groups, students learn
more when they work collaboratively than when they work individually (Barron, 2003; D. W. Johnson &
Johnson, 1991; D. W. Johnson, Maruyama, Johnson, Nelson, & Skon, 1981; R. E. Slavin, 1996).
However, there is much that can go wrong if teachers design collaborative group work poorly.
A core rationale for collaborative learning is that students have many more chances to talk
productively in small groups than in whole class discussions. In Chapter 13, Discussions and Questioning,
you learned that in class discussions, each individual student has, at most, a few chances to speak. Even if
a teacher reduces her contribution to 25% of all words spoken, the 25 students in her class will speak, on
average, only 3% of the time. But in a collaborative group of four, students will be speaking 25% of the
time on average; in a group of two, students will speak about half the time. In addition, in smaller groups,
there is a greater pressure for students to listen attentively and think about what others are saying.