Computational Reasoning in High School Science and Mathematics

1
Computational Reasoning in High School Science
and Mathematics

• A collaboration between
• Maryland Virtual High School
• and the
• Pittsburgh Supercomputing Center

2
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.

3
Workshop Outline

• http//mvhs.shodor.org/activities/CAST/IntroOutlin
  e.html
• 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

4
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

5
How do the Pennsylvania State Department of
Education Academic Standards address modeling?
Modeling and the Standards
6
Academic Standards for Science and Technology

• 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.

7
Academic Standards for Science and Technology

• 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.

8
Academic Standards for Science and Technology

• 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.

9
Reach Out and Torch Someone!

• Open the Reach Out and Torch Someone link from
• http//mvhs.shodor.org/activities/CAST/IntroOutlin
  e.html
• Using an agent-based pre-built forest fire model
  to explore
• Probability
• Random Numbers
• Averages
• Predictions and Hypothesis-Testing
• Assumptions

10
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?
• Open the Flipping Pennies link from
  http//mvhs.shodor.org/activities/CAST/IntroOutlin
  e.html

11
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.
• http//www.shodor.org/interactivate/activities/fir
  e1/index.html
• Data Analysis
• Open the Fire Analysis link from
  http//mvhs.shodor.org/activities/CAST/IntroOutlin
  e.html

12
Water, Water, Everywhere

• Open the Water, Water, Everywhere link from
  http//mvhs.shodor.org/activities/CAST/IntroOutlin
  e.html
• Using a systems-based pre-built model to explore
• A Closed Cycle
• Equilibrium
• Proportional Reasoning
• Predictions and Hypothesis-Testing
• Assumptions

13
Water, Water, Everywhere
condensation
precipitation
evaporation
14
The Water Cycle Box Model Open the Water Cycle in
Vensim link from http//mvhs.shodor.org/activities
/CAST/IntroOutline.html
15
Water Cycle Excelet

• 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/IntroOutlin
  e.html
• The Math behind the Model
• HAVE HAD CHANGE

16
Pre-Built Models

• 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

17
How to Use in the Classroom

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

18
Next Steps

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