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Computational Reasoning in High School Science and

Mathematics

A collaboration between Maryland Virtual High School and the Pittsburgh

Supercomputing Center

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Workshop Goals

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.

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Workshop Outline

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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What do we mean by computational reasoning? 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

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How do the Pennsylvania State Department of Education

Academic Standards address modeling?

Modeling and the Standards

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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.

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Unifying Themes Grade 10/12 Indicators

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)

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Unifying Themes Grade 10/12 Indicators

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)

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Forest Fire Simulation

Using an agent-based pre-built model to explore:

Probability Random Numbers Averages Predictions and Hypothesis-Testing Assumptions

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Probability Preparation

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?

http://academic.pgcc.edu/~ssinex/excelets/flipping_pennies_CAST_Mod_0.xls

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Simulating a Forest Fire

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.

Open

http://www.shodor.org/interactivate/activities/fire1/index.html

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Water Cycle Simulation

Using a systems-based pre-built model to explore:

A Closed Cycle Equilibrium Proportional Reasoning Predictions and Hypothesis-Testing Assumptions

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water inair

water oncover

water inpan

condensation

precipitation

evaporation

totalwater

condensation fraction

precipitation fraction

water vapor leak

evaporationfraction

leak fraction

The Water Cycle Box Modelhttp://mvhs.shodor.org/water/pan_water_cycle_psc.mdl

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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

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Pre-Built Models

Computational Resources for Teachershttp://mvhs.shodor.org/CAST2008/

The Computational Science Education Reference Deskhttp://www.shodor.org/refdesk/

The National Science Digital Libraryhttp://nsdl.org/resources_for/k12_teachers/?

pager=pathways

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How to Use in the Classroom

To test hypotheses

To simulate processes

To gain a deeper understanding of complex concepts

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Next Steps

Sign up for in-depth workshops on

Excel Systems Modeling Agent-Based Modeling Guided Exploration of Web-based

Simulations