Questions tagged [terminology]

How words are used in mathematics or mathematics education

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8
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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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5answers
715 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 ...
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4answers
757 views

Composite fraction?

What do you call a fraction that has one fraction in the numerator and also one in the denominator? I mean (a/b)/(c/d). The word by word translation from my native language would be: composite ...
5
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2answers
257 views

Is there an equivalent for "tiervenner" in English or other languages?

In Norway a widely used concept is that of "tiervenner", "ten friends" (my translation to Finnish is "kymppikaverit"). This simply means numbers (implicitly positive ...
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1answer
160 views

Is there an **official** name for the following "digit reduction" operation? [closed]

In one of my programs I have a function I call reduce(n) which associates to n the recursive sum of ...
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9answers
4k views

Why do we introduce the notion that triangles are "congruent" instead of just saying that they are "the same" or "equal"?

The assumed age of the students is 10-15 years old. What is the danger in saying that two triangles are "the same" or "equal" instead of saying that they are congruent? It seems to ...
6
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3answers
273 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 ...
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11answers
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What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

The imagined students are in elementary school, say around 9-13 years old. I want to use rather precise terminology when talking to my students. However, it seems like we typically use the same ...
3
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3answers
187 views

What is the English word for the French "repère"?

I'm preparing a holiday class in computer graphics. The class will be held in English. I'm a French speaker and I'm fighting with some words which have lots of meanings to find the right one in the ...
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3answers
162 views

A linear equation -- my approach

Here is an example of a lesson I did on linear equations where my objective was to show that they are equations of first degree. The reason I do it this way is because I tend to find that students ...
3
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1answer
73 views

simple statistics (binomial) terminology

Say I have the problem: I roll a die three times and I am interested in the probability of ending up with two 1's. My impression is that a single roll is called a trial. What is the full 3-roll action ...
5
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2answers
203 views

Term for candidates for inflection points

The critical points of a function $f(x)$ are candidates for local extrema, i.e., if a function changes from increasing to decreasing, or vice versa, it must happen at a critical point. Is there an ...
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5answers
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Is "conjugate of a binomial" a standard terminology?

In several online high school teaching resources (I do not want to single out any) I see that $a-b$ is referred to as the conjugate of $a+b$ with no restriction on $a$ and $b$. I can understand that $...
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8answers
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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 $y=mx+y_0$,...
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2answers
335 views

Weekly quizzes as an alternative for midterms? What is this called?

I have seen (by some of my former instructors) the following strategy applied as an alternative to traditional "midterms and final" assessment in a math course: Students take a quiz weekly. ...
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3answers
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Definition of Trapezoid

From one textbook we use in our High School - Transcription: A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid. And from ...
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 ...
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2answers
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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 ...
9
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5answers
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Is there a name for paths that follow gridlines?

I'm writing up an activity where students are looking at pathlengths that follow along gridlines. Is there a word or phrase that is commonly used to describe those paths, but doesn't include ...
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7answers
11k views

Why don’t American school textbooks recognize negative numbers as whole numbers?

Looking up for definition for whole numbers on Google yields a result which mentions: The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included). I ...
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4answers
3k views

Does this property of subtraction and division have a name?

Addition and multiplication are commutative. Denoting $\circ$ as either such operation, we have $$x \circ y = z \Leftrightarrow y \circ x = z.$$ Subtraction and division have a similar property, where ...
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3answers
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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 ...
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1answer
184 views

In single variable calculus, do you distinguish between critical and singular points?

In some texts, a critical point is when the derivative exists and is zero, and a singular point is when the derivative does not exist. So I suppose, at $x=0$, $|x|$ would have a singular point while $...
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1answer
295 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 ...
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1answer
209 views

What to call a symbol that denotes an "undisclosed" given number? [closed]

Students like to categorize notations to pin down their understanding of exactly what these notations stand for. Thus, given the expressions $f(x_{0})=f(x)|_{x\leftarrow x_{0}}$, $x=x_0+h$, or $lim_{x\...
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5answers
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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 ...
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2answers
179 views

Confusing verbal descriptions of function transformations

While teaching Function Transformations, I found the verbal descriptions of stretch and squeeze really confusing. So for $y = f(x)$, $y = 2f(x)$ is said to stretch $f(x)$ vertically by a factor of $...
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6answers
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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 ...
3
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3answers
743 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....
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3answers
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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 $...
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1answer
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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 ...
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8answers
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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 ...
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3answers
459 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 ...
3
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3answers
450 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 ...
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4answers
625 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 ...
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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 ...
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1answer
706 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)...
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6answers
3k 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 ...
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10answers
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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 ...
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2answers
309 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" ...
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1answer
331 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-...
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1answer
196 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 ...
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2answers
455 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. ...
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3answers
99 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 ...
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1answer
212 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}{...
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3answers
537 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 ...
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2answers
154 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 ...
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4answers
390 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 ...
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4answers
3k 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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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 ...