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.
Itâs about a 30min read so thank you in advance if you really take the time to read it, but I think itâs worth it if you joined such discussions in the past, but Iâm probably biased because I wrote it :)
It isnât, because the âcurrently taught rulesâ 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 isnât already taught, and neither is weak juxtaposition
Thatâs 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 âstrong juxtapositionâ, but note that they are 2 different rules, so you canât cover them both with a single rule like âstrong juxtapositionâ. Thatâs where the people who say âimplicit multiplicationâ 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 partâs easy - I guess you missed the other links I posted. Order of operations thread index Text book references, proofs, the works.
this issue isnât a mathematical one, but a grammatical one
Maths isnât a language. Itâs 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 doesnât prohibit them from teaching additional material.
Thatâs 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 âstrong juxtapositionâ, but note that they are 2 different rules, so you canât cover them both with a single rule like âstrong juxtapositionâ. Thatâs where the people who say âimplicit multiplicationâ 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 partâs 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 isnât you buried in the thread on the Distributive Law? That single reference doesnât even really touch the topic. Your only evidence in the entire thread relevant to the discussion is self-sourced. Citation still needed.
Maths isnât a language. Itâs 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, grammarâs definitions include âthe principles or rules of an art, science, or techniqueâ, of which I think the syntax of mathematics qualifies, as it is a set of rules and mathematics is a science.
That doesnât prohibit them from teaching additional material
Correct, but it canât be something which would contradict what they do have to teach, which is what âweak juxtapositionâ would do.
a single reference
I see you didnât read the whole thread then. Keep going if you want more. Literally every Year 7-8 Maths textbook says the same thing. Iâve quoted multiple textbooks (and havenât even covered all the ones I own).
mathematics is a science
Actually youâll find that assertion is hotly debated.
Correct, but it canât be something which would contradict what they do have to teach, which is what âweak juxtapositionâ would do.
Citation needed.
I see you didnât read the whole thread then. Keep going if you want more. Literally every Year 7-8 Maths textbook says the same thing. Iâve quoted multiple textbooks (and havenât even covered all the ones I own).
If I have to search your âsourceâ for the actual source youâre trying to reference, itâs a very poor source. This is the thread I searched. Your comments only reference âmath textbooksâ, not anything specific, outside of this link which you reference twice in separate comments but again, itâs not evidence for your side, or against it, or even relevant. It gets real close to almost talking about what we want, but it never gets there.
But fine, you reference âmultiple textbooksâ so after a bit of searching I find the only other reference youâve made. In the very same comment you yourself state âhe says that Stokes PROPOSED that /b+c be interpreted as /(b+c). He says nothing further about it, however itâs certainly not the way we interpret it nowâ, which is kind of what we want. Weâre talking about x/y(b+c) and whether that should be x/(yb+yc) or x/y * 1/(b+c). However, thereâs just one little issue. Your last part of that statement is entirely self-supported, meaning you have an uncited refutation of the side youâre arguing against, which funnily enough you did cite.
Now, maybe that latter textbook citation I found has some supporting evidence for yourself somewhere, but an additional point is that when providing evidence and a source to support your argument you should probably make it easy to find the evidence you speak of. Iâm certainly not going to spend a great amount of effort trying to disprove myself over an anonymous internet argument, and I believe Iâve already done my due diligence.
P.S. if you DID want to indicate âweak juxtapositionâ, then you just put a multiplication symbol, and then yes it would be done as âMâ in BEDMAS, because itâs no longer the coefficient of a bracketed term (to be solved as part of âBâ), but a separate term.
6/2(1+2)=6/(2+4)=6/6=1
6/2x(1+2)=6/2x3=3x3=9
