A collaboration between
Maryland Virtual High School
and the
Pittsburgh Supercomputing Center
Participants will gain
 A working definition of computational reasoning by
using simulations to collect and analyze data, test
hypotheses, and illustrate scientific concepts.
 A basic understanding of the capabilities of a variety
of computational tools.
 Insight into the ways in which computational
reasoning can be infused in their teaching.
http://mvhs.shodor.org/activities/CAST/IntroOutline.html
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Three Facets of Computational Reasoning
Meeting the Pennsylvania Standards
Coin-flipping and Forest Fires
Fractions and the Water Cycle
A Smorgasbord of Resources
Next Steps
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Understanding how to analyze, visualize and
represent data using mathematical and
computational tools
Using computer models to support theory
and experimentation in scientific inquiry
Using models and simulations as interactive
tools for understanding complex scientific
concepts
Modeling and the Standards
Unifying Themes
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3.1.7, 10, 12a - Apply concepts of systems,
subsystems, feedback and control to solve complex
technological problems.
3.1.7, 10, 12b - Apply concepts of models as a
method to predict and understand science and
technology.
3.1.7, 10, 12e - Evaluate change in nature, physical
systems and manmade systems.
Inquiry and Design
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3.2.7, 10, 12c - Apply the elements of scientific
inquiry to solve multi-step problems.
3.2.7, 10, 12d – Analyze and use the technological
design process to solve problems.
Science, Technology and Human Endeavors
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3.8.7, 10, 12b - Apply the use of ingenuity and
technological resources to solve specific societal
needs and improve the quality of life.
3.8.7, 10, 12c – Evaluate the consequences and
impacts of scientific and technological solutions.
Open the Reach Out and Torch Someone link from
http://mvhs.shodor.org/activities/CAST/IntroOutline.html
Using an agent-based pre-built forest fire model to explore:
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Probability
Random Numbers
Averages
Predictions and Hypothesis-Testing
Assumptions
Coin flipping
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In 10 trials, will you get an equal number of heads and tails?
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Would you get closer to an even split if you did a thousand flips?
Computer-generated random numbers
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Will the computer do any differently in 10 trials? Should it?
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Open the Flipping Pennies link from
http://mvhs.shodor.org/activities/CAST/IntroOutline.html
Assumptions
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All the trees are the same.
There is no wind.
At a certain probability, the fire can spread from one tree to its
nearest neighbors.
http://www.shodor.org/interactivate/activities/fire1/index.html
Data Analysis
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Open the Fire Analysis link from
http://mvhs.shodor.org/activities/CAST/IntroOutline.html
Open the Water, Water, Everywhere link from
http://mvhs.shodor.org/activities/CAST/IntroOutline.html
Using a systems-based pre-built model to explore:
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A Closed Cycle
Equilibrium
Proportional Reasoning
Predictions and Hypothesis-Testing
Assumptions
condensation
precipitation
evaporation
The Water Cycle Box Model
Open the Water Cycle in Vensim link from
http://mvhs.shodor.org/activities/CAST/IntroOutline.html
condensation fraction
condensation
water in
air
water vapor leak
leak fraction
evaporation
evaporation
fraction
water on
cover
total
precipitation
water
water in
pan
precipitation fraction
Using slider bars and iteration, you can do the same model
in Excel.
Open the Water Cycle in Excel link at
http://mvhs.shodor.org/activities/CAST/IntroOutline.html
The Math behind the Model
HAVE = HAD + CHANGE
Classroom Lessons from CAST Teachers
http://www.psc.edu/eot/k12/exercises_by_discipline.php
Computational Resources for Teachers
http://mvhs.shodor.org/activities/CAST/
Interactive Tools for Mathematics
http://www.shodor.org/interactivate
The Computational Science Education Reference Desk
http://www.shodor.org/refdesk/
The National Science Digital Library
http://nsdl.org/resources_for/k12_teachers/?pager=pathways
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To test hypotheses
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To simulate processes
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To gain a deeper understanding of complex
concepts
Sign up for in-depth workshops on
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Excel
Systems Modeling
Agent-Based Modeling
Guided Exploration of Web-based Simulations
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Contact Cheryl Begandy at begandy@psc.edu
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