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 :)
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.
Correct, but it can’t be something which would contradict what they do have to teach, which is what “weak juxtaposition” would do.
Citation needed.
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).
If I have to search your ‘source’ for the actual source you’re trying to reference, it’s a very poor source. This is the thread I searched. Your comments only reference ‘math textbooks’, not anything specific, outside of this link which you reference twice in separate comments but again, it’s 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 ‘multiple textbooks’ so after a bit of searching I find the only other reference you’ve made. In the very same comment you yourself state “he says that Stokes PROPOSED that /b+c be interpreted as /(b+c). He says nothing further about it, however it’s certainly not the way we interpret it now”, which is kind of what we want. We’re talking about x/y(b+c) and whether that should be x/(yb+yc) or x/y * 1/(b+c). However, there’s just one little issue. Your last part of that statement is entirely self-supported, meaning you have an uncited refutation of the side you’re 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. I’m certainly not going to spend a great amount of effort trying to disprove myself over an anonymous internet argument, and I believe I’ve already done my due diligence.
Citation needed.
So you think it’s ok to teach contradictory stuff to them in Maths? 🤣 Ok sure, fine, go ahead and find me a Maths textbook which has “weak juxtaposition” in it. I’ll wait.
Your comments only reference ‘math textbooks’, not anything specific
So you’re telling me you can’t see the Maths textbook screenshots/photo’s?
outside of this link which you reference twice in separate comments but again, it’s not evidence for your side, or against it, or even relevant
Lennes was complaining that literally no textbooks he mentioned were following “weak juxtaposition”, and you think that’s not relevant to establishing that no textbooks used “weak juxtaposition” 100 years ago?
We’re talking about x/y(b+c) and whether that should be x/(yb+yc) or x/y * 1/(b+c).
It’s in literally the first textbook screenshot, which if I’m understanding you right you can’t see? (see screenshot of the screenshot above)
you have an uncited refutation of the side you’re arguing against, which funnily enough you did cite.
Ah, no. Lennes was complaining about textbooks who were obeying Terms/The Distributive Law. His own letter shows us that they all (the ones he mentioned) were doing the same thing then that we do now. Plus my first (and later) screenshot(s).
Also it’s in Cajori, but I didn’t find it until later. I don’t remember what page it was, but it’s in Cajori and you have the reference for it there already.
you should probably make it easy to find the evidence you speak of
Well I’m not sure how you didn’t see all the screenshots. They’re hard to miss on my computer!
