I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
It’s about a 30min read so thank you in advance if you really take the time to read it, but I think it’s worth it if you joined such discussions in the past, but I’m probably biased because I wrote it :)
A fair criticism. Though I think the hating on PEDMAS (or BODMAS as I was taught) is pretty harsh, as it very much does represent parts of the standard of reading mathematical notation when taught correctly. At least I personally was taught its true form was a vertical format:
I’d also say it’s problematic to rely on calculators to implement or demonstrate standards, they do have their own issues.
But overall, hey, it’s cool. The world needs more passionate criticisms of ambiguous communication turning into a massive interpration A vs interpretation B argument rather than admitting “maybe it’s just ambiguous”.
The problem with BODMAS is that everybody is taught to remember “BODMAS” instead of “BO-DM-AS” or “BO(DM)(AS)”. If you can’t remember the order of operations by heart you won’t remember that “DM” and “AS” are the same priority, that’s why I suggested dropping “division” and “subtraction” entirely from the mnemonic.
It’s true that calculators also don’t dictate a standard but they implement what conventions are typically used in practice. If a convention would be so dominating (let’s say 95% vs 5%) all calculator manufacturers would just follow the 95% convention, except maybe for some very special-purpose calculators.
In fairness, I did quite like the suggestion to just remove division and subtraction! One that should be taken to heart :)
Calculators do not implement “what conventions are typically used in practice.” Entering symbols one by one into a calculator is a fundamentally different process from writing them in a sentence. A basic traditional calculator will evaluate each step as you enter it, so e.g. writing 1 + 2 * 3 will print 1, then 3, then 6. It only gets one digit at a time, so it has no choice. But also, this lends itself to iterative calculation, which is inherently ordered. People using calculators get used to this order of operations specifically while using calculators, and now even some of the fancy ones that evaluate expressions use it. Others switched to the conventional order of operations.
Citation needed.
No but seriously, why do you think it necessarily needs to be different? There are calculators that use actual fraction notation and all that
It’s not that it needs to be different, it’s that it is. The fact that there are calculators with fractional notation is completely irrelevant.