Questions tagged [terminology]

How words are used in mathematics or mathematics education

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18
votes
3answers
1k views

Why are $m$ and $b$ used in the slope-intercept equation of a line?

The slope-intercept form of the equation of a line is often presented in textbooks (in the US) as $$y = mx + b\,,$$ where $m$ is the slope of the line and $b$ is the $y$-intercept. How did $m$ and $...
2
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2answers
2k 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
votes
1answer
164 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
2k 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 ...
10
votes
2answers
2k 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
162 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
180 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
263 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
754 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
366 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
275 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
1k 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
3k 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
192 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
260 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
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1answer
251 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 ...
4
votes
1answer
256 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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3answers
808 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
283 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 ...
5
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0answers
180 views

Is there a name for 'simple' two-input-one-output word problems?

Andy has 4 apples, and then eats 2. How many does he have left? Beth drives for 3 hours at 80 km/h. How far did she go? Carl, Debbie and Earl earned $30 together shoveling driveways. How much does ...
35
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1answer
2k 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 ...
17
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1answer
885 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 ...
10
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2answers
237 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
326 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 ...
17
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3answers
1k 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 ...
11
votes
3answers
461 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
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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 then I'd ...
23
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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 ...
29
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11answers
4k 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 prone to use ...
9
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3answers
1k 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 ...

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