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.

 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

 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

How do the Pennsylvania State Department of Education Academic Standards address modeling? Modeling and the Standards

Unifying Themes  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  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  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 Using an agent-based pre-built forest fire model to explore:  Probability  Random Numbers  Averages  Predictions and Hypothesis-Testing  Assumptions

Coin flipping  In 10 trials, will you get an equal number of heads and tails?  Would you get closer to an even split if you did a thousand flips? Computer-generated random numbers  Will the computer do any differently in 10 trials? Should it?  Open the Flipping Pennies link from

Assumptions  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.  Data Analysis  Open the Fire Analysis link from

Open the Water, Water, Everywhere link from Using a systems-based pre-built model to explore:  A Closed Cycle  Equilibrium  Proportional Reasoning  Predictions and Hypothesis-Testing  Assumptions

precipitation evaporation condensation

The Water Cycle Box Model Open the Water Cycle in Vensim link from

Using slider bars and iteration, you can do the same model in Excel. Open the Water Cycle in Excel link at The Math behind the Model HAVE = HAD + CHANGE

Classroom Lessons from CAST Teachers Computational Resources for Teachers Interactive Tools for Mathematics The Computational Science Education Reference Desk The National Science Digital Library

 To test hypotheses  To simulate processes  To gain a deeper understanding of complex concepts

Sign up for in-depth workshops on  Excel  Systems Modeling  Agent-Based Modeling  Guided Exploration of Web-based Simulations  Contact Cheryl Begandy at