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Questions tagged [language-use]

Use of language in communicating mathematics. Includes all kinds of languages: spoken, written, symbolic etc. There is a separate tag for terminology, which is a narrow subfield of language use.

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What is this symbol called?

I know how to pronounce the first symbol as "theta", but the other symbol that looks like a circle with a vertical slash, I don't know what to call it. I would appreciate any help. Thank you
Teacher's user avatar
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6 votes
3 answers
329 views

Is there any research on the impact of dismissive language (e.g., 'it's just...') in mathematics education? [closed]

I am curious about the effects of certain phrasings in educational contexts, particularly in mathematics. In fields like physiotherapy, using phrases like "it's just lifting your leg" can ...
Humberto José Bortolossi's user avatar
5 votes
4 answers
272 views

Are some natural languages better for expressing mathematical concepts than others?

I don't know if this is the best stack exchange for this question, but I couldn't think of a better one. Please migrate it to an appropriate stack exchange, if this one is not appropriate. Anyway, my ...
user107952's user avatar
15 votes
5 answers
14k views

Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?

I transcribed this excerpt starting at the 22-minute mark, of Okinawa Institute of Science and Technology’s May 19 2020 podcast with Professor Tadashi Tokieda: For example, this is a bit too ...
user95017's user avatar
  • 429
1 vote
2 answers
539 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 ...
ELM's user avatar
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7 votes
6 answers
1k views

Is 'For all $x$' an abuse of language in math?

I chose to ask this question on MESE because I think it's not about mathematics per se but more about how it should be communicated. Quantified statements in mathematics are often written for ...
Harshit Rajput's user avatar
4 votes
1 answer
738 views

How does learning math differ from learning second foreign languages (L2)?

Peer-reviewed publications analogize learning math to learning a L2. But what are the DisAnalogies and CounterArguments? How can you distinguish learning math from learning L2? Luciana Oliveira, ...
user131533's user avatar
-2 votes
1 answer
208 views

Why do we use polysemy?

From Polysemy - Wikipedia: Polysemy (/pəˈlɪsɪmi/ or /ˈpɒlɪˌsiːmi/; from Ancient Greek πολύ- (polý-) 'many', and σῆμα (sêma) 'sign') is the capacity for a sign (e.g. a symbol, a morpheme, a word, or a ...
Humberto José Bortolossi's user avatar
28 votes
7 answers
6k views

What value is there in requiring students to answer word problems in complete sentences?

This is related to my previous question What value is there in requiring students to declare the dimensions of an answer when it is already clear from context? , but with a different focus. A sizeable ...
Robert Columbia's user avatar
-3 votes
2 answers
152 views

Best natural language(s) for conveying, conceptualizing, teaching, understanding, and learning Probabilistic & Statistical concepts & theory?

English can be precise but it is rather 'flowery' and easily gets in its' own way. East-Asian natural languages like Mandarin, Cantonese, Korean, and Japanese are notorious for permitting the ...
NoYouNaiveBaye's user avatar
10 votes
6 answers
939 views

What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?

When I was in late primary and middle school (east coast US, early 1990's), we were assigned a lot of word problems of the following general form: Mary has eight self-sealing stem bolts. She sells ...
Robert Columbia's user avatar
5 votes
0 answers
349 views

Word problems written in past tense, present tense, or future tense

Does anyone have extensive classroom experience regarding the best verb tense to use when writing word problems at an elementary or middle school level? I have been writing some lessons recently and I ...
Ari's user avatar
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6 votes
2 answers
340 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 ...
Tommi's user avatar
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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 ...
Improve's user avatar
  • 1,881
2 votes
3 answers
949 views

How to reduce ambiguity in the following question?

There are $50$ bacteria at 10:00 and each divides simultaneously into 2 every 20 minutes. The process of dividing into two is known as binary fission. Let $n$ be the number of fissions that have ...
Display Name's user avatar
3 votes
2 answers
169 views

Clearest verb phrases for operations

What is the clearest way to indicate various operations along the following lines: $f(x) = 3x$: The function $f$ multiplies its input by 3. $g(x) = x-5$: The function $g$ decreases its input by 5. $h(...
Nick C's user avatar
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8 votes
5 answers
925 views

What's the common word for equations and inequalities?

My instinct is often that there should be some technical word for the common class of equations and inequalities. That is: statements that connect two numerical expressions, with a relational operator ...
Daniel R. Collins's user avatar
4 votes
4 answers
595 views

How to word this exercise about converting "English" into interval notation?

I am writing an exercise for a precalculus homework assignment that deals with the topic of interval notation. The point of the exercise is to convert open, closed, and half open intervals described ...
Nicholas Roberts's user avatar
5 votes
0 answers
218 views

Linguistic recursion issues while writing Mathematics textbooks for Basic School

In Linguistics, recursion is the ability to amend one sentence to another, combining them in different ways. Example: "After I saw the movie, I went to a cafeteria and then I ate a pizza." Without ...
Humberto José Bortolossi's user avatar
7 votes
4 answers
444 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 ...
frombilas's user avatar
8 votes
3 answers
4k views

Can we save the word "unique"?

Increasing numbers of students seem to be using the word "unique" incorrectly. A common example: Question. Define the term "one-to-one" for a function $f$. Answer. Every $x$ ...
David's user avatar
  • 197
4 votes
5 answers
293 views

How to prepare for lecturing in a non-fluent foreign language?

I am giving some lectures on a calculus course in Norwegian. My Norwegian (or, rather, Scandinavic) is good enough to do so mostly without resorting to English, but I would, of course, like to improve....
Tommi's user avatar
  • 7,202
6 votes
4 answers
2k views

What is it called when terms disappear when reducing fractions?

If $a = \frac{x}{b}$ and $a = \frac{c}{b}$, and I solve for $x$ I get $x = c$. $b$ has been removed because it appeared in the numerator and the denominator. What is it called in English what ...
AndreKR's user avatar
  • 170
-2 votes
1 answer
130 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 ...
BCLC's user avatar
  • 574
8 votes
1 answer
164 views

Regions in which "$a \times b$" is read aloud as "$a$ onto $b$" rather than "$a$ times $b$"

(This is only peripherally related to math education, but it seems to be slightly more on-topic here than in MSE; if people disagree, I will gladly remove it and post it there.) I have recently ...
mweiss's user avatar
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6 votes
3 answers
561 views

Stating identity is not the same as knowing value

A discussion with a frustrated 10th grade student sent me here. I had provided two linear function expressions, $f(x)=2x+2$ and $g(x)=-\frac{1}{2}x-2$, now find the intersection of the two lines! ...
Morten Engelsmann's user avatar
5 votes
4 answers
284 views

How to become a good teacher in the classroom when first starting to teach?

This semester is my first time to teach Calculus II in a classroom which contains around 25 students. (In fact, this is a discussion class.) I didn't have much experience about teaching. For instance, ...
Shaoyun Yi's user avatar
2 votes
1 answer
89 views

How to use these actions words for subtraction?

Do the following sentences express 5-2? a. 5 fewer 2 is 3 b. 2 fewer than 5 is 3 c. 5 less 2 is 3 d. 5 gave 2 is 3 I also saw online that "shared" can also mean "...
EXL's user avatar
  • 311
20 votes
2 answers
323 views

Tips for Teaching Math in a Language Foreign to the Teacher

I retired after 25 years of teaching and moved to Israel a year ago. My Hebrew is okay, but before moving here, I had no experience talking about math in Hebrew. I have been learning Hebrew math ...
Amy B's user avatar
  • 8,017
4 votes
3 answers
180 views

How to get kids thinking about the relationship between basic math (algebra) and English (or language in general)

I was wondering, how would you explain to young high school students or grade school kids the relationship between math and English? For me, both are systems that follow certain rules. Math is often ...
Ninosław Brzostowiecki's user avatar
5 votes
1 answer
108 views

Can we use "specific" and "particular" interchangeably all the time?

I am just marking a couple of linear algebra papers in which one of the questions is to determine whether $(A+B)^2=A^2+2AB+B^2$ is true for 2-by-2 matrices or not. One of the students has chosen two ...
Amir Asghari's user avatar
  • 4,438
11 votes
4 answers
4k views

Phrasing the Van Hiele levels in student-friendly language

I teach high school geometry and see many of my students fall in to the trap of "it looks like it, so it's true" -- a Van Hiele Level 0 to 1 thought process. For instance, when talking about parallel ...
Opal E's user avatar
  • 4,043
24 votes
17 answers
4k 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-...
Amir Asghari's user avatar
  • 4,438
27 votes
2 answers
1k views

Can students tell the difference between the "definition if" and the "theorem if"?

The word "if" is used in two meanings in mathematics: Definition. A topological space is compact if every open cover has a finite subcover. Theorem. A topological space is compact if it is ...
Joonas Ilmavirta's user avatar
11 votes
2 answers
238 views

Words used in quantifier proofs

I'm creating a list of "gotcha words" that are often used in writing proofs (particularly quantifier proofs), but frequently in more than one possible way, and that beginners frequently misuse or ...
Mike Shulman's user avatar
  • 6,580
16 votes
2 answers
483 views

Logic in symbols or words

Making precise logical statements is an important part of teaching and learning mathematics. There are many ways to write such statements, and let me divide them into two main types1: writing in ...
Joonas Ilmavirta's user avatar
4 votes
1 answer
2k views

Correct term to say that a number divides another number "evenly"?

This is something that has continued to bother me in general, and recently I had multiple occasions where saying something like "2 divides 14 evenly" has confused students, They expected the result to ...
celeriko's user avatar
  • 5,070
17 votes
3 answers
461 views

Language as a barrier to learn math

It is well recognized that learning number names is not an easy task for native English speaking children. For example, the number name for "11" should be learned quite independently from the name of ...
Amir Asghari's user avatar
  • 4,438
14 votes
3 answers
419 views

Resources for reading mathematics out loud in different languages

Are there reference books or online material for reading mathematics out loud in different languages? For example, the expression1) $$ \int x^2dx=\frac13x^3 $$ is understandable to anyone who has ...
Joonas Ilmavirta's user avatar
13 votes
1 answer
194 views

Mathematics dictionary use for English Language Learners

My class is composed of international high school students coming from different countries and backgrounds. Hence different skills and needs. Our lingua franca is English and it is important to note ...
Taladris's user avatar
  • 1,491
35 votes
7 answers
5k views

Uninsulting way to say "this will eventually be easy"

When presenting a proof, there are usually a lot of parts which look like "obvious", "routine" manipulation to me, and between zero and two genuinely insightful steps. I want to point out the ...
David E Speyer's user avatar
10 votes
2 answers
317 views

Distinction between problems (such as equations), and universal truths

How the distinction between problems (find/describe such values of x that… ) and universal truths (identities) is taught to secondary-school students and higher? Especially in English-speaking ...
Incnis Mrsi's user avatar
35 votes
1 answer
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 ...
Joonas Ilmavirta's user avatar