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Using technology to build
probabilistic simulation models
NCSM 2016, Oakland, CA
April 12, 2016
Ingrid Ristroph
Kathi Cook
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Introduction to the Charles A. Dana Center
What we do
•  Advance effective math and science education for
all students, from kindergarten to college
•  Provide innovative resources that promote student
engagement, motivation, and persistence in support
of academic achievement
•  Work alongside teachers, administrators, and
policymakers at the local, state, and national level
to support education systems that put students on a
path to success
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Introduction: What are simulations?
!  A simulation is a way to model random events, such
that simulated outcomes closely match real-world
outcomes.
!  Simulations can involve physical materials (such as
drawing numbers from a bag, tossing a coin, spinning
a spinner) or generating data on a computer (such as
generating random numbers to represent samples from
a population).
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Selected standards
7.SP.8c
S-IC.2
Investigate chance processes and
develop, use, and evaluate probability
models.
Understand and evaluate random
processes underlying statistical
experiments
8. Find probabilities of compound events
using organized lists, tables, tree
diagrams, and simulation.
c. Design and use a simulation to
generate frequencies for compound
events. For example, use random digits
as a simulation tool to approximate the
answer to the question: If 40% of donors
have type A blood, what is the
probability that it will take at least 4
donors to find one with type A blood?
2. Decide if a specified model is consistent
with results from a given data-generating
process, e.g., using simulation. For
example, a model says a spinning coin
falls heads up with probability 0.5. Would a
result of 5 tails in a row cause you to
question the model?
S-IC.4
S-IC.5
Make inferences and justify
conclusions from sample surveys,
experiments, and observational studies
Make inferences and justify
conclusions from sample surveys,
experiments, and observational studies
4. Use data from a sample survey to
estimate a population mean or proportion;
develop a margin of error through the use
of simulation models for random sampling.
5. Use data from a randomized
experiment to compare two treatments;
use simulations to decide if differences
between parameters are significant.
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Reflecting on these standards
!  What is your experience with these standards?
!  What’s noteworthy?
!  What challenges have you encountered related to
these standards?
!  What teaching strategies come to mind?
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Explore designing and using a simulation
If 40% of donors have type A blood, what is the probability
that it will take at least 4 donors to find one with type A
blood?
How would you design and use a simulation to answer
this question?
Let’s see an example of a simulation built in a Google
spreadsheet.
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Explore designing and using a simulation
If 40% of donors have type A blood, what is the
probability that it will take at least 4 donors to find one
with type A blood?
In our Google spreadsheet simulation, we used three
commands:
!  =RANDBETWEEN(0,9)
!  =OR(C1<4,C2<4, C3<4)
!  =COUNTIF(B1:B200, TRUE)
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Technology for simulations
!
!
!
!
!
Graphing calculators
RNGs either on calculators or online
Spreadsheets
Online applets
Statistical packages or computer algebra systems
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Embedded simulation in online course materials*
Acne medication study
*Example from Dana Center/Agile Mind Algebra II online course program
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Implications
!  How do you ensure teachers have the time and space
to understand these standards?
!  What is the role of simulation in building student and
teacher understanding of statistical concepts?
!  What are the implications for curriculum and materials?
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Conclusion
!  Simulations are powerful for building statistical
understanding for two key concepts: randomness and
variation.
!  These concepts are the foundations of the Law of
Large Numbers, Central Limit Theorem, confidence
intervals, hypothesis testing, and regression
coefficients.
!  Building simulations is a fun way to integrate coding
into curriculum!
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Want to learn more?
Ingrid Ristroph
ingrid.ristroph@austin.utexas.edu
Kathi Cook
klcook@austin.utexas.edu
On Twitter @IngridRistroph and @UTDCKathi
Follow the Dana Center on Twitter @utdanacenter
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