Questions tagged [terminology]
How words are used in mathematics or mathematics education
83
questions
4
votes
1answer
81 views
Are ‘constant difference’ and ‘common difference’ synonymous?
I’ve seen at least two phrases to describe a fixed difference between two numbers, i.e., “constant difference” and “common difference.”
For example, if Sibling A is 10 years older than Sibling B today,...
0
votes
2answers
461 views
Is there a difference between 'subtract' and 'subtract by'?
A basic terminology question for a foreign speaker.
Please correct me if wrong. (Let's ignore the commutative property of + and * here)
...
-4
votes
1answer
189 views
Can you talk about (the rest of the) field axioms when the operations are not closed? [closed]
Note: Updated based on this.
In my course, my instructor posed the following exercise:
Let $S$ be the subset of $\mathbb R^n$, $S=\{(a_1,a_2,a_3...a_n) | a_2 = \pm a_1, a_3=...=a_n=0 \}$. Define ...
5
votes
2answers
269 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 ...
5
votes
4answers
794 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 ...
-4
votes
1answer
163 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 ...
3
votes
3answers
202 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 ...
-2
votes
3answers
169 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 ...
22
votes
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 ...
13
votes
11answers
6k views
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
votes
1answer
74 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 ...
14
votes
5answers
1k views
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 $...
5
votes
2answers
216 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 ...
9
votes
3answers
1k views
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 ...
10
votes
2answers
345 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. ...
9
votes
5answers
2k views
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 ...
14
votes
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 ...
17
votes
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
...
2
votes
1answer
250 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 $...
1
vote
1answer
215 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\...
11
votes
2answers
188 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 $...
32
votes
6answers
3k views
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 ...
9
votes
1answer
312 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 ...
3
votes
3answers
784 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....
16
votes
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 ...
3
votes
3answers
544 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
votes
3answers
276 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
votes
1answer
723 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
votes
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 ...
1
vote
2answers
362 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
votes
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-...
7
votes
1answer
197 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
votes
3answers
102 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
votes
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
votes
1answer
215 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}{...
8
votes
3answers
559 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
votes
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 ...
7
votes
5answers
827 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
votes
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 ...
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
235 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, ...
0
votes
0answers
123 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 ...
7
votes
4answers
398 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
281 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
2answers
403 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 $7$."
$-...
-2
votes
1answer
125 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 ...
13
votes
5answers
649 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
144 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
votes
4answers
628 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
votes
2answers
473 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. ...
