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As mathematics educators, we all have come across students using mathematical notation incorrectly (looking at you, $\frac{d}{dx}$ vs $\frac{dy}{dx}$ or $\frac{\infty^2}{\infty}$). My question focuses on "verbal notation." For example, my hackles go up when I hear the following:

  • "take the prime of $f$" or "$d$-$dx$ the function" or "derive the function" instead of "compute the derivative of $f$" or "find $f'(x)$" (edit: or "differentiate the function"). Double chalkboard-fingernails for "the prime of the prime" and it's ilk.
  • "anti-derivative the function" instead of "integrate the function" or (even better) "find the indefinite integral of the function"
  • "minus/minusing $a$ from $b$" instead of "subtract $a$ from $b$" or "compute $b$ minus $a$"
  • "plus/plussing $a$ and $b$" or instead of "add $a$ and $b$" or "find $a$ plus $b$"
  • "take the inverse of a fraction" instead of "take the reciprocal of a fraction" (debatable, the "multiplicative inverse of a fraction" does appear in sources)

The list goes on from there--I would be curious to hear your pet peeve phrases! My question is this:

Is it overly picky and pedagogical to correct such phrases? If it is appropriate to correct these phrasings, is it situation dependent (tutoring/recitation/lecture) and how would you do so?

I would like to emphasize that this is a question specifically about phrasing and verbalizing mathematical operations. Assume that the hypothetical student is generally performing the correct operations, is capable of reasonably proper written notation, and "plussing $a$ and $b$" would be the correct step.

Edit: Running list of other phrasing

  • "vertexes" vs. "vertices", probably applying to pluralizations of many other words as well (axises vs axes, ...). Credit to kcrisman
  • Opposite of the above, "vertices" or "vertice" to refer to a single object (c.f. $x$-axes etc). Credit to Andreas Blass
  • Misuses of mathematical verbs such as "Solve 16 + 58" or "Prove the integral." Credit to Jack M
erfink
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    I don't see how using the term "Anti-Derivative" is such a peeve. It appears in textbooks often enough. – Weckar E. Mar 16 '17 at 14:02
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    @WeckarE. It is a case of verbing the noun. The action is usually called anti-differentiation, which results in the anti-derivative. – Adam Mar 16 '17 at 14:57
  • @Adam Ah, fair point, that does make more sense. – Weckar E. Mar 16 '17 at 14:59
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    "Plussing" and "minussing" physically hurt me ears when I hear them. – Feathercrown Mar 16 '17 at 20:45
  • Also, "deriving" a function is problematic---are you using physical laws to determine what the function should be? Or are you finding the derivative by differentiating? – erfink Mar 16 '17 at 21:00
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    @erfink Hmm what is wrong with "Find the indefinite integral of the function"? If I had to be money I would guess "Find the anti-derivative of the function" would be the correct option, but I can't see how saying indefinite integral makes it wrong. – Ovi Mar 16 '17 at 22:35
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    I'm personally much more put off by misuses of mathematical verbs such as "Solve 16 + 58" or "Prove the integral", which show actual conceptual confusion rather than just being ignorance of standard terminology. – Jack M Mar 16 '17 at 23:08
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    It would be interesting to see whether students who say things like "taking the prime of $f$" and "d-dx the function" are less likely to know that $f'(x)$ and $\frac{d}{dx} f(x)$ mean the same thing. – Daniel Hast Mar 17 '17 at 14:31
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    @Ovi: Indeed, finding the indefinite integral means finding the collection of all antiderivatives of the function, whereas "Find an antiderivative of the function" would only require us to find one...e.g. when carrying out integration by parts. There is, as you say, a distinction! – Jon Bannon Mar 17 '17 at 17:19
  • For the more efficient ones: math is logic's shorthand. (If we had to do 80 pages of logic every time we wanted to add 1+1 we wouldn't get very far.) Why not make the more efficient verbalizations an acceptable standard?
    • – James Foit Mar 17 '17 at 00:54
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    @JamesFoit The question is not really about using shorthands, but about using the wrong words. The correct and rigorous (and useful for the future) phrase is not necessarily and longer. Precision is important, and we want the verbalizations to remain efficient in the future. – Joonas Ilmavirta Mar 17 '17 at 09:29
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    On the first bullet a very natural option that you missed is "differentiate the function". – Git Gud Mar 18 '17 at 13:30
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    I've encountered the problem opposite to "vertexes"; students who know "vertices" sometimes form the singular "vertice". – Andreas Blass Mar 18 '17 at 18:07
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    What's wrong with $\frac{d}{dx}$ that's a completely reasonable linear operator. – DRF Mar 21 '17 at 11:04
  • @DRF Read that out loud as "dee dee ehks the function." I absolutely agree with the fact that $\frac{d}{dx} f(x)$ is reasonable written notation, even ignoring that it should be $\mathrm{d}$ and not $d$. Or was it a question about the written notation note about $\frac{\mathrm{d}}{\mathrm{d} x}$ vs $\frac{\mathrm{d} y}{\mathrm{d} x}$? – erfink Mar 22 '17 at 03:08
  • @user615 If we want to go down that path, then certainly calling the field "calculus" (literally, "calculation" from the Latin "small pebble/stone" as used in an abacus) is horribly undescriptive. While the original terms of "infinitesimal calculus" or "differential calculus" are better, they are unwieldy and incomplete in the modern conception. I find the most confusion to your point about "the derivative" arises when we want to talk about deriving formulas, as in coming up with appropriate formulae to model a situation, rather than differentiating them. – erfink May 16 '21 at 05:36
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    (1) For me, a major one is how completely our typical students (in the US) are confused between "formula", "equation", and "expression". They almost never use "expression", and use "formula" or "equation" randomly in place of any of the three. For example, for the task of finding the derivative of (x+3)^2, a student may ask: "Do I take the derivative like this or do I simplify this equation?" [Note: they actually would use an F-word instead of simplify, but you don't want me started on that one...] – zipirovich May 19 '21 at 04:19
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    (2) Or from my most recent experience of teaching linear algebra, there so many phrases like that! A few examples off the top of my head: "the matrix has free variables" or "the matrix is inconsistent" (instead of the system of equations whose augmented matrix this is), "the matrix is linearly dependent" (instead of its column vectors), and so on, and so forth... – zipirovich May 19 '21 at 04:24
  • Yes, you need to correct language usage. It stems from poor teaching of the English language. Do they actually teach grammar? Barely. Same with someone answering "it is when..." when you ask "what is...". – Rusty Core Nov 04 '22 at 22:35
  • I don't think any of the examples you gave actually hamper mathematical understanding, so they seems unimportant when I am wearing my math educator hat. (As a fellow human, sure, some of these grate on me, but don't get me started on my laundry list of petty linguistic grievances.) – David Steinberg Nov 04 '22 at 19:48
  • What, pray tell, is wrong with "vertexes"? Yes it's non-standard, and students do need to know the standard plural, but the regular plural is perfectly transparent in meaning and insisting on using loan inflections is just inkhorning snobbery – No Name Aug 29 '23 at 10:05