Student-Directed Project: Vaccination Rates
I introduced my algebra students to network theory through a series of challenge problems (such as the famous "Handshake Problem" illustrated below). They became very excited about it and asked to learn more about real-world applications of nodal network maps.
Eighth graders use node maps to illustrate their solution to the Handshake Problem. The problem in question is relatively simple: if there are n people in a room, what is the minimum number of handshakes that must occur if each person is to shake the hand of each other person. This problem can be solved algebraically, but students took a network theory approach by drawing nodes and connecting them to represent each handshake. The resulting maps actually have some very interesting geometric properties, which two of my students investigated as a side project.
Of course, network theory is integral to many computer functions. However, my students decided that they were more interested in modeling diffusion patterns based on human contact, so they elected to study the spread of communicable diseases. They examined numerous effects on disease transmission, from vaccination rates to recovery and mortality rates. As the images below show, modeling disease transmission involves some very complicated math. However, because this math was connected to an advocacy project, students were eager to engage with it. Thus, even as mathematical knowledge can enable advocacy work, advocacy work can inspire students to seek additional mathematical knowledge.
Node maps of disease diffusion. The image on the dry erase board to the left features maps showing the the spread of an infectious disease when 60% of the population is vaccinated (on the left) and when 20% of the population is vaccinated (on the right). The image on the graph paper to the right models a situation in which 80% of the population is vaccinated and people recover from the illness after 24 hours. Clearly, these models have the potential to become very complicated very quickly.
My scholars were amazed to see how quickly a disease could become an epidemic if too few people were vaccinated against it, so they set out to learn more about vaccinations. They each independently researched a disease and presented their findings to one another in a round-table conversation.
Samples of student research notes about diseases and vaccinations. Each student used his or her notes while presenting findings to the rest of the group.
After the presentations, my students unanimously agreed that influenza was the most relevant to the their lives. This was hardly surprising at the end of an unusually severe flu season. Furthermore, they had been dismayed to learn that only about 40% of students enter flu season vaccinated and that that percentage is still below 60% at the end of flu season. They began brainstorming ways that they might be able to share their mathematical findings about the effect of vaccination rates on the spread of communicable diseases and help to address this public health issue.
Student-created brainstorming document about increasing flu vaccination rates. This was the product of a scholar-led conversation about the role they could play as community advocates on this issue. The conversation ranged from ways that they might be able to reach and inform the public (at the top) to potential legislative solutions to the problem (at the bottom). The note that "we don't have CHILDREN!!" at the top right of the page is not just an idle doodle; my students noted that they might hear this as pushback against their efforts to convince parents to vaccinate their children.
After one more round of research about influenza—my scholars are committed to being thorough when they craft a presentation—the entire group worked together to create an informational "one-pager" that synthesized their findings and opinions about the topic.
Notes from final round of research (left) and one-pager (right). Deciding what information to include on the one-pager was a challenging assignment for the group, but they did an excellent job of exchanging contrasting ideas and referring back to their advocacy mission. Although they may choose to update this document further, it is currently an excellent summation of the information that they most want to share with the general public.
Now that my students have created such a clear and compelling one-pager, they are in the process of contacting local leaders to increase their awareness of the issue. Ultimately, their goal is to convince policymakers to enact some sort of regulation or law that increases the rates of youth flu vaccination rates. They believe that they have the ability to do this, and they are eagerly working to schedule their first meetings with those in power.
Students prepare to send their one-pager to Mayor Muriel Bowser and the D.C. City Council. They are asking to meet with elected officials in order to explain their math and their opinions about vaccinations. In the end, they plan to effect real improvements in the public health of their community.