Computational Reasoning in High School Science and Math This module is an introduction to the whole CAST program. It explains the overall goals of CAST, and the rationale and design of the Professional Learning Program. Some of the slides in the presentation can be inserted into other modules to reinforce the overall goals if/when only those modules are presented – e.g., for a shorter PLE.

The Pittsburgh Supercomputing Center A university-based computing and research organization serving scientists and researchers across the nation. Mission: Provide state of the art high performance computing environments for solving large-scale computational problems in all fields of science such as: Violent storm modeling Molecular biology Origins of the universe New educational mission: introduce tools of computational scientists to secondary school math and science teachers PSC offices are located at 300 S. Craig St., on the campus of Carnegie Mellon University in Pittsburgh, Pennsylvania. This is an optional slide that introduces PSC, and provides some of the background to the creation of the program – bringing the tools of modern science to the classroom.

Computation and Science for Teachers (CAST) A program to infuse computational reasoning into secondary math and science instruction A collaboration of the Pittsburgh Supercomputing Center (PSC), the Maryland Virtual High School (MVHS) and the SW PA Math&Science Collaborative (MSC) A Professional Development Experience for middle and high school math and science teachers.

CAST Goals The goals of the CAST program are to: Increase the use of computational reasoning to support theory and experimentation in scientific inquiry. Increase the use of interactive computational tools such as modeling and simulation to support the teaching of scientific and mathematical concepts. Improve the learning experience and engagement of students in math and science. Have goals written on a chart and posted where all can see and refer to as they move through the session. Discuss what each goal means – don’t necessarily read them word-for-word. Foreshadow how each goal will be accomplished.

What is 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 concepts in science and mathematics Computational Reasoning (our definition – CAST/MVHS) means: Understanding how to analyze, visualize and represent data using mathematical and computational tools This includes graphing data, identifying trends, and recognizing error. Using computer models to support theory and experimentation in scientific inquiry Just as variables must be carefully defined in a scientific experiment, so must assumptions about variables be made explicit in a computer model designed to represent a real world problem. Building a model requires a deep understanding of the problem being represented. Many science problems are done on computers – the model is run before any testing is done in the real world Using models and simulations as interactive tools for understanding complex scientific concepts Interacting with a computer model by running it under various conditions is similar to conducting an experiment. The results achieved by varying the parameters in the model help the student understand the underlying concepts. Depending on the audience, might want to point out that this is related to but different than the idea of “Computational Thinking”, which more broadly includes the types of thinking and ideas that comprise computer science.

Why Computational Reasoning? Addresses Common Core Standards in Mathematics Standards for Mathematical Practices MODEL WITH MATHEMATICS Reason abstractly and quantitatively Use appropriate tools strategically Look for and express regularity in repeated reasoning Standards for Mathematical Content Making Inferences and Justifying Conclusions Understand and evaluate random processes underlying statistical experiments Make inferences and justify conclusions from sample surveys, experiments and observational studies. Point out how computational reasoning is relevant in mathematics. Modeling / using equations crosses all domains. In these models we are doing virtual experiments. We will be using models of coin tossing and forest fire burning to illustrate these Common Core Standards.

Why Computational Reasoning? (cont) Supports Science Practices recommended by the 2011 Framework for K-12 Science Education Developing and using models Using mathematics, information and computer technology, and computational thinking Supports teaching science as inquiry by providing: Models of real world events that are difficult to demonstrate in wet lab experiments Opportunities for careful observation and analysis of scientific investigations The ability to test hypotheses, analyze results, form explanations, judge the logic and consistency of conclusions, and predict future outcomes. Point out how computational reasoning is relevant in science. In science, we can use models to represent difficult real-world events. Have to be able to challenge models. Do the results of the model make sense? This leads to critical thinking skills that we want students to have. We will be using models of coin tossing and forest fire burning to illustrate how computational reasoning supports inquiry-based learning. I would also add that this approach to teaching math and science really helps to integrates the STEM disciplines (especially S, M, T) and helps to mutually reinforce math and and science concepts. You cannot teach computational science without an emphasis on the math!

CAST: Professional Development Program The CAST Professional Development Program is an integrated set of modules to train teachers on how to incorporate computational reasoning and tools, such as modeling and simulation, into their middle and high school math and science curriculum Point out how computational reasoning is relevant in science. In science, we can use models to represent difficult real-world events. Have to be able to challenge models. Do the results of the model make sense? This leads to critical thinking skills that we want students to have. We will be using models of coin tossing and forest fire burning to illustrate how computational reasoning supports inquiry-based learning. I would also add that this approach to teaching math and science really helps to integrates the STEM disciplines (especially S, M, T) and helps to mutually reinforce math and and science concepts. You cannot teach computational science without an emphasis on the math!

CAST Two-Track Program The introductory track is a set of modules that focuses on how to use models and simulations that already exist and are available over the internet, with enough understanding about how such models work to know how to use them effectively in the classroom. The depth track is a set of modules that provides more in-depth understanding and hands-on experience with the different modeling tools. This track is intended for new CAST PDP trainers and also teachers who desire a deeper understanding of the tools. Both tracks explore three modeling tools: Excel models Agent models System or Aggregate models Describe design of overall program. No need to go into more description of the three types - that will come.