How Fractions Help Us See the Big Picture

by Eoin Bastable April 15, 2021

My oldest daughter is a fifth-grader and is learning about fractions and percentages in her math class this year. She made a big conceptual leap from whole numbers to fractions. The lessons she is learning on comparing and interpreting fractions may prepare her to understand and appraise risks better than most adults.

At this point in the pandemic, it has become 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 lessons I have learned from the pandemic, applying basic math to accurately interpret all this data may be a critical and life-saving one.

Psychology researchers from Kent State University have been exploring how to address a common misconception known as the whole number bias.¹ Whole number bias can lead 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 that 3/9 is larger than 3/7. In our daily lives, these errors may seem trivial but they could result in consequential decisions for our 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 sites and personal acquaintances. It made me wonder if it had to do with our preference for whole numbers over fractions. After all, it is easier for many of us to grasp whole numbers than interpret percentages or ratios.

Yet, fractions provide us with critical information to compare the risks of catching a common cold versus a potentially deadly virus. Or, can help us understand what positivity rates represent (i.e., positive tests/total tests x 100) in our neighborhoods or state. It can be confusing to interpret what fractions really are telling us if don’t slow down (as I tell my daughter) and take the time to put numbers into context. Research even suggests under stressful or ambiguous conditions, we may be more susceptible to misinterpreting numerical data, which can impair our ability to appraise risks for ourselves or others.²

The good news, especially for my daughter’s math teacher, is that the effects of whole number bias can decline with age and experience. For example, 8^th graders have been shown to outperform 4^th graders on assessments of factional equivalency and magnitude.³ The bad news is that whole number bias affects us into adulthood and may influence choices about whether we decide to 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 moving toward the end of the pandemic and will not have to experience another one anytime soon. But fractions remain important for my 5^th grader to understand and can help her (and the rest of us) make smarter decisions. It’s important to accurately perceive and weigh the risks of contracting an infectious disease, buckling our seat belts, or just eating healthier. All of these types of decisions can be influenced by numerical information we use to inform our choices and actions.

So, maybe we need to rethink how we present numerical data, especially when we share fractions, rates, or ratios. It may be that using number lines, pie graphs, and other types of simple data visualizations can go a long way to more effectively communicating the risks or benefits of our individual or collective actions.

For me, a simple lesson I have learned during the pandemic is to go back and review fractions with my daughter to be less susceptible to whole number bias. I definitely want to be sure I’m seeing the full picture instead of a fraction of it.

Citations:

1. Thompson, C. A., Taber, J. M., Sidney, P. G., Fitzsimmons, C., Mielicki, M., Matthews, P. G., … Coifman, K. (2020, June 15). Math matters during a pandemic: A novel, brief educational intervention combats whole number bias to improve health decision-making and predicts COVID-19 risk perceptions and worry across 10 days. https://doi.org/10.31234/osf.io/hukyv
2. Choi, S. S., Taber, J. M., Thompson, C. A., & Sidney, P. G. (2020). Math anxiety, but not induced stress, is associated with objective numeracy. Journal of Experimental Psychology: Applied, 26(4), 604.
3. Braithwaite, D. W., & Siegler, R. S. (2018). Developmental changes in the whole number bias. Developmental Science, 21(2), e12541