Questions tagged [terminology]
How words are used in mathematics or mathematics education
109
questions
4
votes
4
answers
330
views
Educational resources commonly address slant asymptotes. Why not general polynomial asymptotes?
Back in 2018, I wrote a post about asymptotes of rational functions in which I addressed not only horizontal and slant/oblique asymptotes, but also the general case of "polynomial asymptotes.&...
- 6,342
1
vote
1
answer
109
views
Idea of using LLMs to help communicate ideas in math
What do you guys think about the ideas presented in this short text: https://github.com/yougetyourmanwww/AI-for-math/blob/main/AI.md
The text is about how LLMs like chatGPT can be used for when doing ...
- 19
1
vote
2
answers
395
views
How should an educator answer a student who asks "Can this theorem be deduced in other systems of set theory?"
If the educator decides to handle the situation by declaring that the question is beyond the scope of the course, then would it be fair to ensure that the course description and course syllabus ...
- 352
1
vote
4
answers
213
views
Naming the procedure of converting the place values of digits
Let's say I have the numeral 2.263,3 thousands, and convert it to 2.263.300 units.
How do we describe what I have done to the numeral regarding units ?
I know it has to do with the place values of the ...
- 147
-5
votes
1
answer
116
views
Does the "Middle School Mathematics domains" refer to (I) through (V) topics?
Does the "Middle School Mathematics domains" on page 3 of https://www.ets.org/content/dam/ets-org/pdfs/praxis/5164.pdf refer to the the following 5 topics/categories?
(I) Numbers and ...
- 93
1
vote
3
answers
285
views
Is it correct to state that a cone has no faces?
Faces are attributes of polyhedra, so it doesn't make sense to ask how many faces a cone has.
Are there traditional scholars that use faces attached to cones? How do different countries deal with the ...
- 1,931
7
votes
3
answers
2k
views
What's it called when multiple concepts are combined into a single problem?
A lot of students complain about "never being shown that before". What's the idea called when you test multiple concepts or one or two new ones along with some old ones in a word problem, ...
- 303
0
votes
1
answer
140
views
‘Induction on’ vs ‘Induction with respect to’ in math
I heard one mathematician who said “induction on 𝑛” and another who said “induction with respect to 𝑛”. Do these two expressions mean exactly the same thing mathematically?
If so, then are they ...
guest
3
votes
0
answers
123
views
congruency: how widely used?
Today I was made aware of the term "congruency" as a word related to congruence in the same way that equality is related to equation. I have never seen the term "congruency" used ...
- 3,258
2
votes
1
answer
172
views
Importance of etymological approach to terminology
Here I have two issues related to this post.
How can etymological approach to a language be used to improve creativity skills of mathematics in students;
I think, knowing the evolution which has ...
- 955
2
votes
1
answer
193
views
What is the terminology for integers with the same oddness or evenness?
If two integers are either both negative or both positive, we can say they have the same sign.
How about two integers that are either both odd or both even? Is there any term for them?
1
vote
1
answer
567
views
Triples or triplets in Pythagoras theorem
We usually say (3,4,5) , (5,12,13) as Pythagorean triples. What is much better way to refer those sets of numbers, Pythagorean triples or Pythagorean triplets?
According to the normal usage we say ...
- 955
8
votes
5
answers
872
views
What should I call the "important" values of x?
When analyzing the functions
$f(x) = \sqrt{x-5}$
$g(x) = \frac{1}{x-5}$
$h(x) = 2^{x-5}$
we know that it is useful to think about what happens at $x = 5$.
For the function $f$, this logic will ...
- 21.2k
3
votes
2
answers
159
views
Word for an object being extended: Given F, a function that extends F is called an extension and F is called the extension __?
If a field L extends a subfield K then L is called an extension of K and K is called the extension's base field. See extension field for a definition.
What is the analog of "base field" when ...
- 31
3
votes
5
answers
508
views
Why do we explicitly state the equality of two things when we know they're equal
Recently my brother in high school and I were talking about some math when he said
If we know two things are the same i.e. equal why do we need to state
that they're the same? What he was trying to ...
- 447
21
votes
7
answers
2k
views
Is there a canonical name for a polynomial-like expression allowing for negative powers?
When introducing the techniques of differentiation, polynomials come up all the time as great examples to familiarize students with the "power rule" and the linearity of differentiation.
A ...
- 313
4
votes
1
answer
195
views
Why is there variation in the meaning of "Standard form" for a quadratic?
I'm teaching this year out of "Precalculus with limits" by Ron Larson [7th ed], and the following expression appears in the unit introducing polynomial functions:
$f(x)=a{(x-h)}^2+k$
He ...
- 419
5
votes
4
answers
751
views
what could be some replacement language for the term "spoon feeding"
In some cultures, there is an expression of "spoon feeding" type of instruction, where the teacher shows how to do steps to a problem, and then students are assigned minor variants thereof. ...
- 493
2
votes
2
answers
209
views
Is coefficient same as constant?
I was studying about polynomials when I stumbled upon this video
https://www.youtube.com/watch?v=vBfdYuoc3x4&list=PLjS5lmipV2HJEaKfdeVSKdprfFxinzmNw&index=2
The video says that a monomial has ...
- 121
27
votes
11
answers
4k
views
How can I validate the existence of percentages above 100?
I once encountered a math educator whose personal pet peeve was the "give 110%" meme. He drilled into his students that 100% was the literal maximum. Percent came from "per cent" ...
- 389
5
votes
1
answer
518
views
Definition for Mathematical Formula
Imagine that you were writing an elementary book, for example for high school learners, and at the beginning you had a glossary where you wanted to write the definitions for common mathematical words (...
- 173
5
votes
2
answers
963
views
Is "Annular Ring" redundant?
I've come across the term annular ring in parentheses following washer in my calculus textbook: "has the shape of a washer (an annular ring)". The definition of the word "annular" ...
- 153
3
votes
5
answers
2k
views
What term describes the relationship between tenth, hundredth, thousandth and the number ten?
What term describes the relationship between tenth, hundredth, thousandth, et cetera (1/10, 1/100, 1/1000, ...) and the number ten? (Despite what some may say, I don't accept that "decimal" ...
Chris Shiherlis
0
votes
1
answer
250
views
Why do so many children's book confuse discs with circles? [duplicate]
The difference between a disc (disk) and a circle is crystal clear to me:
However, in many children's books, a disc is usually called a circle:
Why do many children's book confuse discs with circles?...
- 4,255
13
votes
5
answers
2k
views
Use of language: "perfect square". is this useful or a hindrance? [closed]
I have recently been noticing the tendency to use the term "perfect square" when "square number" is really what is meant.
Usually I have seen it at elementary level: introductory ...
- 925
4
votes
1
answer
142
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,...
- 329
1
vote
2
answers
5k
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)
...
- 129
-4
votes
1
answer
229
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 ...
- 574
6
votes
2
answers
318
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 ...
- 6,751
5
votes
4
answers
1k
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 ...
- 51
-4
votes
1
answer
179
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 ...
- 135
4
votes
3
answers
466
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 ...
- 135
-2
votes
3
answers
188
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 ...
- 187
24
votes
9
answers
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 ...
- 1,881
17
votes
12
answers
7k
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 ...
- 1,881
3
votes
1
answer
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 ...
- 183
14
votes
5
answers
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 $...
- 1,228
5
votes
2
answers
249
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 ...
- 2,163
9
votes
3
answers
2k
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
2
answers
458
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. ...
- 3,996
9
votes
5
answers
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 ...
- 483
13
votes
7
answers
12k
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 ...
- 141
18
votes
4
answers
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
...
- 362
2
votes
1
answer
765
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 $...
user13544
1
vote
1
answer
236
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\...
- 866
11
votes
2
answers
293
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 $...
- 111
32
votes
6
answers
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 ...
- 9,194
11
votes
3
answers
583
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 that the notation means "$L$ is the limit of $f(x)$ as $x$ approaches $c$". It ...
- 379
3
votes
3
answers
1k
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....
- 155
18
votes
8
answers
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 ...
- 500