Hacker News Reader

Comment by wombatpm | Hacker News Reader

If Twitter and TikTok is any indication, schools do not spend enough time on order of operations

5 - 2(3 - 1) - 5 = ?

This ironically brings us back to the point of the original article: if spending that much time teaching people to do it right didn’t help, spending even more time doing that in the same way is hardly going to.

Also, respectfully, it doesn’t matter. Not having learned maths in English, I don’t know the mnemonic, I don’t care to know it, and I find even the concept of it completely asinine. (For eighteenth-century mathematicians, addition and subtraction bound tighter than multiplication and division, and they could calculate perfectly fine.) You can look up the precedence table if you need to—as long as you need to understood the idea of precedence (and not order of operations, for goodness’ sake). You won’t then be able to calculate fluently, but fluency is a different problem with a tedious and time-consuming solution, and given the time crunch I’d rather talk about some actual Maths as She Is Spoke instead.

It's the more ambiguous ones I see that get people to argue about how PEDMAS is interpreted. Your example is unambiguously -4. But consider:

6 / 2 (1 + 2) = ?

I approach the problem the same as I would 6 / 2(x + y). When the multiplication is missing 2(x + y) is a single term. The implicit multiplication is part of the parenthesis and reduces the problem to 6 / 6. People who argue that you have to strictly use PEDMAS left-to-right will divide 6 / 2 first and get 9.

Neither way is wrong as long as you can explain the process but everyone wants to argue and have there be a single answer.

I’ll stick my chin out, and claim that nobody who knows anything about math would ever write the expression like that. Either use parentheses or a long, horizontal division bar making it obvious what groups with what. As given, it looks like some small-minded school teacher (I’m not saying all teachers are small-minded, just a few of them!) who has taught a set of rules, with little regard for actual practice outside the classroom, and then tests to exactly those rules.

I'm sure you can see how having a single correct answer for a math problem is useful.

When calculating by hand, it’s useful to have multiplication × (not dot, if you value your sanity at all) binding as tight as division / and multiplication-by-juxtaposition binding tighter than that. On the other hand, this only comes handy when your intermediate results are so large that one or two levels of (unambiguous) fractions still aren’t enough, and if at all possible you shouldn’t be communicating results that unwieldy. If you really need to, don’t confuse your readers and use some bloody parens. (You’ll probably need more than one kind.)

I see it as more important to realize that not all questions are well formed enough to have a right solution.

A test question like "6 / 2 (1 + 2) = ?" is not asking for the mathematical meaning of those symbols it is asking for "Guess what I as thinking when I wrote this".

(Unless it is a programming class and you are learning how the compiler reads your code)

If Facebook is any indication, schools have been failing to teach order of operations for decades.

My older relatives are the ones I see repost these inane order-of-operation tests, getting the answer consistently wrong.

Are schools failing to teach it, or do some lessons fail to stick through the decades depending on how much math you’re doing? Schools have no control on what your older relatives have been up to.

Today’s Facebook grumpy posters would be the same kids doing “New Math” in the 1960s: https://en.wikipedia.org/wiki/New_Math - just something to consider

My school taught PEMDAS but failed to teach that multiplication and division are equal in priority, nor did they teach that when there is ambiguity working left to right takes priority.

In math notation, division is indicated using fractions, which removes the ambiguity. The idea of equal priority of multiplication and division is a programming thing.

Or that

   ÷ x

is equivalent to

     1
   * —
     x

The thing schools don’t do a great job of doing is explaining when transition from doing ‘arethmetic’ to doing ‘algebra’. Many of the symbols you use in arithmetic continue to be used in algebraic notation, but what they mean changes subtly. Arithmetic is a procedural activity - performing a series of operations to get to an answer. Algebra is a declarative activity - making truthful statements about the world.

For example in arithmetic

   x + y

means ‘add y to x’. But in algebra it means ‘the sum of x and y’. In arithmetic ‘=‘ means ‘gives the result:’; in algebra it means ‘is equal to’.

The failure of teaching to explain that you’re moving on to use those symbols to do something fundamentally different is, I think, one of the things that leaves some kids behind and dooms them to always annoy their relatives in Facebook comment threads about operator precedence.

Reply on news.ycombinator.com