52 votes

Proof of why BODMAS (or BIDMAS) works?

It's purely a matter of how we choose to define the notation. The main reason for it is that it lets us write polynomial expressions (which are extremely common) without parentheses, e.g., $x^3 + 3x^2 ...
Daniel Hast's user avatar
  • 4,893
46 votes

Should we stop differentiating between ln and log?

Unrelated to US, in Germany the notation through school and university was quite consistent: $\ln$ using base $e$ $\log$ using base $10$ $\log_x$ using base $x$ I may not know enough about the US ...
Apfelsaft's user avatar
  • 629
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
36 votes

Parentheses around negative numbers

It is not a good idea to against a convention, unless you have strong reasons for it. That said, you might not want to punish those going against the convention, either. An obvious reason for having ...
Tommi's user avatar
  • 7,025
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
30 votes

Misuse of parentheses for multiplication

It is actually wrong to say that parenthesis means multiplication. In $(2)(5)$ it is the lack of an operator between the parenthesis that implies multiplication, NOT the parenthesis. The parenthesis ...
smernst's user avatar
  • 401
28 votes
Accepted

Grating mathematical phrases---How to correct?

Personally, I don't think we attend to this sufficiently in lower-level mathematics (where it's actually needed most). Students need that vocabulary to interface with books, future teachers, tutors, ...
Daniel R. Collins's user avatar
27 votes
Accepted

Why do we write $x$ instead of $1x$?

I think the basic answer is that there are all sorts of things that we could write, but don't. We usually leave off things that are redundant, but we can add them back in when convenient. For ...
johnnyb's user avatar
  • 1,247
26 votes
Accepted

Why are $m$ and $b$ used in the slope-intercept equation of a line?

This is also borderline not-an-answer, but it might be a nice broadening of your students' worldview to know that the "$m$" and the "$b$" are not universally accepted. Showing them this map (even ...
Chris Cunningham's user avatar
24 votes
Accepted

Writing Fractions "Correctly"

I think that, depending on the maturity level of the students, you could just talk to them about why writing $\frac{1}{3}x$ rather than $1/3x$ makes it much clearer what you mean. They should ...
Mike Pierce's user avatar
  • 4,845
24 votes

How to help new students accept function notation

Start by talking about functions in general, not only about functions that can be expressed by a simple formula in x and y. Examples: The function that maps every non-empty list to its first element. ...
Uwe's user avatar
  • 591
24 votes

How to help new students accept function notation

You might remind them that $y$ is just a name for a number. When they draw a plot, they draw a bunch of points: maybe $y=3$ here, $y=5$ there, and $y=-2$ over there. But at some point (no pun ...
fvy's user avatar
  • 241
22 votes
Accepted

Misuse of parentheses for multiplication

To answer the ultimate question ("Can anybody explain where this writing tradition comes from?"): It's explicitly taught that way by many U.S. instructors and textbooks. Examples: From the otherwise ...
Daniel R. Collins's user avatar
22 votes

How to help new students accept function notation

You should tell them these two main benefits: (1) Function notation is concise! For example, instead of writing "Find $y$ when $x=5$" one can simply write "Find $f(5)$" This becomes very appreciable ...
Lex_i's user avatar
  • 496
22 votes

Should we stop differentiating between ln and log?

You are wrong about undergraduate courses always treating $\log$ as $\ln$. To my memory, all of my undergrad chemistry and physics (not just general, but majors texts), engineering, calculus, diffyQs, ...
guest's user avatar
  • 237
22 votes
Accepted

Allowing nonstandard mathematical language and/or notation

I think, while teaching, the principal way to judge mathematical language is not whether it's standard, but whether it's effective communication. This difference applies principally to communication ...
Milo Brandt's user avatar
21 votes

Multiple students writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ -- why?

When a student writes incorrect notation, ask them to read it out loud. I would say something like: Something here doesn't look right, but we can fix it. Could you read this work out loud? I think ...
Chris Cunningham's user avatar
21 votes

Should we stop differentiating between ln and log?

I would argue that we should never use $\log$ for $\log_{10}$ anymore, only warn that this was historically often done. Sticking to the ISO convention is probably safest: $$\begin{aligned} \log_{e} ...
leftaroundabout's user avatar
21 votes

Why do we still teach the determinant formula for cross product? And is it as bad as I think it is?

My answer is probably not very useful when teaching in high school. I'll just mention here a few reasons why this definition is in fact a good one, and why it's a good idea to teach this formula at a ...
Michał Miśkiewicz's user avatar
19 votes

Should we stop differentiating between ln and log?

In mathematics, $\log$ means natural logarithm. So, as you become a mathematician, sometime during that process you must learn this. That standards document is for natural sciences, not for ...
Gerald Edgar's user avatar
  • 7,489
19 votes

What is the preferred way to denote the Pythagorean theorem equation?

Common knowledge The formula $a^2+b^2 = c^2$ is common knowledge and the words for hypotenuse and leg (is "cathetus" not used in English?) are basic mathematical vocabulary. Including these ...
Tommi's user avatar
  • 7,025
19 votes

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

The usual physics convention is that variables have units built into them, so you don't need to (indeed, shouldn't) write the units separately. For example, Wikipedia writes In classical mechanics, ...
David E Speyer'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
18 votes

Misuse of parentheses for multiplication

I disagree that it is "terribly harmful". Do not prevent them from writing $(2)(5)$. Instead prevent them from writing things that are actually wrong. Thinking that $\sin x$ is $\sin$ times $x$ ...
Gerald Edgar's user avatar
  • 7,489
17 votes
Accepted

Framework for Compound Inequalities

Just because you've defined a meaning for $a < b < c$ does not mean that any mishmash of other relational operators becomes equally well-defined as notation. Stick with what you've defined for a ...
Daniel R. Collins's user avatar
17 votes

What is the right notation to use in multivariable chain rules?

What's wrong with this?: $$ \frac{df}{dt} = \frac{\partial f}{\partial x} \frac{dx}{dt} + \frac{\partial f}{\partial y} \frac{dy}{dt} + \frac{\partial f}{\partial t} \frac{dt}{dt}$$ with $\frac{dt}{dt}...
Adam's user avatar
  • 5,683
17 votes
Accepted

How to teach using brackets in sums?

I would say that in terms of order of operations, the summation symbol is between multiplication/division and addition/subtraction. So when you write $\sum_i a_i+b_i$, the implication is to do $\sum_i ...
Aeryk's user avatar
  • 8,013
17 votes

Parentheses around negative numbers

Others have talked about legibility, so I want to address the importance of the parentheses in an expression like $$17\color{red}{-}(\color{blue}{-}59)$$ from the perspective of educational psychology....
Justin Hancock'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

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