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DIFFERENCES IN STUDENTS’ USE OF
COMPUTER SIMULATION TOOLS
AND REASONING ABOUT
EMPIRICAL DATA AND
THEORETICAL DISTRIBUTIONS
Robin L. Rider
East Carolina University
Hollylynne S. Lee
North Carolina State University
Presented at the Seventh International Conference on Teaching Statistics
Salvador, Brazil, July 3, 2006
Simulating an Event
□ Gives the students a
tangible way to
visualize the process
of an experiment
and the outcomes
□ Gives access to
large quantity of
outcomes from
repeated trials
□ Student Created Option for user to
determine probabilities
and set up simulation
□ Researcher/Teacher
Created - The purpose
of the simulation for our
research is for the
probability to remain
unknown to the user
The Task
□ Used a common
context – Six sided dice
□ Premise – The
production of the dice
may have led to
biasness
□ Each group of students
must make a decision
of whether their dice is
biased and what is
possible probability
distribution for the
outcomes on their dice
□ At least two groups
explored the same dice
□ After listening to group
presentations, the class
as a whole must
determine which of six
companies to
purchase dice from,
assuming they want fair
dice
□ Emphasis on providing
compelling evidence
for the inferences they
were making
□ Tool set for each class
was very different
Example
□ icots.pbe
□ Screenshots
Context of 6th Grade Study
□ End of two week
CSM intensive
study on
probability
□ Sample size,
variability,
inferences
□ Very familiar with
PE software
□ Four function
calculators were
available
Context for AP Stats Study
□ What is AP Stats?
□ End of course
□ Heavy emphasis on
Graphing calculators
for computation,
minimal use of
simulations
□ Well versed in
confidence interval
and hypothesis testing
procedures
□ Given access to PE
and Graphing
Calculators
Results
Middle School Students
□ Larger Samples n>1000
□ Used Stability of results to
support claims
□ Many were successful in
fairness predictions
□ Reasonable estimates for
probability distribution
□ Repeated sampling of size
100-500
□ One very large sample
1000<n<7000
□ Some used small samples n
< 100 but were intensely
criticized by their peers
AP Stats Students
□ Smaller samples 30<n<500
□ Typically performed tests for
Goodness of Fit
□ Tended to use single sample
to estimate probability
distribution
□ Only one group used the
underlying theory of Central
Limit Theorem
□ Groups with incorrect
procedures or hypothesis
test were intensely criticized
by their peers
Dynamic Nature of Graphs
□ Middle school
students used the
dynamic nature of
the graphs as to
describe the
distribution during
data collection
□ The dynamic
representation
became an analysis
tool
□ High school
students used the
graphical and
tabular displays to
describe the
distribution of the
data in its final state
after the simulation
was complete
Conjectures of Differences
Between Groups
□ Curricular Emphasis
□ Statistical Tools
Available
□ Exploratory Tools
□ Asking questions of
data that inform
more data
collection
□ AP Students felt no
need to experience
random process
□ Variability
□ Randomness
□ Familiarity with
Software in
curricular
experiences
□ AP Stats saw it as a
statistics problem
□ Middle School
Students saw it as a
probabilistic
problem
Questions We Have
□ Would AP Stats
students with
different curricular
experiences
approach the
problem differently?
□ How do similar age
students (high
school) with
different statistical
tool sets approach
the problem?
□ Longitudinally with
younger students,
can we strengthen
the foundation of
probabilistic
understanding that
is useful for statistical
inference?
Final Thoughts…
□ “Data analysis is like a give
□ Where or how do we
and take conversation
promote the detective
between the hunches
approach to data analysis?
researchers have about some
□ Tukey suggested statisticians
phenomenon and what the
do more with data …to be
data have to say about those
“data detectives” to search
hunches. What researchers
among data for interesting
find in the data changes their
and informative results. He
initial understanding which
described this as exploratory
changes how they look at the
data analysis. (Tukey, 1977)
data, which changes their
understanding and so forth.”
(Konold & Higgins, 2003, p.
194)
How can probability simulations help promote EDA and this
back and forth conversation?
References
□ Konold, C. & Higgins, T. L. (2003). Reasoning about
data. In J. Kilpatrick, W. Martin, & D. Schifter, (Eds.).
A research companion to principles and standards
for school mathematics (pp. 193-215). Reston , VA :
National Council of Teachers of Mathematics.
□ Tukey, J. W. (1977). Exploratory data analysis.
Reading, MA: Addison-Wesley.
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