The Curious Case of Storytelling in Mathematics

There is a mystery I've long tried to unravel. What exactly is the quality that some teachers have to bring students to the edge of their seats, to not only compel them to dutifully "pay attention" but to become engaged and even absorbed in the concept presented? Perhaps you can think of that teacher or that moment for you. Perhaps a lecture, sermon, or a relative telling a story captivated you completely. Think of one, and try to relive the moment. How did that experience make you feel? Did it transform you in some way?

The Transformative Power of Narrative Transport

A well-told story, like a great lecture, has the unique power to evoke deep emotions, drawing us into the lives and experiences of its characters. When we engage with a story, our feelings become intertwined with those of the characters or presenter, creating a sense of "narrative transport."

Narrative transport refers to the psychological process where a person becomes fully immersed in a story and feels part of the narrative world. The audience experiences a deep connection with the story's characters, events, and emotions, often leading to a temporary suspension of disbelief and a decreased awareness of their real-world surroundings.

This phenomenon can result in strong emotional responses and even influence attitudes and behaviors. For me, the Moth Radio Hour is one example of an experience that creates this reaction. I do not know what it is like to be a woman, a black man, or a man who has had to hide who he loves. But, hearing these stories transports me to be able to imagine, if only for a moment, what that must be like. In those moments, I gained the ability to be genuinely empathetic toward those issues. I feel something that literally changes me, both brain and body. The more engaging and well-crafted the story, the more likely it is to induce narrative transport.

Some key factors increase the probability of narrative transport with the audience. These include the quality of the storytelling, the characters' relatability, and the story's relevance to the audience. When these elements are present, listeners are more likely to lose themselves in the story, experiencing the events and emotions as if they were happening to them. You have been there, and you know what this feels like.

Why Student Engagement Matters

Researchers have found that success in school is a direct function of three main factors related to engagement (Patrick et al., 2007):

1. The degree to which students feel a sense of emotional support from their teacher.
2. Collaborative academic support from other students.
3. Encouragement from their teacher to discuss their work.

As a result of its significance, student engagement now drives teaching methods and metrics for effectiveness (Parsons & Taylor, 2011). There are patterns in this research, such as intensity, emotion, experience, adaption, and belief. Sound familiar? If you still think it all seems outlandish, stay with me for a moment.

“Pedagogy should at its best be about what teachers do that not only helps students to learn but actively strengthens their capacity to learn.” ~David Hargreaves

Storytelling engenders an intense and emotional connection, cementing its role as a powerful and universal aspect of the human experience, resonating across cultures and generations. This is also true in education. Educational research (Aaronson et al., 2007; Chetty et al., 2014; Kane & Staiger, 2008) has long positioned the human teacher as the most vital component of student learning and growth. The slippery question in the age of artificial intelligence (AI) is why?

Taking that line of thought one step further, I argue that a teacher’s ability to tell stories about and through content is a defining human element of teaching. Similar to storytelling, we will not all love the stories and content similarly. However, there is a case to be made that storytelling will increase the probability of engagement. Additionally, research shows that when students listen to the same story, their brain activity becomes synced, or what researchers call aligned (Suzuki et al., 2018). This only moves into the higher-order areas like the frontal cortices of the brain when listeners hear a real-life story. In Jerome Bruner's essay ‘Two Modes of Thought,’ he labels a second mode of thought as narrative. I believe Bruner's words are important because he calls storytelling a "mode of thinking." Are you at least intrigued? There is plenty of narrative-related research about the narratives of self that a teacher carries. Or ethnographic research techniques called narrative inquiry. However, for this article, I want to explore telling stories about and through mathematics that help students learn mathematics.

How Do You Tell Stories in Mathematics Class?

The art of storytelling with and through content like mathematics is the same as the art of telling a great story to invoke narrative transport. First, you need to know and understand the context and material deeply. For example, a great story set in the 1800s cannot be told well without the research that will make it authentic. Similarly, a great story in mathematics requires knowing the context of mathematics and recognizing that it has a history. Telling a story in mathematics class is not a lecture but part of the classroom dynamic. Often, once you begin to look for those opportunities for authentic stories about content, you'll see them in abundance. And lastly, like any great storyteller, you must practice, try again, and practice more. Competence and skill do not come from anything more than courage, learning from your mistakes, and persistence.

You may be thinking, well, that all sounds great — but what the heck does mathematics storytelling actually look like? Permit me to tell you the story of mathematics’ unsung hero, the story about nothing, the lowly zero.

More than 3000 years ago, the first human civilizations began using zero. For fun, that would be roughly 100 generations ago in your family. The ancient Babylonians lived in a region corresponding to modern-day Iraq, centered in the Mesopotamian plain between the Tigris and Euphrates rivers. The city of Babylon, the capital of the Babylonian Empire, was located near the modern city of Hillah, about 50 miles south of Baghdad—lots of water and lots of food. Thus, a thriving civilization achieved enough security in various ways to pursue intellectual discovery and invention.

These clever humans invented a positional number system with a base of 60. We still use base 60 systems today, based on the work of the Babylonians. One hour of time is divided into 60 minutes, and one minute is divided into 60 seconds. Thus, a measurement of time such as 3:23:17 (3 hours, 23 minutes, and 17 seconds) can be interpreted as a whole sexagesimal number (no sexagesimal point), meaning 3 × 60^2 + 23 × 60^1 + 17 × 60^0 seconds. Look at you, walking around using base 60 systems! Our system today is base 10; the Babylonians chose base 60 because of the number's diverse divisibility. Base 10 has its merits, but we get weird stuff like repeating decimals because of it.

In positional number systems, zero or a mark representing zero was essential to distinguish between numbers like 10 and 100. For example, in the number 102, the zero indicates that there are no tens, which is crucial for representing the number accurately. 12 and 102 would be the same if you did not have it. Not useful. The Indian mathematician and astronomer Aryabhata is often credited with using zero as a placeholder in his place-value number system some eight centuries later than the Babylonians. The concept was further refined and formalized by the Indian mathematician Brahmagupta in the 7th century CE. Brahmagupta’s work provided the rules for arithmetic involving zero and negative numbers, marking a significant advancement in mathematics.

More intriguing was the invention of zero as a quantity of “nothingness.” Philosophical and cosmological ideas also influenced the development of zero in Indian culture, where the concept of 'nothingness' had deep significance. Mathematics and many forms of human religion have a long history of explaining the inexplicable. When it can be explained, mathematics does provide a rational explanation. When it cannot, it is left up to a god.

"Science without religion is lame; religion without science is blind." "God is a mystery. But a comprehensible mystery. I have nothing but awe when I observe the laws of nature.” ~Albert Einstein

By learning the story of zero, you can suddenly see that it’s a mystical, religious, and mathematical concept adapted and built by some of humanity's finest minds when necessity prompted its invention. That’s right, mathematics is invented. This means it is fallible, messy, and has a history—just like you.

Can Anyone Become a Storyteller of Mathematics?

Yes, some will have more natural talent than others. We call them storytellers or orators and often see them as organically charismatic. However, just like public speaking, anyone can become more adept at it with practice.

At MathTrack Institute, the principles of storytelling are embedded in our mathematics-for-teaching approach. The GROWTH framework offers a section focused on unpacking mathematical concepts by encouraging teachers to ask intriguing questions about the mathematical concepts they are teaching. This is an effort to deeply understand and know the concept well enough to tell stories about it.

This is the (W) part of GROWTH or Weave Together Concepts. This is achieved by exploring:

• Who is this topic useful for?
• What assumptions about a topic like zero need to be questioned in your original understanding?
• What language needs to be adapted to better fit our understanding?
• Why is this topic relevant and exciting?

Additionally, this Weaving involves exploring the collective history of the topic. There are some great mathematics history books out there (Boyer & Merzbach, 2011; Cajori, 1894, 1928; Fink et al., 1903; Kaplan, 2000; Katz, 1993), but asking the right questions and using Google or ChatGPT are also effective in quickly gathering clear and concise information:

• When was it invented?
• What problems was it solving at the time it was invented?
• How long did it take to be developed? What problems arose from its invention? (Like, what does quantity mean if it describes nothing?)
• What did the world look like when we did not have zero?

Narration Versus the Perfect Lecture

The substance and impact of the quality of teachers’ lesson plans have been well documented in research (Fernandez & Yoshida, 2004; Praetorius et al., 2014; Stentoft & Valero, 2010). The Gates Foundation invested nearly $50M in researching and defining quality lessons and methods for reliably measuring them (Kane et al., 2013). A well-designed lesson makes students feel good and supports them, allowing them time to collaborate, reflect, and problem-solve their mistakes. This is useful. However, a Harvard research study counterintuitively found that students listening to a well-crafted lecture overestimate how much they have learned. There is a curious "perfection pitfall" in teaching (Deslauriers et al., 2019).

Case in point, if you were asked various questions about the topic you just watched, especially ones slightly nuanced from the lecture format, research says that almost all students overestimate what they learned. They say things like, “The teacher tested on stuff he did not even teach us!” Learning is messy, knowledge is messy, mathematics is messy. Narratives can give humanity to all topics in mathematics, even ones that, on the surface, you may think are mundane. Uncertainty and a lack of clarity should be cherished rather than avoided—especially regarding learning and brain development. The Growth Mindset literature (Boaler, 2015, 2024; Dweck, 2006) clearly illustrates that the most successful students and adults can find comfort in a lack of clarity and value mistakes.

“Perfection is not attainable, but if we chase perfection, we can catch excellence.” ~ Vince Lombardi

“Perfection is the enemy of progress.” ~ Winston Churchill.”

Find Your Inner Storyteller for Mathematics

Storytelling is innately human, like teaching our youth, and we are hard-wired to give and receive stories. The narrative, especially the personal narrative, is one of the most potent forms of communication in existence. The neuroscience behind this is clear (Suzuki et al., 2018). The auditory cortex activates to process the sounds of the words, while the sensory cortex ignites to imagine details of experience (e.g., sights, smells, tastes, and movement. The narrative literally transports to brain functioning that captivates our minds. The giver and receiver in this narrative transport help to define who we are– which can have profound implications. People, like teachers, are essential to our society because of their disproportionately powerful position as storytellers and their trust in the care of our children. Stories build empathy, empower passion, and help to make cohesion out of the chaos of learning. They also provide cohesion, memory transfer, and the ability to recall information clearly.

When these elements are present in the teaching of mathematics and in all content, students are more likely to lose themselves in the story and retain more information and cohesion. Knowing how to tell a mathematics story requires knowing mathematics-for-teaching. This is precisely what we support at MathTrack Institute. Through storytelling, we can change the narrative that some are “math people” and others just aren’t. That is a false narrative, albeit a powerful one. Let’s flip the script and tell a new story. Mathematics is human; so my story is that you are a math person—and I’m sticking to it.