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38 votes

Correcting how a student writes symbols

Personally, if I can make up an ordinary math problem where the student's alternate/new/strange symbols lead to an incorrect response, then I think that's grounds for correcting the student. (Of ...
Justin Skycak's user avatar
35 votes
Accepted

Explaining Sigma-Notation

I've experienced positive results by first having students spend some time writing out sums in full (or using ellipsis notation if there are many terms). That way, it gets annoying to spend so much ...
Justin Skycak's user avatar
19 votes
Accepted

Correcting how a student writes symbols

Not sure if this is the case but: is this student a Spanish speaker? What they write looks like ñ, so if that's the case it could just be that they are interpreting 𝜋 as a letter they know, specially ...
Tyrannogina's user avatar
17 votes

Correcting how a student writes symbols

This isn't a moral conundrum, and your students shouldn't be snowflakes who freak out when they're corrected on something like this. They need your guidance in fixing their incorrect habits while they'...
kjfdhg's user avatar
  • 187
16 votes
Accepted

Why is it written $\tan^{-1}$?

It's the functional inverse rather than the multiplicative inverse. Somewhere along the way, notation arrived at function composition being written as $f(f(x))=f^2(x)$, so the functional inverse ...
Adam's user avatar
  • 5,873
15 votes

Correcting how a student writes symbols

I think the real-world operational point is not that there is some sacred correctness to "orthodox" writing/font styles, but that writing in a very unorthodox style will cause one's readers ...
paul garrett's user avatar
  • 14.7k
11 votes
Accepted

Is there a resource for learning to read mathematical notation/equations/formulae?

The video, https://www.youtube.com/watch?v=ooqQZ-_f_bg (U. Adelaide, "Understanding Maths Notation"), goes from elementary math through calculus notations. I don't know a source that ...
user1815's user avatar
  • 5,760
10 votes

Why is it written $\tan^{-1}$?

I will start by noting that I have written an answer to a similar question on Mathematics SE, and would direct you towards that answer for some additional discussion. In my precalculus class, I tend ...
Xander Henderson's user avatar
  • 8,224
9 votes

Correcting how a student writes symbols

These kind of syntactical glitches need to be corrected immediately, firmly, and clearly. As others have stated: it's immensely easier to fix these things earlier, rather than later when bad habits ...
Daniel R. Collins's user avatar
8 votes

Is there a standard convention for interpreting ambiguous absolute value expressions?

I don't know about standards, but I read these things using a left to right, greedy algorithm. More specifically, the bars are like parentheses but you don't automatically know if they are opening or ...
Adam's user avatar
  • 5,873
8 votes

Is there a standard convention for interpreting ambiguous absolute value expressions?

If I want to have nested absolute-value expressions, I would use different sizes $$ \big|x + 2|x + 3|x + 4\big|, $$ with variations possible $$ \bigg|x + 2|x + 3|x + 4\bigg|. $$
Gerald Edgar's user avatar
  • 7,607
7 votes

Is there a preferred way to format a negative exponent?

One of my biggest frustrations in teaching (and in speaking to other instructors, particularly elementary and high school instructors) is a belief that mathematics is prescriptivist and inscrutable. ...
Xander Henderson's user avatar
  • 8,224
6 votes

Mnemonics for memorizing the difference between a closed interval and an open interval

Honestly this all feels a bit over the top to me. I think all that needs to be said is that the open interval $(a,b)$ fits inside the closed interval $[a,b].$ That's what I've always thought was the ...
Justin Skycak's user avatar
6 votes
Accepted

Correct notation of a Sample space

It's true that you typically refer to a random variable by a capital letter (e.g., $X$) and a particular value by a lowercase letter (e.g., $x$). So, $P(X = x)$ would represent the probability that ...
Justin Skycak's user avatar
6 votes

Is there a resource for learning to read mathematical notation/equations/formulae?

Here's a general workflow for identifying the meaning of an unknown mathematical symbol/expression: use an online tool (like webdemo.myscript.com/views/math) to convert a drawing of the symbol/...
Justin Skycak's user avatar
4 votes
Accepted

Is there a preferred way to format a negative exponent?

Both are proper. If the entire answer is $x^{-1}$ or $1/x$ then I would mark both correct and would not fuss about it. I think this sort of fuss is one of many reasons a lot of kids don't like math. ...
Peter Flom's user avatar
4 votes

Is there a standard convention for interpreting ambiguous absolute value expressions?

As I was looking at your expression, something just seemed typographically off, and then I realized that it was the missing padding around the bars that you see when mathematics is well-typeset. This ...
Kyle Miller's user avatar
3 votes

Is there a resource for learning to read mathematical notation/equations/formulae?

If you are a teaching assistant, you should ask your professor to give a short instruction of the notation he uses, this would be much better for you and the students. He could do it in a lecture or ...
trula's user avatar
  • 449
3 votes

Explaining Sigma-Notation

For a textbook reference, you'll find that big-sigma summation notation is covered in most textbooks for college algebra and precalculus, complete with scaffolded exercises on the topic. On the one ...
Daniel R. Collins's user avatar
3 votes

Is there a preferred way to format a negative exponent?

I would say that both are ok, but you might be careful when dealing with inverse functions, like $\sin^{(-1)}(x)$: does it mean $\frac{1}{\sin(x)}$ or does it mean $\arcsin(x)$?
Dominique's user avatar
  • 2,165
3 votes

Why is it written $\tan^{-1}$?

Once we understand the reason $\tan^{-1}$ can mean the inverse tangent and that most people prefer to write this function as $\arctan$, your neighbor's daughter's question brings up an issue that ...
KCd's user avatar
  • 3,536
3 votes

Order of operations pemdas

I don't have historical proof but the following explanation feels so intuitive to me that I'd be shocked if there were a different reason. When you use multiplication and addition for simple real-life ...
Justin Skycak's user avatar
2 votes

Correct notation of a Sample space

There is no correct here. While it is common to use capital letters for random variables and the corresponding lowercase letters for the values they assume, this convention is not a strong one and ...
Dan Fox's user avatar
  • 5,869
2 votes

The word "numeral", is it being taught and does the word exist for it in your language?

I was taught "numeral" in the New Math era, and if you had asked me in my youth what it meant, I would have probably replied, "What? You mean like zero through nine?" In my mind, I ...
user1815's user avatar
  • 5,760
2 votes

Is there a resource for learning to read mathematical notation/equations/formulae?

Questions about [reading-aloud] [mathematics] expressions are on-topic on the English Language Learners stack exchange. For example, this question asks how to read an equation including a summation, ...
Jasper's user avatar
  • 3,178
1 vote

Is there a resource for learning to read mathematical notation/equations/formulae?

Quarter of a loaf answer, but one of the things I like about some texts is that they will have a list of symbols, to include even Greek alphabet. And will have a glossary. It seems most appropriate ...
Guest troll's user avatar

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