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Questions tagged [terminology]

For questions about the use of terms (words) used in mathematics, or used in teaching mathematics. Not to be confused with: [tag:definitions].

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227 views

In teaching mathematics, should one always follow some international standards such as ISO 80000-2?

ISO 80000-2:2009 is a standard describing mathematical signs and symbols developed by the International Organization for Standardization (ISO). In teaching mathematics, should one always follow this ...
7
votes
4answers
372 views

Is the constant term a coefficient?

I'm a baby boomer who was taught that the constant term of a polynomial is a coefficient, being the constant factor for the x^0 term. That's not what's taught today. Current text books are vague on ...
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0answers
47 views

“Small” real numbers [duplicate]

At least for me, my intuition for what numbers are large or small comes entirely from positive numbers. I find it challenging to use the word "small" correctly when talking about negative numbers. ...
7
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8answers
2k views

What is an intercept?

I have always taught my students that the $y$-intercept of a line is the $y$-coordinate of the point of intersection of a line with the $y$-axis, that is, for the line given by the equation $y=mx+y_0$,...
5
votes
4answers
193 views

What is the value in creating distinguishing terminology between the $x$, $y$, and $(x, y)$ values of a possible point of extremum?

I've been out of a math program for about four years now. My wife is starting a CS degree, and finished her first calculus course last semester. I tutored calculus throughout my entire undergrad, ...
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0answers
80 views

What is the best term for “probability measure” in an undergrad introduction to probability course?

The function $P$ that takes an event $A$ as input and returns the probability $P(A)$ as output is called a "probability measure" when we are developing probability using measure theory. I have also ...
6
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4answers
329 views

Should I describe the function $x \mapsto f(x_0) + f'(x_0)(x - x_0)$ as “linear” in a freshman calculus class?

One of the most important ideas of calculus is $$ f(x) \approx f(x_0) + f'(x_0)(x - x_0). $$ The approximation is good when $x$ is close to $x_0$. This approximation is very useful because the ...
5
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2answers
163 views

How to explain NP-hardness and NP-completeness to students

Computer science is becoming more and more important for mathematicians nowadays. Terms like big data, algorithm, artificial intelligence and others are frequently on the news. Many mathematical ...
5
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3answers
336 views

How to Teach Middle School Students to Read Square Roots?

This exact quote from my standard American Algebra 1 textbook states when first introducing rational square roots: $\sqrt{49} = 7$ is read "The positive square root of $49$ equals $7$." $-\...
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1answer
86 views

When a geometrical figure a special case of another [closed]

Squares are special types of rectangles. Are circles special types of ellipses/ovals? Are cones special types of pyramids? I guess the answer is no because of the 2D basis: circles are not special ...
8
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4answers
228 views

What is a recommend way to describe a negative number with large absolute value?

Sometimes when we discuss limits verbally, we may say that a variable $x$ being "very small" (assuming that $x$ is a real number). But this could mean any one of the following: The number $x$ is a ...
3
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2answers
129 views

Should Measurement of Angles Using Degree (and perhaps Common Logarithm as well) be Avoided in Pre-Calculus?

People use degrees and radians to measure angles and though degree measurement is acceptable and is widely used in everyday life, it is not in the International System of Units and mathematically it ...
7
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1answer
158 views

Why isn't the term *inequation* widely used in english?

Just as we distinguish between an equation and an identity, why don't we distinguish between an inequation and an inequality? We solve an inequation and we prove (or establish) an inequality. In ...
3
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2answers
168 views

How to explain Chinese remainder theorem?

I want to explain Chinese remainder theorem to master level computer science students. There are two versions of CRT one is number theoretic and second requires the definition of ideals, groups etc. ...
6
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3answers
178 views

Terminology: degree of coefficient?

It's clear that a polynomial has a "degree". For instance our $$x^2 + 2x + 3$$ is a of degree two. Can we apply the "degree" terminology to the coefficients? Here we have the coefficient tuple $[1\ 2\...
14
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3answers
455 views

Explaining to students why $m$ and $b$ are used in the slope-intercept equation of a line

The slope-intercept form of the equation of a line is often presented in textbooks as $$y = mx + b\,,$$ where $m$ is the slope of the line and $b$ is the $y$-intercept. How did $m$ and $b$ become ...
2
votes
2answers
227 views

Definition of root of equation/expression

Related: Where does the word “roots” come from when talking about zeros A student recently wrote: The positive root of 3 sin x = x is near 2. I am questioning the student's use of of the word ...
9
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1answer
114 views

Is there a base-independent term for numbers written out with decimal/binary points?

How can I refer to a number written out in its decimal expansion (e.g., 1.25) or binary expansion (e.g., 1.01) to distinguish it from a number expressed as a fraction? I am teaching students to use ...
8
votes
1answer
492 views

What is the term for the marks used to show congruence in geometric figures?

When looking at a given picture to be used in a geometric proof, often times single, double, or triple "slashes" mark off equal line segments or arcs. What is the correct term for these? I've seen ...
9
votes
1answer
618 views

What is the difference between “numeracy” and “number sense”?

Is there a difference between numeracy and number sense, or are they synonymous? In my language they are often both translated to the same word (tallforståelse). I'm thinking that perhaps numeracy ...
4
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3answers
145 views

Proper ordering of phrase “multiplied by”

Which of these is the correct ordering: a polynomial multiplied by a monomial a monomial multiplied by a polynomial if what I want to achieve is something like 3x(x+5)? Here are my initial ...
3
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2answers
173 views

“A” or “The” Cartesian plane?

Which is correct terminology: "A Cartesian plane" or "The Cartesian plane"? (As in the directions for a section of homework being, "Plot a point on ______ Cartesian plane." In that context, I feel ...
4
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3answers
239 views

“The following are equivalent”

What do you say to the following way of teaching "if" and "the following are equivalent"? Has somebody ever taught it like this? An implication A -> B can be viewed as asserting that B is at least as ...
7
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3answers
203 views

A good antonym for reducing/simplifying equivalent fractions

I am looking for a good antonym for reducing/simplifying equivalent fractions: 'reduce' and 'simplify' both make sense to me when dividing, but I'm struggling to name what it is we do when we multiply ...
3
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1answer
219 views

How to explain “fractional terms”?

as I can see there are mainly two ways to introduce fractional terms. Two examples to demonstrate the two variants: $\frac{a^2+3}{a}; \frac{3}{2c}$ $T(a) = \frac{a^2+3}{a}; T(c) = \frac{3}{2c}$. In ...
6
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2answers
119 views

Name to use for codomain/range/target

There are many questions about how best to teach functions, for example why don't we teach codomains in HS and should we teach them at all. On Math.SX there are questions about the "right" name for ...
12
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3answers
890 views

Mathematical education slang

Amir Asghari recently asked a question about mathematical slang. He was "looking for "non-mathematical" terms or phrases that are used to refer to mathematical objects (of any kind) mainly for ...
22
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16answers
1k views

Examples of Mathematical Slang

Unless you have taught highschool algebra in Iran, you could not make sense of the phrase: Elephant and Teacup Identity! This is what teachers use to refer to the following identities: $ (a+b)(a^2-...
7
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2answers
170 views

Alternative terms for 'mathematical understanding'

When I talk to other research mathematicians, there is pretty uniform agreement that we want our (university) students to understand the maths we teach them rather than just memorise processes. As far ...
9
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1answer
182 views

When did the term and taught technique 'cross multiplication' enter into common use?

The title says it all, I suppose. I'm interested to know when/where the term/technique cross multiply came into use. Sources would be nice. In case it's unfamiliar to anyone, or in case the usage of ...
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13answers
2k views

What could be good non-mathematical analogies to explain the difference between the words theorem, proposition, lemma and corollaries?

What could be good non-mathematical analogy/analogies to explain the difference among the words - theorem, proposition, lemma and corollaries to high school students? I am looking for analogies that ...
6
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1answer
225 views

What is a less anglo-centric collection of persons than Andy, Beth, Carl, Debby and Earl?

These five imagined persons have accompanied me for some time. We've had a bunch of laughs and a few tears. I love them dearly. That said, I'd like to retire them in favor of a more culturally diverse ...
8
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4answers
1k views

Correct pronunciation of 'xth' (and workarounds for those who find it a tongue-twister)

This is to some extent a cross-posting from English Language & Usage. How do you pronounce “xth”? I am asking a slightly different question -- but only slightly. I was attempting to offer ways ...
5
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1answer
150 views

Definition of “curriculum”

In standard usage does the word "curriculum" mean That which ought to be taught and learned, as prescribed by authorities (i.e. teachers and textbook authors and the like); or That which actually is ...
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4answers
664 views

Difference in meaning of 'algebra'

The other day, in a conversation with colleagues, I realised that the word 'algebra' means different things to us. To me, it brings to mind the study of algebraic structures: vector spaces, groups, ...
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2answers
227 views

Does “factor” mean simply the multiplication (of any functions, numbers etc)

I am sorry I am not directed with the education of math. But granted, let me ask the above question. In my language (actually Japanese), the words corresponding with the factor and divisor, seem to ...
27
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1answer
1k views

Metonymy in mathematics

Metonymy is a figure of speech where a word or another expression is used to mean something other than its literal meaning. This phenomenon is not restricted to the "usual human languages" (such as ...
15
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1answer
627 views

Where does the word “roots” come from when talking about zeros

We often use the word roots when referring to the solutions of an equation. For instance, when we have a polynomial $P(x)$, we call its zeros the roots of $P(x)$. For some polynomials we can relate ...
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2answers
183 views

Using terminology for the different concepts of rational number

In elementary maths education literature, they distinguish multiple concepts that rational numbers are used to represent: fractions, quotients, ratios, rates, and possibly more. These words seem to be ...
10
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2answers
225 views

Term and reference for the problem of students “overassociating” concepts with each other

I am writing a paper directed at a physics-education journal and I want to briefly refer to the phenomenon of students “overassociating” (in lack of a better term) mathematical concepts with each ...
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3answers
863 views

“Proof” meaning in maths and society

When we ask students to prove a particular result in a math class, students often reply with examples. For example, if I state: if a number is even its square will be even, and ask the students to ...
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3answers
290 views

Common phrases having different meaning

When talking with students it frequently happens that they misunderstand what you meant. The common example is the amount of rigor that one would consider "a proof", but there are other things, like ...
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7answers
1k views

The word “and” rather than “or”

I asked my students the following question. Q: Express $\cos(\pi+x)$ in terms of $\sin$ and $\cos$. A: $-\cos(x)$. Students: Yeah, but where is the $\sin$ part? If I got this in an exam ...
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5answers
4k views

What is the proper verb for “doing” an integral?

It's time to write exams, and when writing in committee we often discover differences in usage between various instructors. Here's an example I noticed today. What is the proper verb to use in a ...
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11answers
3k views

Are the words “easy,” “basic,” “clearly,” “obviously,” etc., ever helpful?

This is a very basic fact from... It then clearly follows that... Obviously, we have... The proof is trivial... I could add plenty of other phrases to this list that mathematicians are ...
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1answer
373 views

Standard word for a formula that is always true

If it is known from context that variables $x$ and $y$ represent integers, an open Boolean formula such as $x \ge y \Rightarrow x+1 > y$ evaluates to true regardless of the value assigned to ...