Next message: Dennis McCowan: "[Channel-talkpupmath] Session Two"
I'd like to respond to your excellent questions posed in the previous
As series producer of the Private Universe Math series, I asked the same
questions when I first learned about the study.
The district of Kenilworth, NJ is quite small, in fact, it has only two
schools (1 ES, 1 MS/HS). In the early years of the study, students
moved through grades 1-3 as a group for three years. This made it
attractive to the researchers, since they could follow students'
thinking for an extended period without having to pull students out of 3
The selection of the original class of 25 students was truly random; the
researchers picked one of the school's classes, and whoever happened to
be in that class was in the study. After the early elementary years,
there was the normal attrition with students moving to other districts,
going to private schools, etc. By middle school, the researchers had
decided to try to follow a group of these students in more depth, so
instead of taking a whole class, they would work with subsets of
My understanding was that they were making a conscious effort to make
their group representative of the entire student body. Certain students
(i.e. Stephanie) were included because they could do a good job of
articulating their thinking, but by no means were these students
necessarily the "star" pupils of the school.
In terms of socio-economic scale, the students were very representative
of the town. Personally, I don't know if there were any special needs
students included in the study, but I don't believe that the selection
process was designed to exclude these children. In my personal
experience, today they are typical young adults in all respects, except
that they love math more that most students and feel comfortable doing it.
I'm sorry, but I can't answer your other question about manipulatives.
What do you think? Do you think it would be better if students were
forced to come up with their own representations of the problem instead
of having manipulatives?
In reply to:
> A question raised about the children we saw in the tape: Were all
> students in the grade taped? How were those we ended up watching
> actually selected? Are they representative of the Kenilworth
> children? Were "special education" children part of the study?
> Yet another question- manipulaties were provided for "Towers" but none
> were provided for the "Cups Plates and Bowls" problem. What was the
> thinking behind that decision? If doll cups, plates, and bowls had been
> provided, would that bhave hgelped or hindered the mathematical growth
> of the students?
> Dennis McCowan
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