Introducing
Distribution initiates
students in
concepts of
distribution,
sampling, and
inference in
two related
contexts, measurement
and natural
variation. In
the measurement
context, distribution
of measures
emerges from
differences
among measurements.
What emerges
is the notion
that although
each measurement
is not the same,
the variation
among measurements
are structured.
Students then
are guided to
account for
structure by
considering
different sources
of variation,
including the
nature of the
measuring device
and individual
differences.
These sources
of variation
link the activity
of individual
measurers to
the aggregate
structure of
the collection
of measurements.
Students invent
displays and
indicators (statistics)
of best guesses
about true measure
and precision
of measure.
These
are intended
as gentle introductions
to statistics
and to the
qualities of
display. The
generality
and utility
of student inventions
are tested in
multiple batches
of repeated
measure data
constructed
by students.
Tinkerplots is used as a
tool that first
accompanies
paper-and-pencil
and then replaces
paper-and-pencil
media. Sampling
studies are
conducted to
explore sample-to-sample
variation,
and these studies
form the backdrop
to inference.
What might
happen if we
measured again?
Students conduct
experiments
with model rockets
with rounded
nosecones to
create a reference
distribution
of measures
of apogee.
The reference
distribution
is used to
locate, first,
additional measures
of apogee of
rounded nosecones,
and second,
new measures
of apogee of
pointed nosecones.
Can we infer
that nosecones
make a difference
in light of
sample-to-sample
variation?
In
the second context,
students examine
distributions
of samples of
Wisconsin
Fast Plants during
the life cycle
of the plant.
Does the distribution
change, and if
so, how and why?
Experiments are
again conducted
(e.g., light,
fertilizer levels),
and students use
distribution and
sampling distribution
to make inference
about the effects
of levels of
light and fertilizer
on plant growth.
