Computational Reasoning in High School Science and Mathematics A collaboration between Maryland Virtual High School and the Pittsburgh Supercomputing Center

Workshop Goals Participants will gain n A working definition of computational reasoning by using simulations to collect and analyze data, test hypotheses, and illustrate scientific concepts. n A basic understanding of the capabilities of a variety of computational tools. n Insight into the ways in which computational reasoning can be infused in their teaching.

Workshop Outline n Three Facets of Computational Reasoning n Meeting the Pennsylvania Standards n Coin-flipping and Forest Fires n Fractions and the Water Cycle n A Smorgasbord of Resources n Next Steps

What do we mean by computational reasoning? n Understanding how to analyze, visualize and represent data using mathematical and computational tools n Using computer models to support theory and experimentation in scientific inquiry n 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

Standards for Science and Technology Inquiry and Design The nature of science and technology is characterized by applying process knowledge that enables students to become independent learners. These skills include observing, classifying, inferring, predicting, measuring, computing, estimating, communicating, using space/time relationships, defining operationally, raising questions, formulating hypotheses, testing and experimenting, designing controlled experiments, recognizing variables, manipulating variables, interpreting data, formulating models, designing models, and producing solutions.

Unifying Themes Grade 10/12 Indicators n Describe/apply concepts of models as a way to predict and understand science and technology.  Distinguish between different types of models and modeling techniques and apply their appropriate use in specific applications. (gr. 10)  Examine the advantages of using models to demonstrate processes and outcomes. (gr. 10)  Apply mathematical models to science and technology. (gr. 10)  Appraise the importance of computer models in interpreting science and technological systems. (gr. 12)

Unifying Themes Grade 10/12 Indicators n Describe patterns of change in nature, physical and man made systems.  Describe how fundamental science and technology concepts are used to solve practical problems (e.g., momentum, Newton’s laws of universal gravitation, tectonics, conservation of mass and energy, cell theory, theory of evolution, atomic theory, theory of relativity, Pasteur’s germ theory, relativity, heliocentric theory, gas laws, feedback systems). (Gr. 10)  Recognize that stable systems often involve underlying dynamic changes (e.g., a chemical reaction at equilibrium has molecules reforming continuously). (Gr. 10)  Analyze how models, systems and technologies have changed over time (e.g., germ theory, theory of evolution, solar system, cause of fire). (Gr. 12)

Forest Fire Simulation Using an agent-based pre-built model to explore: n Probability n Random Numbers n Averages n Predictions and Hypothesis-Testing n Assumptions

Probability Preparation Coin flipping n In 10 trials, will you get an equal number of heads and tails? n Would you get closer to an even split if you did a thousand flips? Computer-generated random numbers n Will the computer do any differently in 10 trials? Should it? n AST_Mod_0.xls AST_Mod_0.xls

Simulating a Forest Fire Assumptions n All the trees are the same. n There is no wind. n At a certain probability, the fire can spread from one tree to its nearest neighbors. Open n

Water Cycle Simulation Using a systems-based pre-built model to explore: n A Closed Cycle n Equilibrium n Proportional Reasoning n Predictions and Hypothesis-Testing n Assumptions

The Water Cycle Box Model

Water Cycle Excelet Using slider bars and iteration, you can do the same model in Excel. See pan_water_cycle_CAST.xls The Math behind the Model HAVE = HAD + CHANGE

Pre-Built Models Computational Resources for Teachers The Computational Science Education Reference Desk The National Science Digital Library

How to Use in the Classroom n To test hypotheses n To simulate processes n To gain a deeper understanding of complex concepts

Next Steps Sign up for in-depth workshops on n Excel n Systems Modeling n Agent-Based Modeling n Guided Exploration of Web-based Simulations