# Questions tagged [notation]

For questions about good use of notation, comparison of specific notation, motivation of notation.

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### Effective Strategies for Helping Students Recognize Nonsensical Expressions? (HS - Undergrad Level)

I'm not entirely how best to pose this question, so that it fits within the guidelines (so edits / suggestions for modification are warmly welcome). I'm interested in exploring effective strategies ...
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### What's a good notation to show elements of relation composition?

Teaching discrete mathematics, we pose (from the textbook) questions on finding compositions of relations, notably, relations on very small finite sets with only 3 or 4 elements (as an introductory ...
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### Why do we write $x$ instead of $1x$?

I am currently student teaching for an Integrated Math 1 class (which is similar to Algebra 1) that consists of 9th graders. I have been teaching my students how to solve linear systems using ...
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### Why do we still teach the determinant formula for cross product? And is it as bad as I think it is?

The cross product is an important vector operation in in any serious multivariable calculus course. In most textbooks that I'm aware of, right after the definition, we always introduce the ...
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In the textbook I am using to teach mathematics to high school students I found the following illustration about composition of functions. I do not agree with this illustration. For me $g$ is the ...
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### Students writing $f(x^2+1)$ when they probably mean $f(x)=x^2+1$

Over the past years teaching freshmen calculus I've repeatedly seen students make the following type of error: Suppose they have to express some quantity $y$ as function of $x$, when the relation ...
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### Undergraduate Vector Calculus Notation Mess

Question 1: What are your arguments in favor of the big array of different notations used in the context of undergraduate vector calculus: line integrals, surface integrals (of scalars and fields), ...
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### 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 ...
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### 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 ...
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### Notation in the definition of matrix multiplication

When matrix multiplication is introduced, it is usually introduced with an additional variable: Given two multiplicable matrices $A$, $B$, one defines the product $C=AB$ to be the matrix given by some ...
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### Are there standard notations for 'number talks' / ‘math talks?'

I’m a homeschool teacher of a nine-year-old, and we sometimes have one-on-one ‘number talks’ (a.k.a. 'math talks') similar to the activity used in primary school classrooms. Part of this process ...
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### Should we stop differentiating between ln and log?

In many U.S. middle schools and high schools, $\ln$ and $\log$ are treated differently, with the intent that $\log$ is equivalent to $\log_{10}$. However, in undergraduate courses and in the academic ...
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### How should one approach the concept of "plus or minus", such as in the numerator of the quadratic formula?

The numerator is structured like: $$(-b)\pm\sqrt{b^2- 4ac}.$$ Is it confusing or acceptable to distinguish between the following two things? An idiom; and What is or seems to be a compositionally ...
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### Teaching asymptotic notations at the beginning of calculus [duplicate]

I'm thinking about teaching calculus by firstly introducing the asymptotic notations (big-Oh, little-oh, and $\sim$), secondly explaining their "arithmetic" (things like how to sum little-oh's and ...
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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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### A different symbol for the indefinite integral/antiderivative?

Examples. An indefinite integral (or antiderivative) of $\cos$ is $\sin$: $$\int \cos = \sin.$$ Edit: There has been much unexpected confusion with the above statement. I define the above statement ...
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### How to help new students accept function notation

I am struggling to help some of my new precalculus students accept function notation -- something new to them this term. I am looking for strategies to help them adopt this new notation. Their main ...
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### Naming arbitrary constants: subscripts, primes, or just more letters?

When choosing names for arbitrary constants either during a lesson or while working with a single student, should one use$\{n_1,n_2,n_3,\dotsc\}$ or $\{n, n', n'', \dotsc\}$ or $\{a,b,c,\dotsc\}$? Is ...
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### What is the notation for polynomial long division in Norway?

I will be teaching a calculus-type course in Norwegian. Our textbook is unfortunately in English (the curse of a small language), but any custom exercises should be and all exams have to be in ...
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### Notation for change of basis matrix

As far as I can tell, it's only a slight exaggeration to say that every text has a different notation for a change of basis matrix from (say) $\mathcal{B}$ to $\mathcal{C}$. That's not even to talk ...
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### Are there any negative consequences in applying operations/functions to a whole equality?

Some of my students solve equations not by applying the same operations on the left and right sides of an equation, but by applying the operation to the whole equality. For example, they may write ...
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### 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 ...
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### Duodecimal by Stealth

It is widely recognised that the Duodecimal number system is superior to the decimal system. However, it is plainly obvious that trying to introduce such a system would be difficult, especially in a ...
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### Multiple students writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ -- why?

I'm currently teaching a couple of courses that have a calculus prerequisite, and within the last week I've had two students make notational mistakes that amount to writing $y\frac{d}{dx}$ rather than ...
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### Can $y^{(n)}$ be used as a way of representing higher order derivatives?

I have never seen this notation, but I think that it follows in a similar vein for function notation. So if $y=f(x)$, then $y''=f''(x)$. Then by that, can we say that $$f^{(n)}(x)=y^{(n)}$$
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### How students write their work, and learning outcomes

While teaching students mathematics, I have noticed that some seem sloppy in the way that they write down their work. For example, a student is given a question: What is the area of the rectangle? <...
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### Who actually uses $\mathbf i$, $\mathbf j$, $\mathbf k$ for the standard unit vectors?

I am wondering which research communities use the notation $\mathbf i$, $\mathbf j$, $\mathbf k$ for the three-dimensional unit vectors. The calculus textbook I have to use (Stewart) uses that ...
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### Framework for Compound Inequalities

I have been presenting compound inequalities like $3 < x < 7$ as being a shorter way of saying $3 < x$ and $x < 7$. From this point of view, though, I end up having to admit that ...
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### Is "hat notation" for unit vectors commonly used in mathematics?

As an undergraduate, I clearly remember learning and using "hat notation" to describe unit vectors. That is, if $\vec{v}$ is any vector (in 2 or 3 dimensions) then $\hat{v}$ denotes the unit vector ...
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### Why is multiplication taught using cross notation at first?

Alert: I am not a math educator. It seems to me that multiplication is first taught using the cross notation, for example $3\times 5=15$. First question - is that even correct? Maybe not all schools ...
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### Writing Fractions "Correctly"

I very often see students writing, for example, $1/3x$ when they mean $\frac 13x$. I used to tell them not to write $1/3x$ beause it looks like $\frac{1}{3x}$ until I realized that, according to ...
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### How to denote angle?

I'm teaching mathematics on my free time for young pupils. Once I have seen that they denote angles like $\angle ABC$. But sometimes I have difficulties to understand whether they mean an angle or its ...
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### Design of a math exam using multiple choice or computer

I'm teaching math in first years of university (matrix algebra, differential analysis, etc.) since maybe 5 years, and I usually give written (paper) exams to the students. I'm looking for ideas to ...
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### Misuse of parentheses for multiplication

I'd like to raise the issue of constant misuse of parentheses in the U.S., and I'm wondering if anybody else shares the same feelings, has had the same issues, knows any history behind it, and can ...
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### How to reasonably denote lines, line segments and rays?

I'm teaching geometry at high school for the first time soon and am struggling to find a reasonable notation for lines, line segments and rays defined by two points $A$, $B$ (and a direction). At the ...
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### Notation of line segment and its length

I have sometimes seen a notation where $AB$ could mean either the line segment or its length. Why do the same notation can be mean both? Should one teach pupils to use for example notation $d(A,B)$ or ...
as I can see there are mainly two ways to introduce fractional terms. Two examples to demonstrate the two variants: $\frac{a^2+3}{a}; \frac{3}{2c}$ $T(a) = \frac{a^2+3}{a}; T(c) = \frac{3}{2c}$. In ...