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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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3
votes
3answers
111 views

What is the name of the form of the line equation $y = m(x-x0)+y0$

I have been looking everywhere for the name of this form of equation of a line $y=m(x-x_0)+y_0$. It's not quite point-slope. It's the same form you would write in the linear approximation of a ...
6
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2answers
161 views

The word “numeral”, is it being taught and does the word exist for it in your language?

I am a mathematics educator from Lithuania and I have recently realized that there is no separate word in our language for the word "numeral". To be more precise there is no term to describe the ...
8
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1answer
462 views

An alternative to “two column” geometry proofs

I'm a high school teacher in New York State (US), starting in on my first year of teaching Geometry. One of the things that really intrigues me is that the Regents exam (the state-mandated final exam)...
0
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6answers
423 views

Is there a more telling name for “Calculus 2”?

I see a lot of places where "Calculus 1" is referred to as "Introduction to Calculus", or "Single-variable Calculus." "Calculus 3" is referred to as "Multiple-variable calculus." Is there an ...
1
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2answers
163 views

Interpretation of how to define “bigger” and “smaller” real numbers

This is a variant on the question small real numbers. I have a disagreement with someone about the meaning of "bigger" real numbers. Say we have the real number $-1.$ Is $0$ "bigger" or "smaller" ...
2
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1answer
310 views

What are “PreK‐12th‐grade students”?

I am reading the paper Effects of game‐based learning on students' mathematics achievement: A meta‐analysis and can't find a definition for the term "PreK‐12th‐grade students". While I know that "K-...
6
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1answer
184 views

Are there textbooks that cover most etymological aspects of mathematics?

In most of the science textbooks I read, I observed that most of them contain the terms, definitions and etymology too. But nowadays, the mathematics textbooks are becoming more formal and contain ...
3
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3answers
89 views

How to verbalize the correct statement of mixed units?

I want help phrasing the instructions in a math question. The issue is the correct way to express mixed units. For example, if an answer is “25 inches,” I don’t want to accept “25 inches” or “1 foot ...
10
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10answers
2k views

Vocabulary for giving just numbers, not a full answer

I am a math teacher from China, teaching a course in English. Some students of mine are really good at finding answers for math problems designed in a quiz, however they are unable to write down ...
4
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1answer
194 views

The terminology for an excluded solution

I am not a native math teacher. I have a question related to a terminology when solving an algebraic equation. Assume that we are solving some complicated equation like $x^{3}-\sqrt{1-x^{2}}-\frac{1}{...
7
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3answers
342 views

“Amplitude” of Tan and Cot functions

The amplitude of a sinusoid is the distance from its axis to a high point or a low point. When we read this, it follows that Tan and Cot don't have an amplitude. Nor do SEC or CSC. Now, I'm in an ...
8
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2answers
144 views

Math Lessons with Two Parts and a Combination

This is fairly open ended, so I understand if people consider this to be off-topic. I'm interested in creating math lessons where two groups each learn how to use a different simple math skill, and ...
6
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3answers
256 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 ...
9
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4answers
581 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 ...
0
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0answers
62 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. ...
5
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7answers
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
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4answers
202 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, ...
1
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0answers
89 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
352 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
176 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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2answers
362 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
93 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 ...
9
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4answers
284 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
134 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 ...
5
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4answers
582 views

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

Just as we distinguish between an equation and an identity (or equality), why don't we distinguish between an inequation and an inequality? We solve an inequation and we prove an inequality. In French ...
4
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2answers
303 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
207 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\...
15
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3answers
501 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
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2answers
605 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 ...
10
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1answer
141 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
1k 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
904 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
votes
3answers
154 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
votes
2answers
178 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
votes
3answers
247 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
votes
3answers
306 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
votes
1answer
245 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 ...
5
votes
2answers
148 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
905 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
2k 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
180 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
200 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 ...
20
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12answers
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
votes
1answer
238 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
votes
1answer
240 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 ...
19
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4answers
683 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, ...
11
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2answers
241 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 ...
29
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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
654 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 ...