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These materials are part of a collection of classroom-tested modules and courses developed by InTeGrate. The materials engage students in understanding the earth system as it intertwines with key societal issues. The materials are free and ready to be adapted by undergraduate educators across a range of courses including: general education or majors courses in Earth-focused disciplines such as geoscience or environmental science, social science, engineering, and other sciences, as well as courses for interdisciplinary programs.
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Unit 10: Coupled Economic and Environmental Models

Louisa Bradtmiller (Macalester College)
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These materials have been reviewed for their alignment with the Next Generation Science Standards as detailed below. Visit InTeGrate and the NGSS to learn more.

Overview

In this unit, students develop a model based on the "tragedy of the commons." The model includes both economic components (maximizing profit) and environmental components (the amount of land needed per sheep). They use the model to test different scenarios of resource management.

Science and Engineering Practices

Using Mathematics and Computational Thinking: Use mathematical, computational, and/or algorithmic representations of phenomena or design solutions to describe and/or support claims and/or explanations. HS-P5.2:

Planning and Carrying Out Investigations: Plan an investigation or test a design individually and collaboratively to produce data to serve as the basis for evidence as part of building and revising models, supporting explanations for phenomena, or testing solutions to problems. Consider possible confounding variables or effects and evaluate the investigation’s design to ensure variables are controlled. HS-P3.1:

Planning and Carrying Out Investigations: Make directional hypotheses that specify what happens to a dependent variable when an independent variable is manipulated. HS-P3.5:

Engaging in Argument from Evidence: Evaluate competing design solutions to a real-world problem based on scientific ideas and principles, empirical evidence, and/or logical arguments regarding relevant factors (e.g. economic, societal, environmental, ethical considerations). HS-P7.6:

Engaging in Argument from Evidence: Compare and evaluate competing arguments or design solutions in light of currently accepted explanations, new evidence, limitations (e.g., trade-offs), constraints, and ethical issues HS-P7.1:

Developing and Using Models: Develop and/or use a model (including mathematical and computational) to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems. HS-P2.6:

Cross Cutting Concepts

Systems and System Models: When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models. HS-C4.2:

Systems and System Models: Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models. HS-C4.4:

Systems and System Models: Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales. HS-C4.3:

Stability and Change: Feedback (negative or positive) can stabilize or destabilize a system. HS-C7.3:

Cause and effect: Cause and effect relationships can be suggested and predicted for complex natural and human designed systems by examining what is known about smaller scale mechanisms within the system. HS-C2.2:

Disciplinary Core Ideas

Human Impacts on Earth Systems: The sustainability of human societies and the biodiversity that supports them requires responsible management of natural resources. HS-ESS3.C1:

Human Impacts on Earth Systems: Scientists and engineers can make major contributions by developing technologies that produce less pollution and waste and that preclude ecosystem degradation. HS-ESS3.C2:

Performance Expectations

Earth and Human Activity: Create a computational simulation to illustrate the relationships among management of natural resources, the sustainability of human populations, and biodiversity. HS-ESS3-3:

This material was developed and reviewed through the InTeGrate curricular materials development process. This rigorous, structured process includes:

  • team-based development to ensure materials are appropriate across multiple educational settings.
  • multiple iterative reviews and feedback cycles through the course of material development with input to the authoring team from both project editors and an external assessment team.
  • real in-class testing of materials in at least 3 institutions with external review of student assessment data.
  • multiple reviews to ensure the materials meet the InTeGrate materials rubric which codifies best practices in curricular development, student assessment and pedagogic techniques.
  • review by external experts for accuracy of the science content.


This page first made public: Sep 15, 2017

Summary

How do people treat commonly held resources? Ecologist Garrett Hardin

suggested that, in the absence of any restrictions or incentives, rational people will tend to drastically overuse any common resource. In this exercise, students will explore a model of the most well-known example of the Tragedy of the Commons, that of sheep grazing on commonly owned land. The model is based on Hardin's assumption that without any rules, herders will continue to add sheep to the land since the benefits (in this case, profit from selling milk) accrue solely to the herder, while the costs (depleting the grass) are borne by everyone. While the models described below use the sheep grazing example throughout, there are many other "commons" in the modern environment, including the atmosphere with respect to the emission of carbon dioxide or air pollutants. Students will experiment with different mechanisms for regulating the commons, and will be introduced to the economic concept of discounting as it applies to comparing costs or benefits between two time periods.

Learning Goals

On completing this module, students are expected to be able to:

  • Create quantitative models that combine natural and human systems.
  • Demonstrate the connections between human decision-making and resource availability.
  • Compare different models of resource management in the context of sustainability.
This exercise addresses several of the guiding principles of the InTeGrate program. In particular, it requires the use of systems thinking to address an interdisciplinary problem, develops students' abilities to use numerical modeling to generate and test hypotheses, specifically addresses long-term sustainability of human behavior, and addresses a grand challenge facing society, anthropogenic warming.

Context for Use

This unit is intended to be used in a three- to four-hour class period that meets once a week. It can be used as part of this modeling course or it can be adapted as a lab exercise for a course in Earth science or climate. For this module, students should come to class prepared to take a short quiz on the assigned reading. Thereafter they will be led through a series of prompts designed to help them create and experiment with a number of simple models using the iconographic box modeling software STELLA (see https://www.iseesystems.com/store/products/ for different options for purchasing student or computer lab licenses of STELLA or for downloading a trial version).

For those learning to use STELLA, we suggest the online "play-along" tutorials from isee systems. You can find them here: isee Systems Tutorials.

Description and Teaching Materials

In addition to the Hardin paper, students should complete the Unit 10 Student Reading, which contains extra background information as well as some explanation of some of the mathematics involved.

Students should complete the Tragedy of the commons reading quiz (Microsoft Word 2007 (.docx) 50kB Aug11 16) before coming to class. The

Tragedy of the commons reading quiz key


This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

can be found here.

In class, students should be provided with a copy of the Tragedy of the commons exercise (Microsoft Word 2007 (.docx) 189kB Dec4 16) .

The

Tragedy of the commons exercise answer key


This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

contains answers as well as tips and strategies instructors can use to guide students through the exercise and information on typical stumbling blocks.

Instructors can download the STELLA tragedy of the commons models here:

  1. Basic commons model TOC basic (Stella Model (v10 .stmx) 12kB Aug11 16)
  2. Commons with limit on sheep TOC limit (Stella Model (v10 .stmx) 13kB Aug11 16)
  3. Commons with profit-driven sheep addition TOC profit (Stella Model (v10 .stmx) 11kB Aug11 16)
  4. Commons with discount rate TOC discount (Stella Model (v10 .stmx) 13kB Aug11 16)

The model was created using STELLA Professional and should open on any subsequent version of STELLA. If you are using an earlier version of STELLA, the complete model graphic and equations can be found in the answer key so that you can reconstruct the model yourself.

Teaching Notes and Tips

We generally post the readings and assignments for students to an LMS site (e.g. Moodle, Blackboard, Canvas). Students can open the assignment in Microsoft Word on the same computer they are using to construct the STELLA model and then answer the questions by typing directly into the document. Students can either print a paper copy to hand in to the instructor or email their modified file to the instructor. It is straightforward to copy graphs and model graphics out of STELLA and to paste them into Word. Simply select the items to be copied, hit copy in STELLA, and paste into Word. Alternatively, you can have students use screenshots. There is no need to export graphics to jpg.

We teach the course in a three- to four-hour block once a week because we have found that models require a lot of uninterrupted time to construct. If students have a 50- or 75-minute class period several times a week, they spend at least 20 minutes of subsequent class periods trying to figure out where they were in the exercise at the beginning of the week. This is not a good use of time, hence the recommended three- to four-hour class session once per week. However, we also know that sustaining attention for this length of time can be difficult. We therefore recommend allowing students the freedom to take breaks throughout the modeling session to get snacks or coffee.

A typical 4-hour class session might be broken up into the following sections:

  • 20-minute discussion of the reading to ensure all the students are familiar with the mathematics behind the model.
  • 1.5 to 2 hours to build the model.
  • 1.5 hours to conduct experiments.

Assessment

Answers to exercise questions are located in the answer key for this unit (see Description and Teaching Materials section above). Instructors may download an assessment rubric for the modeling exercise here: Assessment rubric (Microsoft Word 2007 (.docx) 121kB Jan8 15). Rather than assign a point value to every question in the exercise, we employ a holistic approach that determines the extent to which a student has correctly built the model, supplied appropriate documentation of equations and units, thoroughly answered questions throughout the assignment, and provided appropriately labeled graphs and figures in answering questions.

References and Resources

The original article: Hardin, Garrett, 1968, The Tragedy of the Commons, Science 162, n. 3859, p. 1243–1248.

More recent critiques and context: Basurto, Xavier and Elinor Ostrom, 2009, Beyond the Tragedy of the Commons.

TierneyLab blog post from the New York Times The Non-tragedy of the Commons

Background on the discount rate: Grist (silly): Discount rates with otters

Environmental Defense Fund: The cost of climate change 100 years from now

Conservation Strategy Fund: Cost-benefit discounting

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These materials are part of a collection of classroom-tested modules and courses developed by InTeGrate. The materials engage students in understanding the earth system as it intertwines with key societal issues. The collection is freely available and ready to be adapted by undergraduate educators across a range of courses including: general education or majors courses in Earth-focused disciplines such as geoscience or environmental science, social science, engineering, and other sciences, as well as courses for interdisciplinary programs.
Explore the Collection »