Episode 46: Innumeracy--the Mathematical Equivalent of Illiteracy

In this episode, April outs herself as being "bad at math;" but after researching, writing, and publishing this episode, she's taken a vow to become more numerate. You should, too! Listen to the episode to find out how.

Episode 46 Show Notes

Bio of British economist Geoffrey Crowther: https://en.wikipedia.org/wiki/Geoffrey_Crowther,_Baron_Crowther

A great article about the history of innumeracy (honestly I don't know what "captive board" refers to): https://www.captive.com/articles/how-numerate-is-your-board-the-case-for-captive-board-numeracy

Here's the link to the download for Paulos' book on innumeracy: https://jirsresourcecentre.wordpress.com/wp-content/uploads/2011/04/innumeracy.pdf

The OECD's discussion of numeracy skills among Americans: https://www.oecd.org/en/topics/adult-numeracy-skills.html

How many students need to take remedial math classes? Lots of them. I disagree, however, with the idea that the cure for this is to no longer require algebra courses in higher education, although something definitely needs to change: https://washingtonmonthly.com/2026/02/26/almost-no-one-needs-college-algebra-anymore/

Martin Gardner's home page: https://martin-gardner.org/#:~:text=First%20and%20last%2C%20he%20was,people%20all%20over%20the%20world

Math anxiety explained: https://pmc.ncbi.nlm.nih.gov/articles/PMC6087017/

Discalculia: https://my.clevelandclinic.org/health/diseases/23949-dyscalculia

Gender differences in math performance: https://pubmed.ncbi.nlm.nih.gov/2138794/

The crazy story of the GoFundMe project to build the wall: https://en.wikipedia.org/wiki/We_Build_the_Wall

Why people misunderstand probability: https://untamedscience.com/blog/why-humans-are-bad-at-understanding-probability-and-what-science-says-about-it/

Diego Ribiero's excellent Medium article: https://neverforget-1975.medium.com/innumeracy-8b2112c5787b

A review of Innumeracy in the Wild: https://newbooksnetwork.com/innumeracy-in-the-wild

Plane vs. car accidents: https://www.fellermanlaw.com/blog/is-flying-safer-than-driving/

Career Addict article about becoming more numerate: https://www.careeraddict.com/develop-numerical-skills

Khan Academy website:  www.khanacademy.org

Duolingo website: https://www.duolingo.com/math

Tablet Class Math YouTube channel: https://www.youtube.com/user/tabletclass

Financial Literacy Resource Directory: https://www.occ.gov/topics/consumers-and-communities/community-affairs/resource-directories/financial-literacy/index-financial-literacy-resource-directory.html

The UK's National Numeracy Challenge page: https://www.nationalnumeracy.org.uk/

Transcript

Episode 46: Innumeracy--the Mathematical Equivalent of Illiteracy

I’m going to start this episode with a confession—I was always really bad at balancing my checkbook, back when checkbook balancing was an actual thing. My husband still insists on doing it himself, but I don’t know anyone else who does that. I can’t tell you how happy I was once banks had websites and apps that pretty much handle all that stuff for me; I’ve always believed that I just can’t do math. And honestly, I don’t think I’m the only otherwise smart person who admits to being somewhat mathematically ignorant. And I also don’t think that it’s considered all that bad if you’re “bad with numbers.” I mean, think about it—most of us wouldn’t want to admit that we can’t read. But many of us, no matter our intelligence or educational level, have no problem saying that we lack math skills, as if it’s some kind of badge of honor. So many people struggle to figure out anything to do with numbers—finances, statistics, probabilities, any kind of numerical information. This mathematical ignorance has a name—innumeracy.

Way back in Episode 10 I talked about why we tend to misunderstand probability and risk. You don’t need to go back and listen to that, but you might want to because, well, it’s a good episode! This time, I’m going to go a little deeper into some of the things I talked about back then. We’re going to find out what innumeracy is, why so many people struggle with it, look at some examples that might apply to your own life, and discuss ways that we all can become more numerically literate. Let’s get started.

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Before we discuss innumeracy, we need to look at the origins of the word “numeracy,” which means numerical literacy. It’s a very recent word, coined in 1959 by the late British economist Geoffrey Crowther, who wanted it to be the equivalent of “literacy” but of course related to numbers. After that, the term “innumeracy,” which obviously means the lack of numerical literacy, was first used by cognitive and computer scientist Douglas Hofstadter in a Scientific American article in the 1980’s. The term was popularized in 1988 by mathematician John Allen Paulos in his book, “Innumeracy: Mathematical Illiteracy and its Consequences.” By the way you can download a pdf of the entire book, I’ll put the link in the show notes. Just a warning, unless you’re good at math already, which as I said many people are not (myself included), it might be hard to get through, so I’ll just give you the Cliff Notes version: to put it simply, Paulos says that being bad with numbers should not be treated as lightly as it is, and that the problems of innumeracy come at a fairly high cost to society. We treat it as if it’s not a big deal, but it is, and it impacts us in ways we really haven’t stopped to think about. And when he says we should be more literate when it comes to numbers, he’s not talking about things like advanced calculus, he’s simply saying that we should be able to understand numbers well enough to make informed decisions. Just as verbal and written literacy helps us to make sense of verbal and written claims, numeracy helps us make sense of quantitative or numerical claims. 

According to the Organization for Economic Cooperation and Development, a large portion of the population is classified as innumerate. Some of these people, roughly 25% of the US adult population, would be considered functionally innumerate, which means they can only perform basic mathematical functions involving whole numbers, but struggle with anything else, including measurements, graphs, fractions, or percentages. Another roughly 40% would be considered intermediately numerate, as they can interpret basic statistics and graphs but have difficulty with more abstract concepts like ratios, rate increases, or complex, multi-step math problems—I think I might fall into this category. That leaves only about 35% of adults who would be considered either numerate or highly numerate, which means fully 65% of us, well, we got issues when it comes to numbers. 

But why is that? Why do so many people struggle with innumeracy? Well, there are several factors that can play into this:

1.     The most obvious one is poor early math education—many K-6th schoolteachers have only very basic math skills and may be intermediately numerate themselves. Most often, a teacher who really likes math tends to want to focus on it and will gravitate towards teaching math classes in junior or senior high school, leaving the primary grades to teachers who don’t have as firm a grasp on math and may not be that interested in it. A lot of early math training is focused on rote memorization and speed tests rather than helping students understand and appreciate the concepts underlying math. The late science writer Martin Gardner, who many described as “the best friend mathematics ever had,” said that when math is taught to young people by someone who isn’t truly interested in the subject, the class tends to be bored also. Bored students aren’t motivated to learn, and that can set them up to not care about math; then when they get to math classes in the upper grades, they already have a negative opinion of the subject and their ability to understand it, and do barely enough work to pass the course. In fact, an alarming number of incoming college students (over 50% at the community college level) have to take remedial non-credit math courses, just so they can qualify to take the actual math courses that meet graduation requirements. And many people who don’t finish college report that the major issue keeping them from getting that degree was the difficulty they faced trying to fulfill the math requirement.

2.     John Allen Paulos is one example of someone who overcame inept math instruction in his early years and went on to become a famous mathematician. He says that many people believe there are “mathematical” and “non-mathematical” minds, which of course plays in to the whole idea that some people are bad at math and that’s ok. “I’m a people person, not a numbers person” is the kind of statement that really annoyed Paulos; he had little patience with people who proudly claim that they can’t balance their checkbook.  (I feel like he’s talking to me there) And this contributes, of course, to a climate of cultural normalization that being bad at math is somehow acceptable. 

3.     Then there’s math anxiety, which is a legitimate condition with physical, psychological, and mental symptoms that can be the result of negative past experiences with math along with the societal belief that some people just can’t do math. A 2018 paper in the journal Psychology Research and Behavior Management titled “Spotlight on Math Anxiety” says that approximately 17% of the US population suffers from high levels of math anxiety, and that fully 93% of us have felt some level of math anxiety at some point. That tells me that even people that are good at math sometimes feel anxious about it, but I’m sure that the more you feel like math just isn’t your jam, the more likely you are to have math anxiety.

4.     And, there is a cognitive disorder called discalculia, that affects the areas of the brain that handle math and number-related skills. It’s related to dyslexia, which affects a person’s reading ability; and like dyslexia, dyscalculia causes processing difficulties in the brain, but with numbers instead of words. It’s something that can appear in childhood, between the ages of 6 and 9, and may be connected to adhd or autism spectrum disorders. There’s also a form of it called acquired dyscalculia that can happen at any age, usually due to certain medical conditions or brain damage. Obviously if you have something like this it’s highly likely you’d also have math anxiety because you literally CAN’T do math.

5.     And the final reason we’ll discuss for being bad at math is—being female. Now hear me out--There’s a longstanding belief that men are better at math than women, but is it true? Well, it’s complicated. Research has shown that there is little gender difference in math skills between boys and girls in the primary grades, in fact girls slightly outperform boys at this stage. But once they hit high school, males tend to not only catch up, but outperform females, and that can continue on into college and throughout their lives. Women earn only about 30% of PhDs in mathematics, and that holds true for other related fields, like computer science and engineering. So what’s behind those disparities?

a.     Well, it’s culture. Culture plays a big role—gender norms and stereotypes often cause teachers, parents, and peers to discourage girls from excelling in math. Just being reminded of the stereotype that men are better at math can cause girls and women to perform poorly on math tests. 

b.     Self-confidence plays a very big role here; boys are simply more confident in their math abilities, even when the girls are getting better grades. And boys tend to be more confident even when their answers are wrong.

c.     Also, boys tend to be more competitive and try to get the answer faster, so if there’s a time element involved in a math test, they are more likely to complete it, while girls are more interested in accuracy than speed and it can take them longer to get to the correct answer.

As you can see, the reasons why we cling to the idea that we’re “bad at math” are many. But you still might not think it’s that big of a deal, because like me you have calculators and bank apps and maybe even financial consultants and so you can outsource all that “thinking about numbers” stuff. But can you really? Let’s find out.

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Sure, lots of our formerly annoying financial tasks are now done for us. And that certainly makes our lives a bit easier and less frustrating. But honestly there’s so many more ways that we use mathematics, probabilities and statistics in our daily lives. And because we are often not knowledgeable enough about how these things work, we can come to some incorrect conclusions, and use those bad conclusions to make bad decisions about things that might actually matter to us. Here are just a few of the ways that innumeracy can impact us:

• First, we might have difficulty with scale incomprehension: That is when you have trouble conceptualizing large numbers like millions, billions, or trillions. People often think that a million and a billion, and even a trillion, because they’re all big numbers, are somehow similar in nature.  I mean, they sound the same, right? Well, a million seconds is about 11 ½ days. A billion seconds is about 31 ½ years. A trillion seconds? Over 31 THOUSAND years. They are NOT similar. Here’s an example of how that misunderstanding was used to get money out of people: Back in 2018, a GoFundMe campaign called “We The People Will Build the Wall” was established to raise $1 billion dollars from regular citizens to construct the wall between the US and Mexico. The campaign organizer assured people that they could absolutely meet that billion-dollar goal. But here’s what he didn’t tell them—in order to raise a billion dollars, every single man, woman, and child in the U.S. would have had to give around 30 bucks, which doesn’t sound like a lot, but everybody would have had to do it. Well, about 300,000 people donated to that fund, and that’s certainly a lot of people. But there were well over 300 million people in the US at that time, and 300,000 is only 0.1 percent of that (not 1 percent, 0.1 percent, which is a tiny percentage); the vast majority of us were like, umm, no thanks. Now, they did raise about $25 million dollars, which is admittedly a lot of money. But $25 million is only 2.5% of a billion, so their fundraising efforts fell more than 97% short. To be clear, a portion of the money was used to erect small sections of fencing on private property along the border, so at least a portion of it went to its intended purpose. I’m gonna skip over a lot of the details of this story because it’s pretty complicated, you can read about it on its Wikipedia page, and I’ll put a link to that in the show notes. Anyway, the original organizer hooked up with Steve Bannon and a few other people, and then they diverted a significant portion of those donations for their personal use, including things like home renovations, boats, jewelry, cosmetic surgery, and paying off credit cards. Many of them ended up getting charged with conspiracy to commit wire fraud and money laundering. Yeah, they took advantage of the general public’s misunderstanding of how much a billion dollars is to get them to feel like they actually could make a difference by donating, and I’m sure the people handling that money hoped the public wouldn’t notice when they used some of it for their own personal gain. You should definitely read this story, it’s pretty insane.
• Then, there’s probability misjudgment: I talked about this in episode 10, we tend to regularly misunderstand odds, which leads to an overestimation of events that really don’t happen all that often, and an underestimation of things that do happen more often and that we should maybe be more concerned about. We are frightened of plane crashes, and not at all afraid of driving to work. Yet we are between 95 and 100 times more likely to be in a car crash than a plane crash. Our brains are wired to trust our feelings more than actual numbers, and while we do hear about instances of fatal car crashes all the time, unless we or someone we know or care about is personally involved in them, they don’t impact our emotions as deeply and vividly as news about plane crashes. So we might opt to drive instead of fly somewhere, not because we want to take our time and enjoy the scenery along the way, but because we think our odds of surviving will be better if we drive. They won’t.
• Coincidence Misinterpretation is another way in which innumeracy impacts us: that is viewing normal statistical coincidences as deeply meaningful or even supernatural in nature. Like, if you’re thinking about someone, and just a few minutes later they call you, you might wonder if you psychically sent them a message and they psychically picked up on it. or if you have a dream about your uncle and then find out the next day that he had a heart attack and died, you wonder if he’s sent you a message from beyond. Our brains are always searching for patterns, explanations, and connections; and the outcome of that may be that we find meaning in simultaneous or consecutive events when, frankly, there just isn’t a causal link between them. Billions of “events” are happening every day, and given enough time, things that have a low probability of happening simultaneously will inevitably occur. That’s just the randomness of life. 
• Which leads me to one of the most disturbing consequences of innumeracy—being vulnerable to things like astrology, psychic predictions, and unverifiable medical claims. Plenty of psychics, for example, make a living by counting on our tendency to apply significance to random occurrences. In his book, John Allen Paulos specifically calls out psychics and pseudoscience as examples of the ways in which an innumerative public can be tricked and manipulated. Our brains are designed to look for patterns, and when you combine our tendency to think emotionally and intuitively with innumeracy, it leaves a lot of us wide open for manipulation. Data scientist and researcher Diogo Ribeiro writes in a Medium article on the topic, “An innumerate public is not just uninformed, it’s vulnerable to misinformation, biased statistics, and skewed interpretations…whether we’re contemplating the future of healthcare, grappling with the implications of climate change, or dissecting economic policies, numbers are often at the heart of the debate. Yet how can there be a debate when a significant portion of the population is unable to engage with the basic data that underpins these issues?”

In a recent episode of the podcast “Speaking of Psychology” the host interviewed Dr. Ellen Peters, author of Innumeracy in the Wild: Misunderstanding and Misusing Numbers.

Here’s what she had to say about the effect of innumeracy (I’ve edited it a bit for clarity):

So one of the ways that innumeracy seems to have impact on people’s lives has to do with their ability to make good decisions. Even though everybody might get the same information,  might be given the exact same choice options…For someone who’s less numerate…what research shows is that their decisions end up being more vulnerable to their own emotional reactions, to how information is framed, to compelling stories that they’re given or images that they’re shown. And what this means when they’re judging and deciding is that they will be more vulnerable to using cognitive shortcuts, the heuristic shortcuts that people take. In fact research shows that they’ll end up being more susceptible to how they’re feeling in the moment.

I found her statement that innumerate individuals are more likely to make an emotion-based decision rather than a rational one pretty concerning. She also gave some other startling facts about the differences between the two groups: even controlling for all kinds of demographics, highly numerate people are more likely to be employed, more likely to make more money, and less likely to have a chronic illness than less numerate people. Now she’s not saying that if you are unemployed or have a chronic illness, that you’re innumerate. But she is saying that those things occur more often in people who are innumerate, which really surprised me. Innumerate people may have less ability or desire to follow complex health regiments, which can impact their quality of life.

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I hope by now you can see that numeracy is something we should take more seriously. It’s critical to our ability to understand and manage our finances and even our health. It’s necessary to help us understand the things we hear from politicians and read in the media. If we don’t have the tools to evaluate numerical claims, we run the risk of becoming vulnerable to manipulation, misinformation, and ultimately poor decision-making. So many arguments depend on evidence that involves numbers, so if we understand how those numbers are being used and what they mean, we’ll be better able to evaluate those arguments.

But you might be wondering, how am I supposed to get more numerate? Shouldn’t I have realized that math is important back in junior high school? Isn’t it too late for me? The answer to that is NO, it’s not too late. There are plenty of things you can do right now to improve your numeracy skills. 

1.     An article about numeracy on the Career Addict website says you should make a habit of consistently practicing math skills in real life scenarios, like taking a recipe that feeds four people and scaling it up to feed eight, or down to feed two. Or figuring out how much paint you’d need to paint your bedroom, or how big of an area rug you’d need to fit under your dining set and not have it look weird because it’s too small or too big. If you can do those calculations in your head, that’s awesome; but there’s nothing wrong with using the calculator on your phone, that’s what it’s for.

2.     If you find you really do need to brush up on your math skills, you can sign up for Khan Academy. It’s free, although they do ask for donations. They recommend that you do at least one lesson a day; they’re very thorough and you get a lot of practice until you feel confident that you understand one concept before you move on to the next.

3.     Then there are some great YouTubers with very helpful channels. My favorite is Tablet Class Math, where a former Junior high school math teacher, John Zimmerman, shows you how to do everything from basic arithmetic all the way to pre-calculus. He first presents a math problem and gives you several possible answers to choose from. You try to solve it by yourself, and he tells you right away if you got the right answer. If you did, you probably understand that particular math concept, but if you got it wrong, he then breaks the problem down, shows you where you made the error in your calculations and clearly explains how to get to the correct answer. It’s great for seeing how much you already know, and where you need to focus to improve your skills.

4.     If you happen to live in the UK, you might want to sign up for something called the National Numeracy challenge. It’s a charity funded by corporate sponsorships, dedicated to improving numeracy skills among UK citizens. I actually am a British citizen, so I tried it out and it’s pretty fun, but it did let me know that while my numeracy skills are a little better than I thought, I do sometimes have difficulty translating word problems into mathematical calculations, so that’s something I need to work on. Plus I love that in the UK it’s called “maths” plural, it makes me feel very British when I say that.

5.     And if you are currently learning a different language through a Duolingo account, you automatically have access to their math feature. It’s organized in the same, gamified way that their language learning is, so if you’re a fan of that style, you might also like it for learning basic math, algebra and geometry.

6.     If finances are an issue for you, Khan Academy has a financial literacy course in addition to their regular math courses. And the U. S. Office of the Comptroller of the Currency offers a Financial Literacy Resources Directory, which has listings for financial education focused on specific topics like fraud and scam prevention, money management essentials, planning for retirement, housing, crypto, disaster preparedness, you name it. 

I’ll put links to all these resources in the show notes so you can check them out. 

If you’ve made it all the way to the end of this episode, you are now aware of the potentially negative consequences of innumeracy—making poor financial choices, falling victim to things like pseudoscience or unverified medical claims, and misunderstanding statistics or risk to the point it could impact your health. But as I’ve shown, there are plenty of things you can do to improve your ability to understand numbers.

For myself, I’ve made a commitment to do just that. I will no longer jokingly refer to myself as being bad at math, and I urge you to do the same. It’s no joke, it’s serious. It doesn’t just apply to our bank accounts; it applies to everything we do. Being numerate will help us, as much as being literate, to think critically about the claims that are being thrown at us every day. Mis and dis-information isn’t always about words, much of it comes in numbers. You need to ask yourself--Where did those numbers come from? How are they being used? What are the people who are giving me that information trying to get me to believe or do? Always check for reliable sources of statistics just like you would for any other claims. Recognize that our emotions are often swayed by stories that can impede our ability to process factual or numerical information. The best arguments are ones that combine solid numerical or statistical evidence with clear facts and compelling stories and examples. Your feelings about something are not a substitution for clear, understandable facts when it comes to drawing conclusions and making decisions about the things that truly matter. Till next time, I hope you use the information in this episode to help you Think It Through.