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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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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(...
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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 ...
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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 ...
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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 ...
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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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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 $x$ ...
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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....
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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 ...
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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 ...
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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 ...
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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!
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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, ...
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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 "...
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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 ...
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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 ...
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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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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