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Researchers should cite this work as follows:

• Jungck, J. (2023). 2010-Jungck-EtAl-Mathematical Manipulative Models-In Defense of Beanbag Biology. SIMIODE, QUBES Educational Resources. doi:10.25334/V7RQ-YJ08

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Jungck, John R., Holly Gaff, and Anton E. Weisstein. 2010.  Mathematical Manipulative Models: In Defense of “Beanbag Biology”. CBE—Life Sciences Education. 9: 201–211.

See https://www.lifescied.org/doi/pdf/10.1187/cbe.10-03-0040 . Accessed 28 March 2023.

This paper offers up samples of projects from the  Bio- QUEST Curriculum Consortium’s 24-yr experience of holding faculty development workshops for biology and mathematics educators.

We quote from an experiential activity on epidemics, but see the paper for more details.

Outbreak in a Cup - epidemic modeling.

Many mathematical models have been used to explore the dynamics and control of infectious diseases. The basic frame- work of these models is to divide the population into groups according to their disease status: susceptible to the disease, infected and infectious, recovered and immune, and so on. The model then estimates the movement of individuals between these disease groups. To demonstrate how to develop such a model and explore the dynamics of a disease in a population, we developed a simple hands-on  exercise.

Game 1a. Students are divided into small groups of two to four students.  Each  group  is  given  one  empty  cup  (the “experiment” cup), a second cup containing approximately 50 brown beans (kidney beans work well and an inexpensive 1-lb bag is usually enough for a class of 24), and a third cup with approximately 50 white beans (navy or northern beans provided they are approximately the same shape as the kidney beans). Each group then sets up the initial scenario by placing 20 brown beans and one white bean into the experiment cup. The stu- dents are then instructed to repeat the following set of   steps:

*** Without looking in the cup, a student from the group selects two beans from the cup.
*** If both beans are the same color, the student simply returns the beans.
*** If one bean is brown and the other white, the student re- moves the brown bean and returns two white beans to the cup.
*** At each time step, record the event that occurs: either no change or a new infection.
*** Repeat this process until told to stop.

Note that the number of beans in the experiment cup should remain constant.

This simple game demonstrates how a disease could move through a population. It is important to discuss the assumptions that underlie this model. For example, no one recovers from this disease. Discussions about these assumptions can lead to any number of variations on this game. For example, some variations could be as  follows:

Reduction in spread rate. Provide the students with a coin to flip when they get the one brown, one white draw. Transmission (e.g., replacing the brown with a white) only occurs if they flip heads.

Vaccination. Using a third color of beans (e.g., beige garbanzo beans or green peas, again making sure there is no difference in size or shape), replace a certain number of susceptible (brown) beans with vaccinated (beige) beans. Track the differences in the number of new infections  as a function of percentage of the population vaccinated.

Recovery. Similarly to the vaccination, use red beans to replace a random infected (white) bean after a given number of draws or at announced times.

This simple game quickly demonstrates to students how to build a mathematical model for the spread of an infectious disease by understanding the basic epidemiology of the  disease.