# Questions tagged [terminology]

How words are used in mathematics or mathematics education

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### Allowing nonstandard mathematical language and/or notation

How important is enforcing standard mathematical language and/or notation? Today, I was questioned by a writing instructor as to how vital it is to correct students when they explain something using ...
1answer
252 views

### Terminology for parts of limit notation

When we talk about: $$\lim_{x\to{c}}f(x)=L$$ Is there a formal name for the number "$c$"? I know of course that it means "$L$ is the limit of $f(x)$ as $x$ approaches $c$". It just would be nice to be ...
3answers
669 views

### The term “unique” for functions and operations

This is long so... TLDR: Proposing the math community steer away from the misleading term unique, with respect to functions and algebraic operations. Instead, use unambiguous. Why not? Analysis below....
8answers
4k views

### Should high school teachers say “real numbers” before teaching complex numbers?

Before complex numbers are introduced in senior high school courses, should we emphasise that solutions (e.g. to quadratic equations) are real solutions? If we do, then when non-real numbers finally ...
3answers
299 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 ...
2answers
207 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 ...
1answer
683 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)...
6answers
1k 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 ...
2answers
241 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" ...
1answer
327 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-...
1answer
194 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 ...
3answers
98 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 ...
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 ...
1answer
211 views

1answer
102 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 ...
5answers
495 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 ...
2answers
141 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 ...
4answers
609 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 ...
2answers
435 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. ...
3answers
291 views

2answers
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### 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 ...
1answer
154 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 ...
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 ...
2answers
1k 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 ...
3answers
160 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 ...
2answers
179 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 ...
3answers
255 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 ...
3answers
680 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 ...
1answer
329 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 ...