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].
6
votes
3answers
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 ...
1
vote
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
votes
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, ...
1
vote
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
votes
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
votes
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
votes
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 $7$."
$-\...
-3
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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 ...
20
votes
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
votes
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
votes
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
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 ...
19
votes
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, ...
11
votes
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
votes
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
votes
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 ...
9
votes
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
votes
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 ...
16
votes
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 ...
8
votes
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
...
12
votes
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 ...
20
votes
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 ...
26
votes
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 ...
8
votes
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 ...
