# Modeling

*Content on this page is derived from participant presentations, discussions, and breakout groups at the Teaching Computation with MATLAB workshops.*

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**

- Translation from idea to model construction
- Identifying and evaluating model assumptions
- Planning and troubleshooting numerical models
- Calibration and verification of a model
- Using models for prediction
- Presentation of modeling result

**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

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