SIAM News Blog

Communicating Mathematics to a Nontechnical Audience

Minitutorial at AN21 Helps Researchers Format Their Conversations

By Lina Sorg

Successfully communicating one’s research to another expert in the field can be difficult, but conversing with someone who has no prior knowledge of the topic in question is even more challenging. During the 2021 SIAM Annual Meeting, which is taking place virtually this week, Anthony Bonifonte of Denison University hosted a two-hour minitutorial that focused on effective communication for nontechnical audiences. Bonifonte drew upon his experiences as a SIAM Science Policy Fellowship recipient; in this role, he works with the SIAM Committee on Science Policy to learn about advocacy and attends the biannual committee meetings in Washington, D.C. Bonifonte also partakes in an annual advocacy day on Capitol Hill, during which he interfaces with politicians and office representatives—who have no mathematics background—about federal investment in applied mathematics and computational science.

Bonifonte opened the session with a quote by Neil deGrasse Tyson: It’s not good enough to be right, you also have to be effective. He noted that researchers often rely on being right as the crux of their arguments, particularly when they are presenting to other experts. When it comes to nontechnical communication, however, they must give the targeted audience a reason to accept their outcomes. Otherwise listeners will not understand or see the value of the material.

Participants then discussed the differences between “technical” and “nontechnical” audiences. A technical audience often consists of experts in the topic at hand or individuals who work in a closely related field, such as presenters and attendees of SIAM conferences. Nontechnical recipients include non-mathematicians like friends, family, and neighbors; students, particularly those who are younger; and anyone who experiences “math anxiety.” Bonifonte added politicians and office representatives to this list. “Think of someone who is very smart but has no math background whatsoever,” he said. “Speaking to them is very different from speaking to a mechanical engineer, for example.”

Next, Bonifonte asked participants to think about communication techniques that benefit a technical versus nontechnical audience. When communicating with other quantitative experts, speakers typically utilize specific phrases and keywords that immediately orient listeners and get them thinking about existing literature. “We talk a lot about using a phrase that brings people into a certain mindset,” Bonifonte said. They also provide enough details about methodology to make their conclusions credible. Referencing shared or common experiences—in terms of education or advisors, for example—likewise brings the audience together over a mutual point or background.

Communicating with nontechnical audiences, however, requires an entirely different skillset. Participants suggested that speakers use metaphors, avoid intimidating technical language and jargon, omit unnecessary details, and focus on applications that are familiar to the listeners. At Denison, Bonifonte teaches a course in data analytics that emphasizes the ABCs of effective communication: accuracy, brevity, and clarity. “If you can master all three of these, you usually have a very effective piece of communication,” he said.

Bonifonte structured the minitutorial around the following three topics: Know Your Audience, Jargon Busting, and So What? When preparing to talk about one’s research, speakers should consider several audience-related factors: the background and education levels of audience members, the number of listeners, level of familiarity with the application area, level of mathematical sophistication, audience interests, and propensity to humor. It is of course beneficial to structure a presentation based on the prospective audience, but one should also be prepared to dynamically adapt their pitch if necessary. For example, when Bonifonte goes to Congress as a Science Policy Fellowship recipient, he prepares multiple different stories and anecdotes. “In the moment, depending on how the conversation is going and what the officers say they’re most interested in, I’ll bring out one of the corresponding stories,” he said. “Your message is the same, but what you say, how you say it, and the examples you give can vary based on who you think your audience is.”

Figure 1. Explanation of various rocket modules using only the 1,000 most common words in the English language. Image courtesy of Randall Munroe.
To put these skills into play, participants entered breakout rooms and practiced 30-second oral pitches for four different audiences: 

  • A SIAM audience or other technically savvy peer group
  • Sophomore undergraduate mathematics majors
  • Fifth-grade students
  • A friend’s acquaintance at a birthday party.

After a group discussion of strategies from the breakout sessions, Bonifonte turned to jargon busting. When speaking to a nontechnical audience, communicators should aim to reduce or break down any complicated words or phrases that they commonly use to converse with their peers. As an example, Bonifonte presented the following phrase: Stochastic gradient descent on piecewise convex functions converges almost surely to asymptotic optimality. “This is a very efficient way of communicating a lot of very precise, specific information,” he said. But while it would be great for a graduate class, it is much too complex for a lay audience. Speakers could instead simply say "This solution method works," which lets listeners know that the method solves the problem at hand. As an extreme example, Bonifonte presented a graphic that explains various rocket modules with only the 1,000 most common words in the English language (see Figure 1). Although the descriptions in this example are almost comically simple, it shows that one can explain even the most complicated ideas with basic verbiage.

Next, Bonifonte introduced a tool to aid in the simplification process: the xkcd Simple Writer. Researchers can insert text—a presentation abstract, for example—into the program, which then identifies words that are not among the 1,000 most common English words. Although such identified “jargon” cannot be further simplified in many cases, the tool identifies phrases that might be overly complex and encourages users keep their audience in mind. “Think about where your audience is at and talk to them at the level they will appreciate,” Bonifonte said. Attendees then returned to breakout rooms and practiced removing and/or explaining jargon-heavy phrases from their research pitches.

The final portion of the session addressed audience interest. Bonifonte encouraged speakers to consider the following questions for nontechnical communication:

  • Why should your audience care?
  • How does your work relate to them?
  • What do they want to get out of talking/listening to you?
  • What will they do with what they learn from you?

Bonifonte shared several telling statistics to put things in perspective. For example, 35 percent of Americans who are 25 or older have a bachelor’s degree, and only two percent hold a Ph.D. Furthermore, roughly 93 percent of adult Americans claim to experience some level of math anxiety. In short, only a very small percentage of the population are quantitatively trained thinkers, meaning that researchers must appeal to the larger population’s priorities. To motivate interest in mathematics or other scientific fields, Bonifonte suggested the use of analogies and stories. “People are immediately drawn to stories in ways that they’re not drawn to dry, technical information,” he said. Though one would likely not use such comparative techniques when conversing with a thesis advisor or SIAM audience, they appeal to individuals who lack formal quantitative reasoning skills.

Bonifonte then recommended that researchers who are engaging with nontechnical audiences focus on the practical applications of their work. Several application areas are typically of particular interest:

  • Topical application areas, i.e., things in the news, popular national debates, and new technology releases (examples include self-driving cars, COVID-19 vaccines, electric vehicles privatized space travel, and facial recognition software)
  • Future scientific discoveries that may benefit from the speaker’s work
  • Applications of similar or related topics that fall just outside the area of study
  • Broader discussions of mathematical applications.

“Feel free to really be broad when talking to someone completely outside the context of any sort of professional organization or academic context,” Bonifonte said, adding that most people do not have many opportunities to chat with mathematicians. He then related the aforementioned suggestions to his experience meeting with politicians and advocating for science, technology, engineering, and mathematics (STEM) funding. For example, a recurring concept in the SIAM Committee on Science Policy is that politicians are interested in three things: health, wealth, and stealth. Politicians want to show their constituents that they are using their tax dollars responsibly and are focused on a high quality of life (health), good jobs and economic prosperity (wealth), and military defense and safety (stealth). The committee thus encourages mathematicians who are advocating in Congress to tailor their applications on one or more of these areas.

Bonifonte concluded the minitutorial by recapping the three points of effective communication for nontechnical interactions. He reminded attendees to begin with a big picture idea before diving into the necessary details. He also encouraged them to think in terms of applications and future discoveries so listeners have something to which they can relate. “The nature of academics and science is small and incremental improvements in collective human knowledge,” Bonifonte said. “Scientists appreciate that, but the rest of the world doesn’t appreciate it so much and needs reminders of why this is important.”

Lina Sorg is the managing editor of SIAM News.

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