11 Commonly Misspelled Words in Matheamtics

No, this isn’t meant to be another stupid post about how ppolee can raed setecnnes wehn the ltetres of ecah wrod are scamrbeld. But if you were paying attention, you may have noticed that the word mathematics was misspelled in the title.

In an ironic twist of fate, the word that I misspell most often is MATHEAMTICS. Sort of. It’s not that I misspell it as much as I mistype it. For unobvious reasons, I tend to transpose the M and A in the third syllable. And statistically speaking, it stands to reason that I’d screw it up often — it’s a word I type frequently.

Spelling is important, as authors Robert Magnan and Mary Lou Santovec claim in their e-book 1001 Commonly Misspelled Words. Spelling is so very important, in fact, they’ve taken great care in writing a description of their book for Amazon. Here’s an excerpt:

It seems that Magnan and Santovec should increase their list to 1003 words and add memory and correct (misspelled as “memeory” and “corret” in the excerpt above). And then at the end of the paragraph, it seems they’re trying to make a joke by spelling knowledgeable incorrectly but then correcting the spelling between the dashes; yet both instances are spelled the same — correctly, in fact — which I suspect was autocorrect fixing the deliberate misspelling before this blurb went to print.

One has to wonder if these mistakes were intentional, to keep the reader on her toes and emphasize how important spelling is. Sort of like the deliberate mistake in this proof that 1 = 2:

(For the infinitely geeky, there’s this follow-up, posted by Anders Kaseorg on Quora:

Suppose there are n proofs that 1 = 2. From this we derive that there are n + 1 – 1 = n + 2 – 1 = n + 1 proofs that 1 = 2. Therefore, by induction, there are infinitely many proofs that 1 = 2.)

But, I digress. My purpose in writing this post was to provide a list of hints for how to spell the most frequently misspelled math words. As it turns out, many of the math words that you’d think would be hard to spell — words with several syllables or lots of letters, like parabola or triangle or differentiation — are actually spelled exactly like they sound. Most of the really hard-to-spell math words are the names of mathematicians, like de Moivre, Poincaré, Weierstrauss, Euler, and Euclid.

The following are math words pulled from a variety of lists of commonly misspelled words.

forth/fourth/forty : there’s a u in the ordinal number, but not in the multiple of 10. To help you remember the difference, keep in mind that 40 is the largest number that, when spelled out, has all its letters in alphabetical order — and that won’t be the case if a u is included.

twelfth : there’s a little “elf” in twelfth, even if you incorrectly say “twelth” without the f.

ninth / ninety : fifth and fifty are parallel, in that both change v to f and drop the e. Sadly, ninth and ninety aren’t. Sorry, I don’t have any tips for remembering this one… except maybe that it’s on this list, which will help you remember that they’re spelled differently.

existence : one i, three e‘s, no a‘s.

height : the three dimensions are length, width, and height, not heighth, regardless of how my father pronounced it. There’s no h at the end.

independent : ants live in colonies, which isn’t very independent. That’ll help you remember that independent ends in –ent, not –ant.

neighbor : the ei takes on a long a sound, despite the i before e rule, and then there’s a silent gh. Yeah, lots of opportunities for goofing up this one. No one would fault you for spelling it nayber.

operator : when AT&T introduced the 1-800-OPERATOR promotion in the mid-1980’s, it was a disaster. The majority of would-be callers spelled operator with an e instead of an o in the last syllable.

perseverance : perhaps less mathy than the other words on this list, but Common Core includes it in Math Practice 1. There’s an a in the last syllable, and there’s no r before the v.

principal/principle : remember that Al wants to collect interest on his principal investment, but Lee likes the pigeonhole principle.

similar : another one that doesn’t have –er at the end.

[Update 8/3/2015: From the twitterverse, we have these additions to the list.

perpendicular : two e‘s, one i, not the other way ’round. @redbucwildcats

mensuration : not hard to spell, necessarily, but hard to pronounce. @pstni

angle : not angel. @mathsjem

frustum : frustrated has two r‘s, but frustum only one, thank you very much. @mathsjem

parallel : one r, two a‘s, three l‘s. @mathsjem

correlation : only double r‘s. @mathsjem]

Passwords, Age Restrictions, and Computer Silliness

My computer has been a bad boy recently.

First, it told me that my password is going to expire approximately 11 months before I was born…

Interestingly, the folks at www.timeanddate.com disagree with the number of days between March 31, 1970, and the date that screen capture was snapped (March 1, 2015). So much for the truism that, “Computers make very fast, very accurate mistakes.” I thought the difference could be explained by excluding the end dates, but that doesn’t seem to be the case, so I’m not sure what ADPassMon is doing. (Then again, I’m not sure why I’m wasting my time checking the calculations of a piece of software whose warning messages suggest the existence of time travel.)

Then, when attempting to register my sons for ski camp, it gave one of the craziest age restrictions I’ve ever seen…

check out the valid ages…

An age of 5.925 corresponds to 5 years, 11 months, 7 days, and 15 hours, which seems quite an arbitrary cut-off for a ski camp. Further, an age of 7.999 years means that kids are eligible for ski camp so long as they are not within 15 hours, 14 minutes, and 24 seconds of their eighth birthday. The framers of the Common Core would be happy with the consideration paid to MP.6: Attend to Precision. Where else have you seen ages expressed to the nearest thousandth? Not even parents of newborns use this many decimal places.

Both of these issues remind me of a childhood friend who wanted to be a writer. He said he wanted to write stuff that would be widely read, cause an emotional reaction, and make people scream and cry. He now writes error messages for Microsoft.

Here’s wishing you an error-free day!

Can You Find the Error?

I used to be the editor of the “Media Clips” column in the Mathematics Teacher journal. One objective of the column was to identify the use of incorrect mathematics in print. The following flyer from H. H. Gregg would have been a great example.

My favorite entry in the “Media Clips” column was a clip from the Salt Lake Tribune on October 11, 2002, which read:

A Salt Lake County Health Department inspector paid a visit recently [to the Coffee Garden restaurant] and pointed out that research by the Food and Drug Administration indicates that one in four eggs carries salmonella bacterium, so restaurants should never use more than three eggs when preparing quiche. [The Coffee Garden’s quiche recipe calls for four fresh eggs.]

Priceless.

Anyway, back to H. H. Gregg. The image above may be too small or blurry to identify the error, so here’s an enlargement.

I gave the flyer to my sons and told them that they could have ice cream for dessert if they were able to identify the math error. I’ll make the same offer to you — first person to post the error to the comments gets an ice cream cone from me.

7 Math Mistakes to be Aware Of

April is Math Awareness Month, and some things to be aware of this month — as well as the whole year through — are common math errors. Here are seven that show up frequently.

Incorrect Addition of Fractions. It’s common for kids to add fractions as follows:

And while that algorithm works for batting averages in baseball, it doesn’t work in most other places. More importantly, this mistake is often unaccompanied by reasoning. For example, a student who claims that 2/3 + 4/5 = 7/9 doesn’t realize that with each addend greater than 1/2, then the sum should be greater than 1. That lack of thought bothers me.

Cancellation of Digits, Not Factors. While it’s true that 16/64 = 1/4 and 19/95 = 1/5, students who think the algorithm involves cancelling digits may also argue that 13/39 = 1/9, and that just ain’t right.

Incorrect Distribution. This one takes a lot of forms. In middle school, kids will say that 4(2 + 3) = 8 + 3. As they get older, they apply the distributive property to exponents and claim that (3 + 4)² = 3² + 4² or, more generally, that (a + b)² = a² + b².

The Retail Law of Close Numbers. A large portion of the population will buy a shirt for $19.99 that they’d pass up if it had a price tag of $20.00. Even though the amounts only differ by one cent, a lesser digit in the tens place makes the price feel much lower. Crazy, but true.

Ignoring the Big Picture. If you are a driver who is interested primarily in speed (and less concerned with price, looks, fuel efficiency, or other factors), would you rather have a vehicle with 305 horsepower or one with 470 horsepower? If you chose the latter option, congratulations! While the owner of a sweet 305-hp Ford Mustang will be sitting at home and sipping a mint julep on his front porch, you’ll still be doing 30 mph on the highway in your Sherman tank.

Correlation Implies Causation. As ice cream sales increase, the number of drowning deaths increases, too. But that doesn’t mean that having an ice cream cone willl make you less likely to swim safely, even if you failed to heed your mother’s advice to wait 30 minutes after eating. It’s just that ice cream sales and swimming-related deaths increase in summer, both of which are to be expected.

Just because two things happen to coincide doesn’t mean that one is the direct (or even indirect) result of the other.

Percents Don’t Work That Way. A 20% decrease followed by a 20% increase does not return you to the initial value. If you invest $100 in a company, and it loses 20% the first year, your investment will then be worth $80. If it gains 20% the next year, you’ll now have $96. Uh-oh.

What common math error do you see frequently, and which one bothers you the most?

Math Clocks

Jiminy. The folks at Clock Zone make a math class wall clock — and I would like to be the first to publicly chastise buy.com, amazon, and anyone else who is selling it. It contains at least two mathematical errors:

SPOILER ALERT: In my rant below, I identify the errors in the clock. If you’d like to identify them for yourself, don’t read any further.

I say “at least” two errors because there may be more. The obvious errors are for 9 (the expression assumes that the exact value of π is equal to the common approximation 3.14) and for 7 (because the equation is quadratic, x = 7 is only one of the answers; the other possible answer is x = ‑6).

More generally, I have an issue with any of the algebraic equations that are meant to represent integers. For instance, the equation 50/2 = 100/x has solution x = 4, but I believe that it is incorrect to say that the equation itself is equal to 4. So perhaps the clock has four errors, if you consider the algebraic equations for 4 and 10 to be erroneous, as I do.

This clock is meant to be a math joke. Edward de Bono in The Mechanism of the Mind (1969) suggested that when a familiar connection (such as seeing the numerals 1‑12 on a clock) is disrupted, laughter occurs as a new connection (seeing mathematical expressions instead of numerals) is made. Sadly, math jokes are supposed to make you laugh… yet this clock makes me want to cry.

To ease the pain, I did a little research and uncovered several clocks of famous mathematicians. I present them here for your enjoyment.

Leonardo da Pisa:

Kenneth Appel:

Rene Descartes:

Karl Friedrich Gauss: