id: 05705127
dt: j
an: 2011c.00770
au: Abrahamson, Dor; Janusz, Ruth M.; Wilensky, Uri
ti: There once was a 9-block $\dots $ ‒ A middle-school design for
probability and statistics.
so: J. Stat. Educ. 14, No. 1 (2006).
py: 2006
pu: Taylor \& Francis, Abingdon, Oxfordshire; American Statistical Association
(ASA), Alexandria, VA
la: EN
cc: K63 U53 D43
ut: college school cooperation; grade 6; scientific concepts; middle school
students; statistics; mathematical concepts; probability; units of
study; learning activities; computer simulation; computer assisted
instruction
ci:
li:
ab: Summary: ProbLab is a probability-and-statistics unit developed at the
Center for Connected Learning and Computer-Based Modeling, Northwestern
University. Students analyze the combinatorial space of the 9-block, a
3-by-3 grid of squares, in which each square can be either green or
blue. All 512 possible 9-blocks are constructed and assembled in a "bar
chart" poster according to the number of green squares in each,
resulting in a narrow and very tall display. This combinations tower is
the same shape as the normal distribution received when 9-blocks are
generated randomly in computer-based simulated probability experiments.
The resemblance between the display and the distribution is key to
student insight into relations between theoretical and empirical
probability and between determinism and randomness. The 9-block also
functions as a sampling format in a computer-based statistics activity,
where students sample from a "population" of squares and then input and
pool their guesses as to the greenness of the population. We report on
an implementation of the design in two Grade 6 classrooms, focusing on
student inventions and learning as well as emergent classroom
socio-mathematical behaviors in the combinations-tower activity. We
propose an application of the 9-block framework that affords insight
into the Central Limit Theorem in science. (Contains 14 figures.)
(ERIC)
rv: