Innumeracy
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2+2=4 |
Innumeracy is a term used to refer to a growing trend in the inability of people to understand numbers, statistics, and probabilities. The first use of "numeracy" as an analogue to literacy was in a 1959 report by Geoffrey Baron Crowther^{[1]} and the derivation "innumeracy" was coined by Douglas Hofstadter^{[2]} and popularized by the book of the same title by John Allen Paulos.^{[3]} Numbers and probabilities are often essential to understanding the world, and ignorance, or even an anti-intellectual stance against understanding how they work, can lead to significant consequences personally and for society as a whole. The potential problems caused by innumeracy are, it must be said, innumerable.
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[edit] What is numeracy?
Numeracy is generally defined as an understanding of, and ability to do basic manipulations with numbers. Addition, subtraction, multiplication, division, fractions, percents, and decimals. When looking at basic innumeracy, it does not include algebra, geometry or calculus. The point is pretty simple: our kids, and in fact most of the adults in studies done in the US and UK, are unable to easily figure out the cost per item or how much they are saving if something is "25%" off.^{[4]}
[edit] Do numbers matter?
One criticism often brought up is the question of just how important skills like numbers and spelling are, in a world of calculators and spell check. After all, most people no longer know how to build a good fire, bake from scratch, or even sew on a button. Everyone carries a calculator with them, in the form of their phone; their browsers check the spelling as they type, and if they really need something, they can find a way to get the information. ^{[5]}
- Working numbers trains a mind for logical, critical thinking. The fact is, math, even basic numeracy, is a logically derived system. Learning to manipulate basic numbers gives you an entry into the thought processes that critical thinking are built upon.
- Basic numeracy allows people to make everyday comparisons. "Is this can of tuna that is 2 times the size of that can of tuna, a better deal, even though it is more expensive?" "Did turning off the lights really affect my utility bill?"
- Numeracy helps in understanding statistics, and therefore being able to understand how to better take risks, or who is selling you a load of bull.
- Numeracy helps you understand major life decisions like when to buy a house, and how to buy a house. If more people had better numeracy skills, they might not have been as willing to buy houses they could not afford, or waive payments off for 5 years, only to be hit with rates that are significantly beyond their reach.
While it is true that you can figure out all of these things with a calculator, people don't really bother. If they had a basic working grasp of these numbers, they could easily calculate much of this in their heads to make better decisions. And without a basic understanding of the underlying mathematics, you can't even work it out with a calculator.
[edit] Why are our kids innumerate
One question often brought up is: Why has there been a drop off in children's numeracy levels over the years? While there are no easy answers, some stepping stones to improvement include:
- Ensuring that math teachers are familiar and comfortable with mathematics (and mathematical pedagogy).
- Not teaching in a rote, test-oriented fashion; for example, not merely teaching that three times three is nine, but how multiplication relates to addition, and so that three times three equals three plus three plus three.
- Connecting numbers to real-world concepts: negation and division are two essential concepts that are poorly understood by a great many students largely because they are only poorly (if at all) connected by teachers to concrete examples, and because explanation of how they logically extend familiar mathematical concepts (for example, division is a means of "undoing" multiplication, and so any true statement involving division can be written in multiplicative terms; likewise, negative numbers arise when one subtracts a large enough value from a positive numbers - Johnny said he'd give you an apple, but already gave all seven of his away; he now owes you one) is often foregone.
In America, these and other issues have for some time been allowed to grow unaddressed because math and science education became trendy in the U.S. in the wake of Sputnik and the Space Race; once America beat the Soviets to the moon, we clearly never had to use math or science again.^{Do You Believe That?}
[edit] A simple test of numeracy
This problem caught the eye recently. It is simple, but astonishingly few were able to solve it.
A baseball and a bat cost $1.10 together. The bat costs one dollar more than the ball. How much does the ball cost?^{[6]}
[edit] See also
[edit] External links
- innumeracy.com
- Understanding Popular Uses of Percentages, Miller-McCune
[edit] References
- ↑ John O'Donoghue. Numeracy and Mathematics. Irish Math. Soc. Bulletin 48 (2002), 47–55
- ↑ Douglas Hofstadter's Innumeracy Exercises, jsomers.net
- ↑ Innumeracy: Mathematical Illiteracy and Its Consequences
- ↑ https://www.theguardian.com/commentisfree/2010/may/03/illiteracy-innumeracy-prisons
- ↑ https://www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-school
- ↑ 5 cents for the curious.