Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

6
votes
4answers
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 ...
-3
votes
1answer
85 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 ...
8
votes
1answer
136 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 ...
6
votes
3answers
480 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! ...
4
votes
4answers
225 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, ...
2
votes
1answer
60 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 "...
19
votes
2answers
185 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 ...
4
votes
3answers
122 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 ...
4
votes
1answer
82 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 ...
10
votes
4answers
479 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 ...
22
votes
16answers
1k 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-...
19
votes
2answers
726 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 ...
12
votes
2answers
161 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 ...
15
votes
2answers
377 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 ...
4
votes
1answer
308 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 ...
15
votes
3answers
244 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 ...
12
votes
3answers
274 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 ...
12
votes
1answer
141 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 ...
33
votes
7answers
4k 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 ...
10
votes
2answers
229 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 ...
26
votes
1answer
983 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 ...