Do mathematicians think about order of operations conciously?

Question

I was thinking about this ---I haven't thought about order of operations for yrs -At what grade level do people typically stop thinking about order of operations conciously and "just do" the math ???
Once you remember do you ever forget it??? Cause this has been worrying me --what if I forgot it all of a sudden how to do it --since im not thinking about it .

Answer 1

Occasionally I do, but only when:

a) I am trying to figure out the best interpretation of a mathematical statement written by someone who obviously does NOT know the order of operations (which unfortunately describes every third question written on Y!A). For instance, if someone writes 1-x/x+1, they almost certainly mean (1-x)/(x+1), not 1 (which is what a strict interpretation would normally yield), but that fact is something you have to think about.

b) I am trying to find the best way to interpret a mathematical statement written in a context where the order of operations remains ambiguous, e.g.sin x². The PEMDAS rules doesn't specify whether trigonometric functions have higher or lower priority than exponentiation -- the convention is usually to allow special functions the highest priority, but someone who meant (sin x)² would usually use the special form sin² x, rather than sin x², and so it probably means sin (x²). Interestingly, trig functions have some of the most irregular usage rules of any mathematical symbol -- sin² x means (sin x)² rather than sin (sin x), but sin⁻¹ x means arcsin x, not 1/sin x. Who the came up with that convention?

c) whenever I am talking about the order of operations

But you're correct that when doing math in practice, order of operations is something that I don't think about consciously. Think of it like the grammar of mathematics -- you notice grammar whenever someone incorrect grammar uses, or sometimes when the rules of usage are ambiguous, or when discussing the English language explicitly, but in the course of ordinary conversation, you don't think about it.

Answer 2

Of course. It most commonly becomes a factor when taking a printed formula in a book where math formatting is used (numbers above the line and below it) and superscript powers are used and it has to be translated into a single line formula suitable for a computer to use. All the parts have to be grouped in parentheses and further grouping be done to enforce the precedence (or order) of operations.

Answer 3

I think it may be somewhat like reading. You first learn the letters and sounds, then make words.

Later, when you're accustomed to reading you don't necesarily consider the mechanics of what was, at one point, such a conscious task.

But occasionally, as when faced with a difficult or unfamiliar word, we draw on our internalized understanding of the rules - the mechanization (if that's a word?) might draw closer to the surface so that it "feels" more like it's a conscious act.

Then... like if you THINK about walking down the stairs as you are taking a HUGE flight like at Rosslyn metro in DC - you may think, "what if i don't take the next step right?"... and for a moment you really think you might forget how to take that next step....(yes, this happened to me)...

but then take it back from the forefront of your thinking and the 'instinct' of how to process these tasks takes over again.

Geesh, I don't know if I answered your question, but I can fully commiserate!
?!

Answer 4

I belive once we have mastered a concept we automatically do it with out thinking.

However, if you haven't used it in a while you might be a little rustly. This is nature but it all comes back once you freshen up.


I see this all the time, especially in math!!!
Math Teacher....

Answer 5

I think sometimes if a problem is complex you think about it, but most of the time, you just DO it. If you really understand what you're doing, you aren't ever going to forget.

Answer 6

i stopped thinking about it when i started high school.
i'm sure you haven't forgotten!
B - brackets
E - exponents
D - division
M - multiplication
A - addition
S - subtraction

oh, and i wanted to add. i think you mean, "do mathematicians think about order of operations UNconsciously?"

Answer 7

Everyone is different. I am sure that there are exceptions. People like me don't trust people. I double check everything. I don't care who did it; it gets checked again.

Answer 8

What can anyone say - after a while of practice, it just becomes a habit.