Its time for the concept of a ‘variable’!
2 + a = 5
In this example, the variable is indicated by the letter a.
What you want to do is make it so ‘a’ is on one side of the = and a numerical value is on the other side.
One way we can do this is by subtracting 2 from both sides.
Left side: 2 + a - 2 gives us ‘a’
Right side: 5 - 2 gives us 3
Thus we are left with
a = 3
Tada!
/and then somehow, something like half or more of currently living Americans can barely pull off anything more complicated than this./
I think I had that book in high school back in the late 90’s early 2000’s, it goes up to the quadratic equation and maybe logarithms and matrices.
BEDMAS
I like GEMDAS personally. “Group” is best, it includes parenthesis and brackets, as well as things under radicals. I find that PEMDAS/BEMDAS causes problems later in math.
But then you would have to define what a “Group” is as well, adding yet another definition needing to be remembered. Terms are actually defined, and cover the first 2 steps, and then the rest are operators (binary then unary).
In my specific context I’m usually tutoring and not introducing the concepts - they’ve all learned PEMDAS and changing one letter is much easier. I suggest “groups” because they absolutely struggle with manipulating expressions inside radicals. I usually pair it with a short discussion of the purpose of notation.
I appreciate your mention of the importance of teaching the difference between operators and terms. My pedagogical background is in the sciences and I’m much better at doing math than teaching it 😅
I would like if math classes (in my area) did more explicitly teach the difference between terms and operators. I say “you can’t divide out the log” pretty much every day.
P.S. feel free to read through and use my thread on order of operations.
inside radicals
I had to look up what that meant (should’ve done that the first time - sorry) - have never heard that before, must be a local terminology.
So, square roots (or other roots) can be expressed as an exponent - e.g. the square root of 2 is the same as 2 to the power ½ - so that’s covered by “E”, exponents! (or I for Index, or O for to the Order of, depending on your area)
I appreciate your mention of the importance of teaching the difference between operators and terms
Thank you.
My pedagogical background is in the sciences and I’m much better at doing math than teaching it
Oh god, welcome to why I have so many people argue with me, a Maths teacher, about it. There’s a whole bunch of Youtubes and blogs out there by Physics majors. I’m like “OMG, why are you trusting someone with a Physics major over someone with a Maths major - god help me”.
I would like if math classes (in my area) did more explicitly teach the difference between terms and operators
So what area are you in? A country will do. You said PEMDAS so I’m guessing the U.S.? I’ve heard via Youtubes/blogs that indeed there is more confusion with what is taught there, but I ended up Googling for U.S. textbooks, and found the same thing being taught in the textbook, so I’m not sure where this “that’s not what they teach in the U.S.” is coming from (why I was Googling for U.S. textbooks in the first place). Is the standard of teachers there actually worse than elsewhere? Or is it perhaps (possibly more likely) that there’s just more U.S. people posting, therefore more people who’ve forgotten the actual rules, and are just (as I’ve seen many times) they’re just blaming it on what they were taught (which I’ve usually found isn’t true at all).
Shit I got this. It’s a book you can buy on Amazon. You’re welcome and good luck!
tl;dr: what if numbers were letters and letters were numbers?
I’m an atheist, but I also have some kind of learning disability that makes me completely able to understand math, even at that level.
So… it’s time to accept Jesus as my lord and savior?
I don’t think you understand the concept of disability
You mean apart from my having an actual physical disability and having received disability payments because of it?
Well it clearly isn’t a learning disability if you can still understand math
I’ve taught a class of kids that has various disabilities. Having a disability doesn’t make you stupid.
Ironically, the existence of consistent mathematical laws derived from thousands of years of experimentation and observation is probably the most compelling argument for intelligent design, more so than any holy book.
What, how?
Self consistent systems do not imply design, imo. There has to be a certain level of self consistency for any entity to exist?
Intelligent design maybe, but at the very least the possibility of higher existence or beings.
