27

I'm no native English speaker, but you can tackle that question from the mathematical point of view as well. The best verb depends on how you view the nature of definite and indefinite integrals. Operators/Functionals Indefinite integrals are operators mapping functions to a set of functions or function (as representative of the equivalence class). ...


19

This is also borderline not-an-answer, but it might be a nice broadening of your students' worldview to know that the "$m$" and the "$b$" are not universally accepted. Showing them this map (even though I do not know its original source, so it may not be accurate in its details) could help their thinking out a bit: Substantial edit: I now no longer believe ...


18

Metonymy and its relatives, metaphor, polysemy, synecdoche occur all over the place in mathematical writing, and sometimes cause students problems and sometimes don't, because those thought processes are basic to our understanding of everything. Where mathematics comes from, by George Lakoff and Rafael E. Núñez. Basic Books, 2000. Exploring the role of ...


17

This is a case where you might be looking for a distinction that's pretty subtle. By definition, the y-intercept occurs at x=0. In one notation, it's literally f(0), where the x is explicitly offered. I'd be ok with a student's answer to "What is the y-intercept?" to be simply the y value, or the $(0,y_0)$ point. If a teacher prefers one, you can ask ...


16

Doctor Peterson in The Math Forum refers to the following sources. From D. E. Smith, History Of Mathematics Vol II (1925), footnote page 393: The Arabs also used jidr (dyizr, root), whence the Latin radix. A longer quote from W. W. R. Ball, A Short Account of the History of Mathematics (4th edition, 1908): The algebra of Alkarismi holds a most ...


16

Elementary algebra is the study of a few specific rings: integers, rational numbers, polynomials with rational coefficients, and rational functions. All the rules for "rearranging" equations are applications of the ring or field axioms. Solving equations can be seen in the framework of algebraic or analytic geometry as studying the solution sets in some ...


16

In my job, I evaluate university math courses for transfer equivalency on a regular basis. In the US, "Calculus 1" typically refers to single variable differential calculus up to the fundamental theorem of calculus. So the course includes limits, the definition of the derivative, techniques and applications of the derivative including trigonometric and ...


15

I can think of a few instances where it might be useful: To situate the current piece of the concept among others coming up To call-back to something earlier in the course that really should be easy to them at this point To intentionally make fun of something you know they thought was stupid (e.g. high school? if you're teaching a proofs course) And, ...


15

The main point here is that these words/expressions should not be used as substitute for an argument. They obviously have some negative effects: You evaluate your students by them and not in the positive sense. If you say "obviously", then it has a message that "it better be obvious". And if it is for someone not clear, then it is an evaluation that this ...


15

It depends a little on context and how careful I am trying to be: If I were being very careful, I might call such a number "a negative number with a large absolute value" or "a negative number with large magnitude." If I am being a little less careful (which I often am when discussing asymptotic behaviour of, for example, rational functions), I'll generally ...


14

I would avoid the verb solve as I reserve this for things like equations, inequalities and problems. An integral is equal to a number or a function, so verbs like find, evaluate etc are more appropriate. I'd use compute only for numerical integration methods. evaluate and find are the two verbs that are used in textbooks and exams that I've come across. I ...


14

Express $\cos(x + \pi)$ in terms of $\sin x$ or $\cos x$ (possibly both). In my opinion, the "or" is logically more correct and the parenthetical recalls/stresses/clarifies this. In general, I am in favor of redundancy and details for such things.


14

The problem with the word "solution" is that it could mean the final answer or it could mean how the final answer was obtained, so I suggest that you don't use it. How about the following? Clearly show how you got your final answer if you want to get full credit for it. If the phrase "full credit" is not familiar to them, you may use "all the points" or ...


13

Origami has things like lemmas, theorems and corollaries. Definition/axiom: The basic folds such as book, mountain, valley etc Lemma: a folding procedure that is used as part of another, such as the bird base or the water bomb base. Theorem: a folding procedure that produces something you wanted, such as the traditional crane. Corollary: a folding ...


13

One of the most colorful names I have heard is the Chicken Mc Nugget theorem: for any two relatively prime positive integers $m,n$, the greatest integer that cannot be written in the form $am + bn$ for nonnegative integers $a, b$ is $mn-m-n$. link1, link2. From the links: The story goes that the Chicken McNugget Theorem got its name because in ...


13

(From a comment) On American math exams, I see the phrase "justify your answers".


12

You ask "Why isn't the term inequation widely used in English?" The answer, however tautological, is that the term isn't used in English because it isn't used in English. Perhaps more usefully, remember that languages change and evolve as speakers of the language (for example) start using new words, stop using old words, alter pronunciation, and play with ...


11

The main reasons both of these are called the same thing are historical. Group theory was more or less invented by Galois to study when one could solve polynomial equations by radicals, and ring theory was more or less invented by Hilbert to solve the main problems of invariant theory, which aimed to find ways to discover when two systems of equations were "...


11

For things in a list, in my experience it is very uncommon to have things indexed by letters other than m, n, i, j, k and sometimes r. Letters whose names end in a vowel sound (like i, j, k) and letters whose names end in a glide (like m, n, r) offer most people no particular problems with pronouncing the "-th" construction. This even goes for unusual ones ...


11

From cooking: Theorem: recipe, something that produces a desired result Lemma: a technique (e.g. creating a roux, proofing dough, preparing a mirepoix, etc.), a procedure that one uses in many different recipes, but might not produce something interesting/tasty by itself Corollary: (really stretching here) extra garnish/styling to slightly modify the dish ...


11

In Central Mexico, the expression \begin{equation} x_{\pm} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{equation} that solves quadratic equations of the form $ax^2 + bx + c = 0$ is called "fórmula del chicharronero" (formula of the chicharronero). The chicharronero is the guy who sells salty snacks made of wheat (called chicharrones). Outside most schools ...


11

In calculus one calls $x \to ax + b$ a linear function. In linear algebra one calls $x \to ax + b$ an affine transformation, and says that it is linear only if $b = 0$. The first order Taylor approximation to a differentiable map is reasonably called the linear approximation of the map. The terminology is reasonable because one is doing function theory, ...


10

I usually phrase it as "Determine $\int x^2\ dx$" or "Determine $\int_1^3 x^2\ dx$". This way 1) it doesn't tip them off to what type of answer they should arrive at, and 2) it allows them to read the symbol $\int$ as either "integral" or (better in my opinion) "antiderivative". For completeness, in some problems I write "Set-up, but do not evaluate, the ...


10

I'm not sure what exactly "standard usage" means, but in educational research (and more specifically in mathematics education research) it is common to distinguish between the intended curriculum, the enacted curriculum. It is also fairly common to refer the attained curriculum and the tested curriculum. When used outside of a research context -- for ...


10

Lemma: A wheel. Proposition: A gear-box. Theorem: A car. Corollaries: Photos of the car at interesting destinations.


10

How about the shoelace formula for the area of an arbitrary simple polygon?                     (Image from Wikipedia.) The formula computes the area from the coordinates of the vertices, essentially by a cross product to compute (signed) areas of triangles.


10

This is an example of what is usually called a flowchart proof (or sometimes a flow proof for short). A quick Google search for "flowchart proof" or "flow proof" shows many, many contemporary examples of the form, including a whole genre of YouTube videos teaching this style of presentation. This style of proof has been promoted at various points since the ...


9

In addition to what @andras-batkai said, seeing words like 'obviously', 'clearly', and so on, in assignments or texts raises red flags and scepticism with me. (Recall that, for thousands of years, it was obvious that the earth was flat. Also, obviously a set contains all of its elements.) As both a former student of formal logic and an occasional tutor, ...


9

Here's what happened: You asked a question using standard phrasing. The student found it surprising that the phrasing allowed the answer given. The student was worried about this and blamed the phrasing of the question. Two things I think it's important that should happen: The student needs to understand what is meant by this standard terminology, and ...


9

Similar to 'drill-and-kill', a common one is 'plug-and-chug'. I guess this refers not so much to the method of teaching (drilling students) as to the method of completing the exercises (running the prescribed algorithm without thought to what it does or why).


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