@Participants: TEA Kay Teacher, BLA Blake Student, BRI Brian Student, JAS Jason Student, MAR Marcus Student, JAM Jamie Student, PAU Paul Teacher, KIR Kiri Student, MEG Megan Student, VAL Vallory Student, DER Derrick Student, SHE Sheena Student, KYL Kyle Student, WIL Will Student
@Media: aids, video
@Comment: AIDS Discussion Clips
*TEA: What I want to do today is I want to take a look at some of the
things that you did and let's talk about them.
*TEA: I want to see if as a group I want us to look at them and decide if
we think that they are an adequate way to represent this data and if
we actually understand what these folks are doing.
*TEA: So, start with one? ▶
@Comment: Clip 1 (aids1.jpg)
*TEA: Jamie, one more time, big voice. ▶
*JAM: I think it's a pretty adequate way of showing information because
you can see where the range is starting and ending and you can see
where the majority of the numbers are. ▶
%com: Cobb views this as a normative conclusion.
*TEA: okay, comments about what Jamie said, or other comments about this?
*DER: I didn't hear what she said. ▶
*TEA: You didn't hear what she said. ▶
*TEA: Jamie, you just have to really, you have a really quiet voice and
it's a big room. ▶
*DER: Speak up. ▶
*JAM: okay, I think that it's an adequate way of showing the information
because you can see where the range is started and ended and you can
see where the majority of the numbers were.
*DER: What (.) what do you mean by the majority of the numbers?
%com: Cobb: Derrick is positioned as failing to understand without
offering an alternative characterization.
*TEA: What do you mean, he, Derrick doesn't know what you mean by the
majority of the numbers. ▶
*JAM: The (.) where most of the numbers were. ▶
*DER: Where most of the numbers are +... ▶
*SHE: I mean like, when she talks about, I think what she's saying, like
when you say where the majority of the numbers were, where they,
where the point is, like, you see where it goes up?
*TEA: I do see where it goes up. ▶
*SHE: Yeah, like right in there, that's where the majority of it is.
%com: Cobb: She is gesturing to identify the locus of the "majority"
without further defining it.
*TEA: okay. ▶
*DER: The highest range of the numbers? ▶
*SHE: Yeah. ▶
*TEA: The highest range? ▶
*SHE: Oh, no. ▶
*VAL: No. ▶
*TEA: Vallory? ▶
*VAL: Out of however many people were tested, that's where most of those
people fitted in, in between that range. ▶
%com: Cobb: She provides a definitional clarification of "majority". The
word "most" is used relationally. Sfard: This represents relating an
intimation to an implementation. Schliemann: This useful
contribution is not picked up by teachers, perhaps because they were
not yet prepared for a discussion of relative frequences, as they
later were for Marissa in 92.
*VAL: With those little +... ▶
*PAU: You mean this range here? ▶
*VAL: Yes. ▶
@Comment: Clip 2 (aids2.jpg)
*TEA: okay, these folks kind of wrote out what they were talking about.
*TEA: This one right here they said +"/. ▶
*TEA: +" the new drug was better than the old. ▶
*TEA: The majority of the old ones are behind five fifty, and the majority
of the new drug was in front of five fifty. ▶
*PAU: First of all, do you know what that person did, what they were
talking about and how they were thinking about it?
*TEA: Vallory? ▶
*VAL: Why did they +... ▶
%com: Cobb: Vallory seeks to provide justification for the partitioning
of T-cell values at 550. McClain: Note that Vallory seeks
justification for 550, not 525, as in report #3. The value of 525 is
a mal-rule concept represent the middle of the range. It is
perceptually clear, but conceptually useless.
*VAL: five fifty? ▶
*VAL: I don't know? ▶
*VAL: Why is five fifty so important? ▶
*VAL: Because the median is really five hundred . ▶
*VAL: no it's not, but it's not five fifty. ▶
*TEA: Kiri? ▶
*KIR: Because five fifty is in the middle of the whole thing, like the whole,
the whole scale. ▶
%com: Schliemann: This is used to introduce a discussion of natural
breaks in distributions.
*KIR: five fifty is in the middle. ▶
*KIR: It might not be the middle of the data, but it's the middle of
whole scale. ▶
*TEA: Oh, so it's like the middle of the range, not necessarily the
middle of the dist, okay ▶
*MEG: Cause, me when I looked at it, five fifty had, it's kind of where.
*TEA: Wait just a minute. ▶
*TEA: Derek, you are going to have to sit up and put that hood down.
*KYL: He doesn't have his hood up. ▶
*TEA: Derek. ▶
*MAR: He's sleeping . ▶
*TEA: Sit up. ▶
*TEA: I'm sorry, can you start over? ▶
*MEG: When I looked at the computer, they were like lined up straight on
five fifty. ▶
%com: McClain: This represents the success of the general attempt to have
students understand the data qualitatively.
*MEG: And then starting to get above it, or all the dots for the old
treatment, and the new treatment had like +...
*TEA: Oh, so it was like a natural break. ▶
*PAU: When I, when I, when I was going around talking to some groups, and
I think it was the group over in the corner here said something
%com: McClain: This shifts the choice of a breakpoint from equal balance
to a separation between hills. Both are still perceptual.
*PAU: What I heard them say I think it is the same thing.
*PAU: They were trying to find the place sort of between the hills.
*PAU: So if they looked at where this kind of hill started and where this
kind of hill finished, they said it's around five fifty.
*PAU: And so that's why they took that break.
*TEA: okay, and this group did a similar thing because they said they
looked at how many of the t+cells counts were between two hundred
and five twenty five, and then they looked at how many were
between five twenty five and above. ▶
*TEA: So they used five twenty five, and these people used five fifty.
*TEA: So they were doing like you were talking about Megan, looking at
where the hills started to change on the graph.
*TEA: Questions or comments about these two ways?
*TEA: Marissa? ▶
*MAR: I would think the second one would be more confusing because it
has, since the old program has more numbers than the new program.
%com: Cobb: The acceptance of this contribution provides strong evidence
that the class had accepted the norm of comparing relative
frequencies. F&E: Marissa may have been viewing the inscription
literally, unlike Blake in 101. F&E: This is the last time that
girls contribute to the discussion. Is Marissa not given adequate
"authorship." McClain: This contribution furthers the teacher's goal
of problematizing absolute frequencies. Teacher foregrounds it
through next comment. MacWhinney: Was this contribution built on
earlier instruction or scaffolded by the classroom discussion? Is
there really evidence that Marissa is processing literally? If so,
notice that teacher chooses not to interpret her as begin literal.
And Marissa accepts this in 94. Is there really evidence that her
authorship is not accepted. Note the intonation of the revoicing and
attention in 93 and the explicit attention in 95. Is her voice
really missing entirely?
*TEA: Oh. ▶
*TEA: So it looks like that there's more. ▶
*TEA: They had fifty six that were above five twenty five, and they only
had thirty seven? ▶
*MAR: So it's like, I guess what I'm trying to say is it's harder to
compare them. ▶
*TEA: What about what Marissa said? ▶
*TEA: she just said there were more people in the old program
so if you actually look at the actual numbers of people,
you find out that they had fifty six that were in this upper range
which is where we want to be
and these only had thirty seven. ▶
*TEA: So somebody might say the old program was better because there were
*TEA: Jamie? ▶
*JAM: This is related. ▶
*JAM: You know like, like a, like a scale drawing where it's not the same
size, but it's the same thing. ▶
*JAM: If you look at it, so you have to +... ▶
*TEA: I know what you're trying to say. ▶
@Comment: Clip 3 (aids3.jpg)
*TEA: So, so Kyle said that from this information he was able to make
this diagram and that by looking at the information he could also
have the diagram. ▶
*TEA: And that that was helpful for him. ▶
*PAU: I've got a question for everybody. ▶
*PAU: Couldn't you just argue, hey, this shows really convincingly that
the old treatment was better, right? ▶
*PAU: Because there were fifty six of them, fifty six scores above five
twenty five, fifty six people with t+cell counts above five twenty
five, and here there's only thirty seven above, so the old one just
had to be better, there's more people. ▶
*PAU: I mean, there's nineteen more people in there, so that's the better
one, surely. ▶
*TEA: Blake? ▶
*BLA: But then there's more people with the old program than there is
with the new program. ▶
%com: McClain: Paul has succeeded in getting Blake to restate the helpful
conclusion of Marissa . Saxe: The fact that no one accepts
Paul's false reasoning indicates that children are using relative
distributions. MacWhinney: But note retreat .
*TEA: Jason. ▶
*JAS: Then you see that there's thirty seven is more than half over five
twenty five and fifty six is not more than half of a hundred
thirty . ▶
%com: Cobb: This is consistent with a normative reading of "majority" as
more than half of the data. McClain: This explanation is not too
*JAS: more of them on the bottom than on the top.
*TEA: okay. ▶
*PAU: Can somebody help me out? ▶
*PAU: Can somebody paraphrase what Blake and Jason are talking about?
*TEA: What was Jason just saying? ▶
*TEA: Somebody help us out with what Jason was just saying.
*DER: I didn't hear him. ▶
*TEA: You couldn't hear him? ▶
*BRI: If you would pay attention. ▶
*DER: okay, I couldn't hear him. ▶
*TEA: okay , guys come on. ▶
*JAS: okay, you see how thirty seven is more than half of nine and thirty
seven together? ▶
*JAS: But fifty six is not more than half of thirty, a hundred thirty and
fifty six put together. ▶
*JAS: There's more on the bottom one than on the top one.
*JAS: right? ▶
*TEA: okay, who can help me out with that, who can say that a different way
so that I might could understand that? ▶
*TEA: Will, can you say it a different way? ▶
*WIL: Well, in that situation it wouldn't matter how many people were in
there because see like. ▶
*TEA: Big voice, Will. ▶
*WIL: on the bottom one you have, see what Jason was saying there's more
than there is below five twenty five and so that means that that one is better
because the top one it only, it doesn't even have close to half of
what the one below five twenty five is on that one. ▶
*WIL: So that means that if, if uh there was the same amount of people
that had like, if they both had the same amount of people and, but,
and they had the numbers and everything, and this one, the bottom
one was a however much more that of +... ▶
*PAU: And Will +... ▶
*DER: No, he's trying to say +... ▶
*TEA: Alright . ▶
*DER: He's trying to say that +... ▶
*TEA: I see. ▶
*WIL: I think that when you add. ▶
*TEA: I don' think that +... ▶
*TEA: Alright, Derrick, you go ahead and then we'll get.
*TEA: Marcus is on this; hang on Will. ▶
*TEA: Big voice now Derrick. ▶
*DER: He's trying to say that, that half, like the thirty seven is over
half the five hundred twenty six, three, five, six, uh, uh, fifty
*DER: uh and uh like it fills more people
then it will probably be higher. ▶
*DER: than sixty than like the one we been working on a similar. ▶
*TEA: I see. ▶
@Comment: Clip 4 (aids4.jpg)
*TEA: So, same job as before, guys. ▶
*TEA: Take a look at this one. ▶
*TEA: This is, this is the old treatment and this is the new treatment.
*TEA: Your first job is to see if you can understand what these folks
did, and then decide if you think it's adequate.
*TEA: okay let's take a look. ▶
*TEA: I've got two people, three people. ▶
*MAR: Four people. ▶
*TEA: Blake, you want to take a shot at it? ▶
*BLA: Yeah, um . ▶
*TEA: Big voice Blake. ▶
*BLA: I think it's adequate because, uh, for one, like you know when
people use the range and stuff but the numbers are the same on this.
*BLA: So that's gonna be like a comparison. ▶
*BLA: They split into four groups. ▶
*TEA: okay, so it's, so it's helpful that the ranges are the same and then,
so +... ▶
%com: F&E: Teacher legitimates Blake's contributions for the third time.
*BLA: And then with the four equal groups, you can tell where the
differences in the four groups. ▶
*TEA: Can you do that by looking at this? ▶
*TEA: Can you, So what do you see when you look at this Blake?
*BLA: That the new treatment worked better than the old treatment.
*TEA: Well, I just couldn't hear you. ▶
*BLA: That the new treatment was better than the old treatment +...
*TEA: And what are you basing that comment on? ▶
*BLA: Because the three lines for the equal groups were all. ▶
%com: McClain: Teacher believes that many of the students do not
understand this explanation.
*BLA: What is that five twenty five? ▶
*TEA: Yeah. ▶
*BLA: Above five twenty five compared to only one of them was over on the top.
%com: Cobb: Views each group as a proportional part or a data set.
*TEA: Ah. ▶
*TEA: Marcus, something to add? ▶
*MAR: Yeah, last time like, it was like kind of crooked, and this time
it's easier to see because it's right under each other.
%com: Cobb: Marcus is not positioned as failing to follow the standard of
requiring relative frequencies set by Marissa in 92. This is not a
contradiction in the analysis because the materials being analyzed
are different in the two cases. McClain: This indicates a retreat
from the purpose of the four-equal-groups graph and evidence that
many students were unable to read this inscription. They needed
practice in creating percentage distributions from raw scores. F&E:
Agree with McClain.
*MAR: So then you have to sort of move it in.
*MAR: Like, I'm not trying to copy what Blake said.
*MAR: But it is good though. ▶
*MAR: Any way, it shows it might help more if they had put the numbers in
the groups so you have a better idea of what you're seeing.
*TEA: Put the numbers in here? ▶
*MAR: In the, in like say the fourth group would be a twelve in there,
and just write the number twelve in there so you know +...
*TEA: Alright, now if guys, if this is, if they divided it into four equal
groups which is what Blake said, then is there some way for us to
know how many are in each of those groups?
*DER: No. ▶
*TEA: Could we do that right now? ▶
*TEA: Derrick says no. ▶
*BLA: If we knew how many +... ▶
*PAU: There's forty, on the bottom one. ▶
*PAU: Wasn't it the bottom one? ▶
*TEA: Forty six. ▶
*PAU: There were forty six and there was one hundred eighty six on the
top one. ▶
*DER: Divide it into half. ▶
*BLA: It doesn't really matter. ▶
*DER: Divide it into half. ▶
%com: F&E: This indicates that Derrick (along with Marcus and Brian)
doesn't understand inscription #5. This illustrates that some
students are unwilling to accept abstract representations without
*BLA: It doesn't really matter cause you can already, it , even if it was
all up against one you that that's still gonna be better because of
where the numbers +... ▶
*TEA: Wait a minute guys, this is important. ▶
%com: F&E: Teacher legitimates Blake's contributions for the fourth time.
*TEA: Blake, go ahead. ▶
*BLA: Well, it doesn't really matter where the all the data is because
you know from where the groups are what, what treatment is better or
where the data stands on both treatments.
%com: Cobb views this as a normative conclusion.
*TEA: okay, so, ya, so Blake says it doesn't really matter exactly how
many, we just know where they are and that's important.
%com: F&E: Teacher legitimates Blake's contributions for the fifth time.
*TEA: McKenna? ▶