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¡Alerta! Our World Is Changing: Revealing Impacts on Our World with Mathematics

Kyndall Brown, Dee Crescitelli, Silvia Llamas-Flores, and Carlos LópezLeiva

Climate change has brought about expansive changes and has had negative global ecological and economic consequences. In addition, the widespread prevalence of environmental pollution has been exasperated by human-caused pollution, which causes devastating harm to our earth’s ecosystem. In our previous blog we discussed reciprocity as being one of the 4R’s, which describes kinship and obligation as “cyclical” or mutual (Harris & Wasileski, 2024, p. 5).  As such, we have an obligation to respect our mother Earth by limiting and/or eliminating human-caused pollution.

This blog explores littering pollution and extreme weather events, both of which, one can argue, serve as exploitation of the Earth and its resources. The intent of this blog is to highlight and raise awareness of the harmful effects of human activity on our Earth through a series of mathematical tasks and ideas designed for high school teachers. The two tasks in this blog focus on the mathematical modeling of face mask disposal and extreme weather events, both of which can be modeled by exponential functions.

In the following activities, students are tasked with doing a model analysis, creating a mathematical model that best represents the data, extrapolating, and making recommendations based on their findings. The extent of scaffolding that is needed to create and interpret the mathematical models depends on the level of experience and exposure that students have with Desmos and running different types of regressions.  The following Desmos linear regression guide is provided for your convenience.  We encourage you to make the tasks/topics your own by scaffolding the activities in ways that are conducive to your individual students’ needs.

Lastly, in addition to the two tasks, there are a series of ideas that can be used to explore other climate change topics using a mathematical lens. The hope is that teachers feel compelled to explore issues of climate change with their students and have meaningful and impactful conversations about what our responsibilities are to our Earth and ways to mitigate the damaging effects of climate change.

 

Extreme Weather 

As students engage with the topic of extreme weather, consider the following discussion topics.  The hope is to encourage students to use a mathematical lens to make informed and responsible decisions about the role of climate change on our Earth.

  • Using a mathematical argument, based on your finding above, what recommendations would you make to stakeholders about climate change?
  • If you were speaking to your high school graduating class, what message would you convey about climate change? Why? How can you use a mathematical argument to help support your message?
  • Based on the extrapolation data, what are some ways that human activity can counter climate change?

 

Activity 1

There has been a significant increase in storms and floods in the 21st century.  According to the International Disaster Database Tracking (EM-DAT), the cumulative number of natural disasters/extreme weather events in Europe since 1939 has significantly increased in recent years (Center for Research on the Epidemiology of Disasters (Em-Dat), n.d).

The data seems to indicate that in the past 100 years, more than 1,500 extreme weather events, including droughts, floods, storms, and extreme temperatures, have occurred in Europe, with approximately 67% of those events taking place since early 2000.

 

Years since 1939, t  Cumulative number of natural disasters in Europe, N
0 11
20 27
40 91
60 536
80 1452
  1. Create a scatter plot of the data and decide which type of function would best model this data. Justify your model selection.
  2. Create a regression model based on the type of function that you selected in part “a”.  How accurate is your model? How do you know, and what does the accuracy tell you about values you extrapolate from the model?
  3. According to your regression model, how many cumulative natural disasters does the model forecast there will be in 2030? 
  4. Using your exponential model, how long will it take for the cumulative natural disasters to double what they were in 1939? Solve algebraically using logarithms.
  5. Using the exponential model, at what rate does the model imply that the cumulative natural disasters are increasing yearly?

 

Littering Pollution – Face Masks

As students engage with the topic of human-caused pollution, consider the following discussion topics. 

  • Irresponsible disposal of face masks contributed to an estimated 1.56 billion face masks (over 10 million pounds) entering oceans in 2020 (Source:  https://populationeducation.org/the-global-impact-of-disposable-single-use-covid-19-face-masks/).
    • Once in the ocean, how can face masks harm marine life and pollute distant shores?
    • What is the global impact of disposable face masks on our earth?
    • What are some strategies that can help mitigate the harmful effects of masks on our earth?

 

Activity 2

The epitome of 2020: COVID-19 face masks. While hard to find in early 2020, disposable face masks are now readily available everywhere. Questions arise about the materials used to make them and the long-term global impact on our environment.  There is concern about using materials, such as polypropylene, that take 450 years to decompose, given the large quantities of used disposable face masks that end up in landfills and our oceans. It is estimated that 1.56 billion disposable face masks entered the ocean in 2020, which is over 10 million pounds of material (oceanasia.org). One of the main concerns is that once in the ocean, face masks can travel to global waters and potentially harm marine life, as well as pollute our shores.

According to a study published in 2022, there is evidence to indicate that the toxic chemicals and organic compounds in face masks, when submerged, release micro- or nanofibers into the marine environment that have an adverse impact on marine ecology and human health (Hui Li, et al., 2022).

Polluting our oceans with disposable face masks unequivocally has detrimental effects on our planet. Continued pollution is a prime example of the lack of respect and responsibility that we have for our environment. Furthermore, the use of materials in disposable face masks that we know take hundreds and hundreds of years to decompose is an example of the irresponsibility that comes with creating and using disposable face masks instead of more sustainable and reusable materials.

The disposable face mask market grew dramatically between 2020 and 2022, largely due to the global Covid-19 pandemic. However, as the pandemic crisis slows down, it is estimated that this market will decrease significantly. In 2020, the North American protective face masks market was reported at $742.1 billion. According to industry trends, it is expected that by 2026, the market will have dropped to $346.7 billion.

  1. Assuming an exponential function best models industry trends, create a mathematical model to represent this data.
  2. According to your mathematical model, by what percentage has the face mask market increased yearly since 2020?  
  3. Using your model, predict what the market will be in 2030. Does your solution make sense? Why or why not? Justify your thinking.

Additional Climate Change Topics to Consider

The following high school lesson ideas explore different concepts centered on the idea of climate change.  

  • Quadratic Modeling – Use quadratic function modeling to create a model for the revenue of disposable face masks over the next several years. Focus can be drawn to the vertex (max revenue), horizontal intercept(s)(when revenue will be $0), and concavity (the rate at which revenues are increasing and decreasing over time). How does the pandemic factor into this, and how will it impact this model?
  • Sinusoidal Modeling – Using the average high temperatures of any given region, create sinusoidal models for various years to compare and contrast the rise in temperature. Students can then use their models to extrapolate based on trends they discover.
  • Exponential Growth and Decay – Explore the dropping cost of solar and wind energy. Students can create comparative models to show which cost is dropping faster. Similarly, students can create mathematical models for solar and wind consumption as a function of time. Once models are created, students can use the idea of doubling and half-life to make predictions.
  • Mathematical Models – Using global economic data, students can explore the soaring cost of climate change, specifically by examining economic losses attributed to weather, climate, and water extremes.

Resources

Other Resources

References

Li, A. S. H., Sathishkumar, P., Selahuddeen, M. L., Wan Mahmood, W. M. A., Zainal Abidin, M. H., Abdul Wahab, R., Mohamed Huri, M. A., & Abdullah, F. (2022). Adverse environmental effects of disposable face masks due to the excess usage. Environmental Pollution, 308, 119674. https://doi.org/10.1016/j.envpol.2022.119674

Center for Research on the Epidemiology of Disasters (Em-Dat). (n.d). Inventorying hazards and disasters worldwide since 1988. https://www.emdat.be/.

Harris, L. D., & Wasilewski, J. (2004). Indigeneity, an alternative worldview: Four R’s (relationships, responsibility, reciprocity, redistribution) vs. two P’s (power and profit). Sharing the journey towards conscious evolution. Systems Research and Behavioral Science, 21, 1-15. https://doi.org/10.1002/sres.631.