We describe how to enable students to learn about the transmission of disease, resistant bacteria, and the importance of taking a “full course” of antibiotics by developing models and simulations to represent the growth and demise of bacteria. By doing these activities, students experience a model of the effects of antibiotics on the population of disease-causing bacteria during an infection. Students learn about the spread of infection through game playing and then, using a simulation, investigate how different variables, such as skipping a day of medication, affect the persistence of the disease. A key concept is that almost every naturally occurring population of bacteria that causes disease has a component that is resistant to antibiotics. Therefore, through graphing data and computer models, students can visually understand why it is important to take a complete course of antibiotics to kill all the bacteria and decrease the likelihood of bacteria becoming resistant, which can be harmful to human health. In this hands-on, inquiry-based activity that is seamlessly integrated with technology, the teacher becomes the facilitator of learning while the student is an active, engaged partner.

“Can you come over and hang out?” Katie texted Elena, her friend from Ms. Collins's sixth-grade class, on a Saturday afternoon. “I can't,” Elena replied. “I just got back from the doctor's office. I got sick last night with a high fever and a bad sore throat. The doctor said I have strep throat and now I am on antibiotics.”

“That's too bad,” Katie wrote. “Well, I wonder how you got that. Will you be back in school on Monday?” “Yes, since I will have been taking the medicine for more than 24 hours,” texted Elena. “But I don't know why I have to keep taking the medicine for 10 days! My stomach is getting upset already.”

Does this sound like a scenario that could take place in a typical classroom? How can we teach students so that they understand how diseases are transmitted and why they need to take their medication for the entire length of time it is prescribed? Conversely, we need to convey the importance of not taking antibiotics for colds or other viruses, since antibiotics only kill bacteria. Here, we present a way to teach students about the transmission of disease and the importance of taking a “full course” of antibiotics. Using technology, students develop models to represent the growth and demise of bacteria.

## Background

The Next Generation Science Standards (NGSS) were developed by the National Research Council (NRC), the National Science Teachers Association, and the American Association for the Advancement of Science (AAAS) and managed by Achieve, Inc. In the standards, the expectation is that students will develop the behaviors and skills practiced by scientists when they investigate and build models and theories about the natural world, and emulate engineers in designing and building models and systems. For example, “Practice 2” is “Developing and Using Models.” Students are expected to use models to “describe, test, and predict more abstract phenomena and design systems” (NGSS Lead States, 2013).

Both scientists and engineers construct and use models as helpful tools for representing ideas and explanations. These tools include diagrams, drawings, physical replicas, mathematical representations, analogies, and computer simulations (NSTA, 2014). According to the NGSS, “Although models do not correspond exactly to the real world, they bring certain features into focus while obscuring others. All models contain approximations and assumptions that limit the range of validity and predictive power, so it is important for students to recognize their limitations” (NSTA, 2014).

By participating in the activities described, students experience a model of the effects of antibiotics on the population of disease-causing bacteria during an infection. In this case, the action of antibiotics on bacteria is simplified and, as with any model, there are limitations, but students can get a good idea of how antibiotics work. Students learn about the spread of infection through game playing and then, using a simulation, investigate how different variables, such as skipping a day of medication, affect the persistence of the disease.

A key concept is that almost every naturally occurring population of bacteria that causes disease has a component that is resistant to antibiotics. Therefore, through graphing data and computer models, students can visually understand why it is important to take a complete course of antibiotics to kill all the bacteria and decrease the likelihood of bacteria becoming resistant, which can be harmful to human health. Students also learn that some bacteria are “stronger” than others and more resistant to drugs.

Prior to the NGSS, the National Science Education Standards (NRC, 1996) and state standards across the country expected students to learn that scientists often create models to explain scientific phenomena. The NRC's Framework describes a vision of what it means to be proficient in science; it rests on a view of science as both a body of knowledge and an evidence-based, model- and theory-building enterprise that continually extends, refines, and revises knowledge (NRC, 2012). The National Science Education Standards state that many students in middle and high school “view models as physical copies of reality and not as conceptual representations. Teachers should help students understand that models are developed and tested by comparing the model with observations of reality” (NRC, 1996, p. 127). The NGSS have been adopted by 17 states and the District of Columbia so far (Heitin, 2014). Helping students develop a strong foundation in their understanding of models can only improve their future understanding of science and mathematical concepts. Unifying concepts in the standards – such as systems, order, and organization as well as models, evidence, and explanation – provide students with powerful ideas to help them understand the natural world (NRC, 1996, p. 115).

## Introductory Activity

We begin by having students play an engaging game that encourages them to think about how diseases spread. “The Infection Game,” developed by Rob Quaden, Alan Ticotsky, and Debra Lyneis (2009), is described in the Creative Learning Exchange newsletter. This game simulates the generic structure of the spread of a contagious activity, or infection, and once students understand how it works, they will be able to understand the spread of a rumor, a fad, or a computer virus (Quaden et al., 2009, p. 1). It is best played with 35 players, so classes can be combined. The rules for the students are as follows:

1. You will receive a sheet to track the results of the game.

2. You will be given a secret number, which will already be filled in on your record sheet.

3. Secrecy and accuracy are very important!

4. You will play the game for several rounds. In the first round, find any other student and quietly tell each other your numbers. Then, on your own, secretly multiply your two numbers together and record the product on the next line of your sheet. This will be your new number for the next round.

For example, if you have a “1” and the other student has a “0,” you will both get 1 × 0 = 0 as the new number on your next line. In the next round, find another student and tell each other your number, multiply them, and record the new product on the next line.

5. Continue to do this until the teacher ends the game (Quaden et al., 2009, p. 1).

After the teacher explains the rules, students can play for about four minutes. The game works like this. The spread of a disease is represented by the multiplication of numbers. Each student is given the number “1” except for one student, who, unknowingly, is given the number “0.” The interactions represent the exchange of germs. Each student approaches another student in class and shares his or her number with the other student. Each student then multiplies his or her own number by the number of the other student to arrive at his or her new number for the next round. Since everyone in class has been given a worksheet with “1” as their number except for one student who, unknowingly, has been given a “0,” the results are an increasing number of “0s” in the class. By the end of about four minutes, most, if not all, students will have a “0” as their final product.

After the game, the teacher should ask who had the first entry of “0” in the beginning of the game. (It should only be one person.) Then ask how many had “0” in the second round, and so on. The teacher's class record should look like Table 1 (Quaden et al., 2009, p. 3).

Table 1.
Data.
RoundNumber of New ZerosTotal Number of Zeros
Start
16
RoundNumber of New ZerosTotal Number of Zeros
Start
16

After all the students have interacted, the class should create a graph with a spreadsheet and plot the number of new “0s” and the total number of “0s” for each round of the game (see Figure 1).

Figure 1.
Students “infected” over time (Quaden et al., 2009, p. 6).
Figure 1.
Students “infected” over time (Quaden et al., 2009, p. 6).

The graph shows one curve on the bottom that represents the new infections each round and another curve above that is “s” shaped for the total number of infected students. Students, either in small groups or as a whole class, can engage in building a table of results and a graph to see the pattern of the spread of the disease. The creation and interpretation of graphs such as this are common expectations of middle school students.

## Using a Computer Simulation

A computer simulation is a “computer program that recreates an abstract, real-world system. Computer simulations are used in science to explore concepts that are difficult or impossible to observe in the real world. In this case, a computer simulation can conduct many trials in a fraction of the time it would take to do it manually.

Thus, the next step, which helps further students’ understanding of why things change, is to teach them about “stocks” and “flows.” A stock can be viewed as any accumulation and a flow as the increasing or decreasing of the stock. Many people think of a stock as a bathtub. In this image the person's body (the bathtub) fills up with bacteria. The inflow to the stock is like the faucet that fills the tub, while the outflow is like the drain that empties it. We did this with sixth-graders; we first explained what a stock is by simply demonstrating how water flows from one cup to another, representing a stock of water and the flow. Once this is understood, and students are at a more sophisticated level, students and the teacher build a stock-and-flow diagram to represent the behavior of the system (Figure 2).

Figure 2.
Stock-and-flow diagram (Quaden et al., 2009, p. 11).
Figure 2.
Stock-and-flow diagram (Quaden et al., 2009, p. 11).

When this is built and run with software such as STELLA (http://www.iseesystems.com/), the students can watch the graphs being built and run the model with different values to see the same behavior develop over time. Through this dramatizing exercise, students can see how quickly germs can spread.

## Hands-On Simulation of a Bacterial Infection

The next activity is from the Science Education for Public Understanding Program (SEPUP, 2010). The introduction to the activity explains that when harmful bacteria reproduce too quickly, the body's immune system cannot control the growing population of bacteria, which leads to an infection. Antibiotics help by killing off the bacteria; however, some bacteria are more resistant to the antibiotic and will not be killed as quickly, thus continuing to grow and multiply. By completing the “full course” of antibiotics, the patient helps ensure that the bacteria are killed off and the infection cured.

We started by asking the students, by a show of hands, how many had ever had an ear infection or strep throat or had taken antibiotics. Predictably, they all raised their hands. We explained that by playing a game using chips and dice, which simulates the bacteria and taking the medication, they would see how antibiotics help cure an infection.

The activity materials include 50 disks (poker chips can be used) in three colors, 15 orange, 15 blue, and 20 green. The orange disks represent the most resistant bacteria, the blue represent resistant bacteria, and the green represent the least resistant bacteria. Students (working in pairs) begin with 20 chips (13 green, 6 blue, and 1 orange) and roll a die to determine if they “took” the antibiotic or if they “forgot” to take it. Students work in pairs and each pair has a die. Students roll the dice, and after each roll, they follow the corresponding directions: rolling a “1,” “3,” “5,” or “6” indicates taking the medication; rolling a “2” or a “4” means that a dose was forgotten. Because the colors represent antibiotic resistance, students remove the green first, then blue, and then orange. In every case, however, if there is a chip of any color left, another chip of that color is added to simulate that the bacteria are still reproducing. Students keep track of the number of each type of bacteria until all are “killed” by the antibiotic.

Students record their data on a table, tracking how many disks of each color are left after each roll. Finally, students graph their data so that they have a visual representation, drawing the demise of the bacteria with green, blue, and orange markers. They can also use Microsoft Excel to graph the data.

There is no set number of rounds in this game, because it depends on how many times the players roll a “2” or a “4,” which means they forgot to take the medication on time, and therefore the bacteria keep multiplying. It can be as few as eight rounds or many more. The teacher can choose 10 rounds to simulate taking antibiotics for ten days. If the “infection” is not cleared up by then, this would be a great opportunity to discuss why sometimes people have to take an additional course of medication or even switch to a more powerful antibiotic. The data can be charted as shown in Table 2. An example of game play is recorded in Table 3.

Table 2.
Chart for recording number of harmful bacteria in your body (Science Education for Public Understanding Program, 2010, C-269).
Round NumberLeast resistant BacteriaResistant BacteriaExtremely Resistant BacteriaTotal
Initial 13 20

10
Round NumberLeast resistant BacteriaResistant BacteriaExtremely Resistant BacteriaTotal
Initial 13 20

10
Table 3.
Example of playing the game. In this case, the person “forgot” to take the antibiotics twice, so the antibiotics worked in 12 days instead of 10.
Number of Harmful Bacteria in Your Body
Round NumberRoll of DieMeaningLeast Resistant BacteriaResistant BacteriaExtremely Resistant BacteriaTotalAction Taken
Initial   13 20 Removed 5 green, added 1 of green, blue, and orange
Took antibiotics 18 Removed 5 green, added 1 of green, blue, and orange
Forgot to take antibiotics 10 21 Added 1 of each color
Took antibiotics 19 Removed 5 green, added 1 of each color
Took antibiotics 10 17 Removed 5 green, added 1 of each color
Took antibiotics 14 Removed 5 (2 green, 3 blue) added 1 blue and 1 orange
Took antibiotics 11 Removed 5 blue, put back 1 blue and added 1 orange
Forgot to take antibiotics  Added 1 blue and 1 orange
Took antibiotics  Removed 5 blue, added 1 orange
Took antibiotics  Removed 4 orange
10 Forgot to take antibiotics  Added one orange
11 Took antibiotics  Removed 4 orange
12 Took antibiotics  Removed remaining 2 orange
Number of Harmful Bacteria in Your Body
Round NumberRoll of DieMeaningLeast Resistant BacteriaResistant BacteriaExtremely Resistant BacteriaTotalAction Taken
Initial   13 20 Removed 5 green, added 1 of green, blue, and orange
Took antibiotics 18 Removed 5 green, added 1 of green, blue, and orange
Forgot to take antibiotics 10 21 Added 1 of each color
Took antibiotics 19 Removed 5 green, added 1 of each color
Took antibiotics 10 17 Removed 5 green, added 1 of each color
Took antibiotics 14 Removed 5 (2 green, 3 blue) added 1 blue and 1 orange
Took antibiotics 11 Removed 5 blue, put back 1 blue and added 1 orange
Forgot to take antibiotics  Added 1 blue and 1 orange
Took antibiotics  Removed 5 blue, added 1 orange
Took antibiotics  Removed 4 orange
10 Forgot to take antibiotics  Added one orange
11 Took antibiotics  Removed 4 orange
12 Took antibiotics  Removed remaining 2 orange

Using this data and creating a graph is an excellent way to review math graphing skills. Being able to interpret or construct graphical representations is a crucial skill for every student, whether or not they want to pursue science- or math-related careers (Ozgun-Koca, 2001). The Common Core Standards require that students use mathematics to model real-world problems, to communicate mathematically, to solve problems, and to use and interpret graphs and organize and describe data. This is also an opportunity to discuss antibiotic resistance. The first antibiotic (penicillin) was discovered by Sir Alexander Fleming in 1929. By the 1930s and '40s, other antibiotics were developed and used to treat urinary tract infections, pneumonia, and other conditions (Todar, 2012, p. 1). Very soon after, in the late 1940s, resistance to antibiotics was noted. Evidence also began to accumulate that bacteria could pass genes for drug resistance between strains and even between species (Todar, 2012, p. 2).

Antibiotic-resistant bacteria constitute a growing public health crisis because infections from resistant bacteria are increasingly difficult and expensive to treat (Sustainable Table, 2015). Resistant bacterial strains have become more prevalent. More than 90 strains of Staphylococcus aureus, a common cause of hospital staph infections, are now resistant to penicillin (SEPUP, 2010).

Antibiotic resistance is one of the most pressing public health issues facing the world today. The Centers for Disease Control and Prevention (CDC) estimates that each year at least two million illnesses and 23,000 deaths are caused by antibiotic-resistant bacteria in the United States alone. Antibiotic resistance limits our ability to quickly and reliably treat bacterial infections, and the rise of resistance could hamper our ability to perform a range of modern medical procedures from joint replacements to organ transplants, the safety of which depends on our ability to treat bacterial infections that can arise as post-surgical complications. Antibiotic-resistant bacteria also pose economic threats. The CDC reports that antibiotic-resistant infections account for at least $20 billion in excess direct health care costs and up to$35 billion in lost productivity due to hospitalizations and sick days each year. (“Fact Sheet,” 2015)

Recently, the Washington Post (March 27, 2015) reported that antibiotic resistance is a mounting problem that causes an estimated 2 million illnesses and 23,000 deaths every year in the United States. There are several factors contributing to the increase in antibiotic-resistant bacteria, in addition to the natural resilience of the bacteria in developing resistance to the antibiotics. One important factor is the overuse and misuse of antibiotics. The antibiotic use rate was 0.85 prescriptions per capita in 2009 for the entire United States, which means almost one prescription for every person in the country (“Antimicrobial prescription data,” 2010). In 1998, 80 million prescriptions for human antibiotic use were filled (Todar, 2012, p. 1). Inappropriate uses of antibiotics in both medicine and agriculture drive up the use rate and the development of resistance; agricultural practices account for over 60% of antibiotic use in the United States. The result is that once-powerful drugs are losing their ability to kill emerging “superbug” strains of disease-causing bacteria.

Random mutations in microbes and the ability of bacteria to exchange genetic material have long been hypothesized to foster the evolution of resistant strains. However, a recent study in the journal Science Advances found that preventing antibiotic resistance may be much more difficult than believed, because the microbes long ago evolved the ability to fight toxins, including antibiotics. Scientists studied the people called Yanomami – hunter-gatherers in the remote mountains of the Amazon jungle of Venezuela – in 2009. These people had never been exposed to Western medicine or diets. Yet the scientists found that the “Yanomami's gut bacteria have already evolved a diverse array of antibiotic-resistance genes…even though these mountain people had never ingested antibiotics or animals raised with drugs” (Gibbons, 2015). This new study suggests that resistance genes have been around in the human microbiome (the trillions of bacteria that live in and on the body) for thousands of years – long before antibiotic drugs were invented. The team of scientists speculated that “antibiotics are not just a human invention. Bacteria evolved strategies to kill each other long before we were around – they were the first inventors of antibiotics. And to defend against this, they developed resistance mechanisms” (Gibbons, 2015).

## Antibiotic Discovered That Is Resistant to Resistance!

A study published recently in Nature (Ling et al., 2015) revealed a new antibiotic called “teixobactin,” which might keep working for more than 30 years because of its unique method of action. It may be resistant to resistance (Feltman, 2015).

Lossee Ling from NovoBiotic pharmaceuticals and Tanja Schneider at the University of Bonn showed that teixobactin works by withholding two molecules – Lipid II, which bacteria need to make the thick walls around their cells, and Lipid III, which stops their exiting walls from breaking down. When teixobactin is around, bacterial walls come crumbling down, and don't get rebuilt. The drug also sticks to parts of Lipid Ii and Lipid III that are constant across different species of bacteria. It's likely that these parts can't be altered without disastrous consequences, making it harder for bacteria to avoid teixobactin's double punch. This might explain why it's so hard to evolve resistance to the drug. (Yong, 2015)

## Stopping Antibiotics Prematurely

Many people stop taking an antibiotic prescription after a few days, when they feel better, although not all the bacteria have been killed. This contributes to the more resistant bacteria reproducing, increasing their population, and increasing the chances that future infections will not respond to the typical course of antibiotics. By playing this game, students will visually see, by graphing, how the population spikes when a dose is “missed.”

Another valuable tool to develop problem-solving skills is the use of simulations. Simulations enable users to play and replay a problem, while changing the values of one variable at a time and then observing the behavior of the system. One simulation that we have developed presents students with the problem of explaining the impact of taking a portion of a prescribed medicine, of sporadically taking a prescription, or of taking the entire prescription (“full course”) as prescribed. The simulation generates a table of values and a graphic representation for each run that engages students in explaining the contrasting patterns of behavior of the system.

One of the advantages of simulations built with an application like STELLA is that the organization of the system is clearly presented in a language that expresses accumulations (i.e., stocks) as rectangles, the movements (i.e., flows) of a substance (e.g., a disease) as pipes, and feedback loops as lines with arrows. With this simple vocabulary, extraordinarily complex systems can be depicted and tested by running the simulation repeatedly.

Our students also learned that by using computer simulations, much time is saved in doing experiments and that scientists can repeat the scenarios many times to investigate the results. In the game play described above, the stock of healthy people flowed to the stock of infected people. The flow at the outset was gradual, since only one student began with a “0” to indicate that they were ill, and then increased as more and more students spread the illness to others. Finally, when most students had been infected, the number of new infections tapered off because many of the interactions were between already ill students. When students have an opportunity to see the system in the iconic representation of stocks and flows or through the generated graphs, they gain valuable conceptual tools that can be applied to any problem that involves change.

A significant network of schools has been integrating systems thinking and the use of dynamic modeling into the curriculum for the past two decades. Information about these efforts is available from the Creative Learning Exchange and the Waters Foundation.

## Conclusion

Student feedback included the following comments:

• “I learned that even if you take antibiotics, the bacteria keep multiplying. That is why you must take antibiotics for an extended period of time.”

• “I liked this project because it helped me understand how an infection works; if you don't treat it the bacteria get stronger.”

• “I learned that bacteria grow in a certain way. I thought it was cool and a lot of fun on learning about bacteria.”

• “I liked the activity. Something I learned is [that] the bacteria still grow when you are getting better.”

• “It showed me how to take care of myself better.”

These student-centered, inherently collaborative learning activities are effective pedagogical techniques that meet the call for the development of communication, collaboration, critical-thinking, and problem-solving skills identified by the Partnership for 21st Century Learning. As an aspect of critical thinking, students are expected to analyze how parts of a system interact to produce outcomes. In addition, one of the interdisciplinary themes articulated by the Partnership is that of health literacy. Student expectations include, but are not limited to, being able to use available information to make appropriate health-related decisions, and to understand national and international public health and safety issues.

The entire concept of scientific literacy includes the ability to make decisions based on evidence and the interpretation of information. The NGSS expect students to understand how models are used by scientists and engineers to explain phenomena and solve problems. The NGSS also “aim to prepare students to be better decision makers about scientific and technical issues and to apply science to their daily lives” (Achieve, Inc., 2013). What better way to apply science than to a common experience – taking antibiotics? In this hands-on, inquiry-based activity that is seamlessly integrated with technology, the teacher becomes the facilitator of learning while the student is an active, engaged partner.

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