Modeling

Modeling in courses that incorporate computation can help students better understand physical systems. Conceptualizing a model gives students the opportunity to define inputs/outputs, conservative quantities, discretization, and boundary and initial conditions. In addition, students evaluate assumptions and make predictions––important skills transferable through STEM. Workshop participants identified a number of strategies and approaches to help develop students' modeling skills. These strategies include providing students with a strong conceptual foundation, scaffolding activities to ease students in and give feedback, and developing clear learning objectives.

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Approaches to Teaching Modeling

During the 2016 workshop, participants identified the following approaches to introduce modeling to students:

• Ask conceptual questions early on and use real life examples
• Using real life examples, for example exploring an Environmental Crisis at Mono Lake can increase student motivation and interest.
• Explore system behavior before the mathematical underpinnings
• Help students develop an understanding of basic system components and relationships before trying to model them.
• Start with low threshold GUI-based tools or pre-packed environments
• MATLAB SimBiology is one example of a visual environment that instructors can use to get students started with modeling.
• Use pedagogical approaches and best-practices
• Scaffolding, metacognition, and cooperative learning can help build student self-efficacy with modeling.

Examples from workshop participants:

Greg Hancock (William & Mary) presented his approach to introducing students to modeling at the 2016 workshop: Introducing Mass Balancing Modeling Using a Controversial Environmental Problem. Hancock focuses on developing clear learning objectives and has the students answer the essential questions to constructing a mass conservation model. Using an environmental issue, water level in Mono Lake, CA, shows students that modeling and MATLAB can help solve real-world problems.

Download the presentation (PowerPoint 30.3MB Oct24 16)

Check out the corresponding teaching activity: Modeling Mono Lake's Water Balance by Phil Resor and Greg Hancock

Greg Hancock's Learning Objectives for Modeling

1. Translation from idea to model construction
2. Identifying and evaluating model assumptions
3. Planning and troubleshooting numerical models
4. Calibration and verification of a model
5. Using models for prediction
6. Presentation of modeling result

Letitia Hubbard (North Carolina School of Science and Math) used the Hodgkin-Huxley model as an example of how to help students develop a quantitative model to solve problems. In addition to the presentation, her teaching activity, modeling a neuron action potential in MATLAB, describes the learning goals, assessment, teaching tips, and necessary background information. To train the students to use models, Hubbard has students discern the physical basis for the model and demonstrate they understand the numerical methods by computing them by hand. Then, the students translate equations into MATLAB code to create the computational tool. Using a simulation, they can explore the impact of different variables on the model.

Download the presentation (PowerPoint 2007 (.pptx) 3.1MB Oct23 16)

Common Challenges and Solutions

Working groups considered common challenges to teaching modeling in undergraduate science courses. Some commonly cited challenges include:

• How to teach modeling when the math background is absent or weak.
• Build student self-efficacy through scaffolding and collaborative group work.
• Getting students to think critically about modeling results (e.g. units, orders of magnitude, common sense intuition)
• Wendy Thomas (University of Washington) describes how she tackled this in her essay: Garbage Out? Verification of Reliable Computations.
• Methods for assessing student knowledge.
• See assessment techniques used by instructors who teach with MATLAB.
• For other examples, see the HPC University Competencies.
• How to assess different teaching methods.
• The Assessment pages from the Pedagogy in Action portal have an overview of assessment tools and approaches.

Resources for Developing Students' Modeling Skills

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Activities

Biology

• Mathematical Analysis of Type 2 Diabetes Predisposition by Gregory Goins, Biology, North Carolina A & T State University
• Modeling an Neuron Action Potential in Matlab by Letitia Hubbard, North Carolina School of Science and Math
• Population Dynamics: Bacterial Growth Curves Provide Data to Calculate Growth Rates and Carrying Capacity by Anne Walter, Biology, Saint Olaf College

Engineering

• Simulation of a Two Storey Structure Under Dynamic Loads by William Cluett, Chemical Engineering & Applied Chemistry, University of Toronto
• Sophomore Bioengineering Final Project by Princess Imoukhuede, Bioengineering, University of Illinois at Urbana-Champaign

Geoscience

• Investigation Solution Methods for the Groundwater Flow Equations by Michael Cardiff, Geosciences, University of Wisconsin-Madison
• Modeling River Long Profiles by Andrew Darling, Geosciences, Colorado State University
• Conservation Equation Model by Gregory Hancock, Geology, William & Mary
• Computational Inquiry into a Hillslope Surface Model by Risa Madoff, Geology and Geological Engineering, University of North Dakota
• Finite Difference Modeling of Hillslope Diffusion by Dylan Mikesell, Geosciences, Boise State University
• Getting Inside the Black Box by Phil Resor, Earth and Environmental Sciences, Wesleyan University
• The Rate of Change in Porosity as a Result of Mineral Precipitation by Aida Farough, Geology, Kansas State University

Mathematics

• The More The Merrier in The Math of Population Ecology by Victor Padron, Mathematics, Normandale Community College

Physics

• Relaxation Method for a Real Parallel-Plate Capacitor by Sean Bartz, Physics, Macalester College
• Modeling a Voltage Divider by Michele McColgan, Physics, Siena College

Community

• Join the Teaching Computation in the Sciences Using MATLAB community to discuss ideas and ask experts questions

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