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 :)
Except it breaks the rules which already are taught.
It isn’t, because the ‘currently taught rules’ are on a case-by-case basis and each teacher defines this area themselves. Strong juxtaposition isn’t already taught, and neither is weak juxtaposition. That’s the whole point of the argument.
But they’re not rules - it’s a mnemonic to help you remember the actual order of operations rules.
See this part of my comment: “To note, yes, PEMDAS is a teaching tool and yes there are obviously other ways of thinking of math. But do those matter? The mathematical system we currently use will work for any usecase it does currently regardless of the juxtaposition we pick, brackets/parentheses (as well as better ordering of operations when writing them down) can pick up any slack. Weak juxtaposition provides better benefits because it has less rules (and is thusly simpler).”
Juxtaposition - in either case - isn’t a rule to begin with (the 2 appropriate rules here are The Distributive Law and Terms), yet it refuses to die because of incorrect posts like this one (which fails to quote any Maths textbooks at all, which is because it’s not in any textbooks, which is because it’s wrong).
You’re claiming the post is wrong and saying it doesn’t have any textbook citation (which is erroneous in and of itself because textbooks are not the only valid source) but you yourself don’t put down a citation for your own claim so… citation needed.
In addition, this issue isn’t a mathematical one, but a grammatical one. It’s about how we write math, not how math is (and thus the rules you’re referring to such as the Distributive Law don’t apply, as they are mathematical rules and remain constant regardless of how we write math).
It isn’t, because the ‘currently taught rules’ are on a case-by-case basis and each teacher defines this area themselves
Nope. Teachers can decide how they teach. They cannot decide what they teach. The have to teach whatever is in the curriculum for their region.
Strong juxtaposition isn’t already taught, and neither is weak juxtaposition
That’s because neither of those is a rule of Maths. The Distributive Law and Terms are, and they are already taught (they are both forms of what you call “strong juxtaposition”, but note that they are 2 different rules, so you can’t cover them both with a single rule like “strong juxtaposition”. That’s where the people who say “implicit multiplication” are going astray - trying to cover 2 rules with one).
See this part of my comment… Weak juxtaposition provides better benefits because it has less rules (and is thusly simpler)
Yep, saw it, and weak juxtaposition would break the existing rules of Maths, such as The Distributive Law and Terms. (Re)learn the existing rules, that is the point of the argument.
citation needed
Well that part’s easy - I guess you missed the other links I posted. Order of operations thread index Text book references, proofs, the works.
this issue isn’t a mathematical one, but a grammatical one
Maths isn’t a language. It’s a group of notation and rules. It has syntax, not grammar. The equation in question has used all the correct notation, and so when solving it you have to follow all the relevant rules.
Nope. Teachers can decide how they teach. They cannot decide what they teach. The have to teach whatever is in the curriculum for their region.
Yes, teachers have certain things they need to teach. That doesn’t prohibit them from teaching additional material.
That’s because neither of those is a rule of Maths. The Distributive Law and Terms are, and they are already taught (they are both forms of what you call “strong juxtaposition”, but note that they are 2 different rules, so you can’t cover them both with a single rule like “strong juxtaposition”. That’s where the people who say “implicit multiplication” are going astray - trying to cover 2 rules with one).
Yep, saw it, and weak juxtaposition would break the existing rules of Maths, such as The Distributive Law and Terms. (Re)learn the existing rules, that is the point of the argument.
Well that part’s easy - I guess you missed the other links I posted. Order of operations thread index Text book references, proofs, the works.
You argue about sources and then cite yourself as a source with a single reference that isn’t you buried in the thread on the Distributive Law? That single reference doesn’t even really touch the topic. Your only evidence in the entire thread relevant to the discussion is self-sourced. Citation still needed.
Maths isn’t a language. It’s a group of notation and rules. It has syntax, not grammar. The equation in question has used all the correct notation, and so when solving it you have to follow all the relevant rules.
You can argue semantics all you like. I would put forth that since you want sources so much, according to Merriam-Webster, grammar’s definitions include “the principles or rules of an art, science, or technique”, of which I think the syntax of mathematics qualifies, as it is a set of rules and mathematics is a science.
That doesn’t prohibit them from teaching additional material
Correct, but it can’t be something which would contradict what they do have to teach, which is what “weak juxtaposition” would do.
a single reference
I see you didn’t read the whole thread then. Keep going if you want more. Literally every Year 7-8 Maths textbook says the same thing. I’ve quoted multiple textbooks (and haven’t even covered all the ones I own).
mathematics is a science
Actually you’ll find that assertion is hotly debated.
P.S. if you DID want to indicate “weak juxtaposition”, then you just put a multiplication symbol, and then yes it would be done as “M” in BEDMAS, because it’s no longer the coefficient of a bracketed term (to be solved as part of “B”), but a separate term.
6/2(1+2)=6/(2+4)=6/6=1
6/2x(1+2)=6/2x3=3x3=9
