E2: Learning a fraction of what I thought
Why fractions can be misleading and what we can do about it.
My daughter is a fifth grader and is learning about fractions and percentages in her math class this year. She is making a big conceptual leap from whole numbers to fractions. Interestingly, the lessons she is learning on comparing and interpreting fractions may prepare her to understand and appraise risks better than most adults.
During the pandemic, it became commonplace to see statistics from the local health authorities and the Centers for Disease Control and Prevention on the current rates of COVID-19 infections, hospitalizations, and vaccinations. Among the many lessons, I learned from the pandemic, applying basic math to accurately interpret all this data seemed like a critical and life-saving one.
It turned out that psychology researchers from Kent State University revealed a common misconception known as the “whole number bias” (Thompson et al., 2020) that can lead any of us to mistakenly think about the numerators and denominators of fractions as whole numbers.
For example, we can perceive 1/5 as smaller than 1/7, or 3/9 as larger than 3/7. In our daily lives, these errors may seem trivial but can actually lead to consequential decisions related to our own or others’ health and safety.
Early in the pandemic, a widely shared misconception was that fatality rates for the common flu and COVID-19 were roughly equivalent (common flu; 0.1% vs. COVID-19; 1-5% or roughly 10x more deadly). I remember this myth spreading quickly through social media and personal acquaintances. It made me wonder about a bias toward whole numbers over fractions. After all, it is easier for us to grasp whole numbers than interpret percentages or ratios.
Yet, fractions provided us with critical information to evaluate the risks of catching a common cold versus a potentially deadly virus. I clearly remember struggling to interpret a positivity rate (i.e., positive tests/total tests x 100). Ah math!
It can be confusing to interpret fractions when we see them unless we slow down (as I tell my daughter) and take the time to put numbers into context. But, research has suggested under stressful or ambiguous conditions, we may be more susceptible to misinterpreting numerical data, which may impair our ability to appraise risks to ourselves or others (Choi et., al 2020).
The good news, especially for my daughter’s math teacher, is that the effects of whole number bias have been shown to decline with age and experience. For example, 8th graders have been shown to outperform 4th graders on assessments of factional equivalency and magnitude (Siegler et al., 2018).
The bad news is that whole number bias stays with us into adulthood and may influence choices about whether or how often we wear a mask in public, travel by plane, or stay home during a global pandemic.
Hindsight, as they say, is 20/20 (i.e., a fraction describing one’s ability to read the smallest row on an eye chart from 20 feet away). Hopefully, we are all a bit more savvy and aware of what positive rates represent now. But fractions remain important for my 5th grader to understand and may help her (and the rest of us) make smarter decisions. It turns out our beliefs about getting an infectious disease, buckling our seat belts, or just eating healthier are all shaped in part by how we interpret the numerical information.
Perhaps, we need to think back to our fifth-grade math lesson and use number lines or other visual tools more often to ensure we are getting the right story from the data we see. Otherwise, our hard-wired preference for whole numbers may only give us a fraction of the story we need to hear.