# Questions tagged [notation]

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

91 questions
Filter by
Sorted by
Tagged with
89 views

### Activities that encourage students to create or evaluate mathematical notations

I'm looking for references about activities that encourage elementary school students to create or evaluate mathematical notations. do you know any?
4k views

### What implication arrows, if any, should I require in teaching?

Q: Solve $x+5=0$. A: $x+5=0\implies x=-5$. This answer would be given full marks. Isn’t it better to tell students to use $\equiv$ or $\iff$? Because that is what lets them say $-5$ is a solution to ...
841 views

### Simple examples of how a good notation or diagram can help to solve math problems

I am looking for simple examples of situations where a good notation/diagram was fundamental for solving an elementary problem in mathematics (I am looking for examples accessible to a basic school ...
4k views

### Parentheses around negative numbers

We teach students that a notation like $$17 - -59$$ is not acceptable or at least not good. Instead we want them to write $$17-(-59)$$ The main reason seems to be that it's more readable if you ...
6k views

### 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 ...
1k views

### 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 ...
306 views

### Do Greek students use Greek letters to denote angles?

In western schools is a tradition to use Greek letters to denote angles. I wonder what about Greek schools do they also use Greek letters to denote angles or do they prefer other kind of alphabet to ...
1k views

### How to teach using brackets in sums?

How one should teach using brackets in summation? For example, why is it correct to write $\sum_i a_ib_i$ but $\sum_i a_i+b_i$ should be written as $\sum_i (a_i+b_i)$ But $\sum_i\frac{a_i+b_i}{2}$ is, ...
196 views

### How to introduce the use of Greek letters in high school?

I am looking for any hints or experience reports or materials/potential difficulties about how to introduce the use of Greek letters in high school Math/Physics.
272 views

### Should one include the unit in the variable? E.g. should one write $x^\circ = 30^\circ$ or $x = 30^\circ$?

I sometimes come across equations like $x^\circ = 180^\circ - \frac{360^\circ}{n}$ where I would write $x = 180^\circ - \frac{360^\circ}{n}$, or like $3 \text{ cm} + x \text{ cm} = 5 \text{ cm}$ where ...
191 views

### Which are the most used Greek letters in math textbooks?

I am looking for a list of the most frequent Greek letters used in high school and college textbooks or some other corpora. I've realized my students don't know Greek letters and I would like to teach ...
459 views

### How to teach brackets?

I was taught in a school that one has to use different brackets in expressions like $\{[(3+4)\cdot 4]^4\}^{1/2}$ to denote the order which subexpression is evaluated first. But can this be recommended ...
7k views

### 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 ...
3k views

### Grating mathematical phrases---How to correct?

As mathematics educators, we all have come across students using mathematical notation incorrectly (looking at you, $\frac{d}{dx}$ vs $\frac{dy}{dx}$ or $\frac{\infty^2}{\infty}$). My question focuses ...
103 views

### What should I do when I, as a math tutor, use incorrect verbal notation?

I do freelance tutoring; the math-related ones are mostly 1-2 hour one-on-one sessions for high school and college students taking calculus classes. Often I find myself scrambling for words - I don't ...
1k views

### Lowercase vs. uppercase letters for matrix entries

For a matrix $A$ in, say for instance, $\mathbb{R}^{m \times n}$, there are at least two different conventions to denote its entry at position $(j,k)$: Denote the entry as $a_{jk}$. Denote the entry ...
175 views

### References for mathematical notation for foreign students in the U.S

I teach quite a few foreign students at a U.S. university. Frequently students are placed in our most remedial math class due to not having placement scores and failing to test out of the course. I ...
2k views

### Why do we use functional composition in the order we do?

Function composition means, roughly, taking the output of a function and applying it to the input of another function. If we define an object C to represent this operation, we could say $C(f,g) = f∘g$ ...
1 vote
240 views

335 views

1k views

### 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 ...
334 views

### Is there a conventional function notation that takes a polynomial and order and yields the coefficient corresponding to the order?

I am writing a book and for the sake of simplicity I want to do something as follows. Coef((-3x^2 +5x -1)(x^2 +1), 2) = -3 -1 = -4 where the first argument ...
670 views

### 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 ...
334 views

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 ...
2k views

406 views

### 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 ...
399 views

### 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 ...
271 views

### 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), ...
2k views

### Should students be asked to use more than one notation for the derivative in an introductory calculus class?

There are many, many ways of writing the derivative of a function $y=f(x)$: $$\frac{d}{dx}y, \frac{dy}{dx},\frac{d}{dx}f(x), \frac{df}{dx}, \dot y, D_x f,f',y',f'(x),f_x$$ and so on. Students often ...