speaking about math

Question

How should one vocalise difficult terms, which have no short names, in a talk? Have you other hints for talking about maths to other people? Do I need all to mention, what I write down on the blackboard?

For example how should I say $\left(D + \frac{b}{2m} - \sqrt{\frac{b^2}{4 m^2} - \omega_0^2} \right) \left(D + \frac{b}{2m} + \sqrt{\frac{b^2}{4 m^2} - \omega_0^2}\right) y = 0 $?

It's probably quite painful to read in the exact way as it is written there. Maybe one should simple say 'We get this equation' and point at it on the blackboard. More generally refers to it by saying 'this...' and 'that...'.

Thanks for your advice

Answer 1

With long equations, it is probably best by far to just write it out and say "this equation". Nevertheless, I think it is worth noting that there is a way to say equations like this out loud, and in principle it should work for any equation. For example, many of us were taught to memorize the quadratic formula in middle school: $$ x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a} $$ "x is equal to the opposite of b, plus or minus the square root of quantity b squared minus four a c, all over two a."

Here's a transcription of the formula you mentioned: $$ \left(D + \frac{b}{2m} - \sqrt{\frac{b^2}{4 m^2} - \omega_0^2} \right) \left(D + \frac{b}{2m} + \sqrt{\frac{b^2}{4 m^2} - \omega_0^2}\right) y = 0 $$ "The quantity capital d plus b over two m minus the square root of the quantity b squared over four m squared minus omega naught squared, end quantity, end quantity, all times the quantity capital d plus b over two m plus the square root of the quantity b squared over four m squared minus omega naught squared, end quantity, end quantity, times y, is equal to zero."

Obviously, there are some order of operations issues and a lot of potential for ambiguity, but using "quantity...end quantity" in theory can remove all such ambiguity. The order can also often be discerned from the context.

As an alternative to "quantity...end quantity", in casual speech with friends I have noticed a common practice of using longer spaces to indicate order. This often comes up in distinguishing $x_n + 1$ and $x_{n+1}$; the first is usually voiced as "x sub n [pause] plus 1" while the second is voiced as "x sub [pause] n-plus-one".

Answer 2

There's no reason you need to say a complicated equation out loud. It's fine to just say "this equation". It took humanity thousands of years to develop a compact notation for describing relationships between numbers - the Babylonians would have to describe it in words, but we don't have to.

Answer 3

I usually LaTeX it. Just say;

\left(D + \frac{b}{2m} - \sqrt{\frac{b^2}{4 m^2} - \omega_0^2} \right) \left(D + \frac{b}{2m} + \sqrt{\frac{b^2}{4 m^2} - \omega_0^2}\right) y = 0

Answer 4

TL;DR Explain properly and don't read out loud.

I must apologize in advance since this is really a subjective opinion from me.

I never really had an ability to just learn equations blindly; rather, I wanted to find the answers on my own. Sure, working through long, tedious equations slows me down, but also gives me complete understanding of everything within the given equations. When I build an equation, I usually do several steps in order to produce the correct result. It's like a tree of throwing and seeing what sticks. When I find the correct way, I spend a little time compiling all the equation chain into ONE equation. Sure, this equation is almost impossible to read- it's like reading obfuscated JavaScript. In programming, it's almost religion to keep code readable. Sadly, that is not the case with mathematics. Some think it's clever to use 1-letter notation as "it's the norm" and bloat all of the stuff into one big pile of symbols. Now have the student decompile this equation. Only few of them will actually do it.

So I'd say., "don't teach what you don't even understand yourself." I have seen many teachers than blindly funnel information down their student throats but don't even know half of what's going on. When a student finally questions an equation as why wasn't it constructed in a different way, the teacher doesn't know because he didn't make this equation.

Show the student how you got to that equation. Show the student the mistakes you've made before reaching this result and why it was wrong. Take it apart and show all the individual parts of the problems this equation solves.

In regards to how to read an equation out load: Don't! Reading it out loud as a machine serves no purpose as human memory is very limited and the student would be better off with it text format so he can copy easily and chew on it.

Answer 5

I currently give one lecture a week in which audio but not video is recorded. For the benefit of students who cannot attend this lecture, I don't have much choice but to read out every symbol as I write it down. About the only shortcuts I can take are to label things if I'm going to use them again later, so I can say, "let's call this equation 7" and then later say "by equation 7...."