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./
And sometimes you have more than one variable. Now if you have n variables and n polynomials containing each of those variables and not coplanar with each other, you can solve for each of those variables by adding or subtracting multiples of those equations from each other and/or rearranging and substituting variables for their equivalent equations.
Now we’ll use this principle to write a ray tracer where we combine the equation for a line (that represents a ray traveling through a focal point and a pixel on a grid in front of that focal point) and the equation for a plane or other 3D primitive to find if they intersect and at what point if they do.
Next lecture we’ll have a guest speaker, the ghost of Joseph Fourier in to tell you why jpegs get more jpegy each time you jpeg them.
Any questions? Oh, actually we’ve run out of time and another class needs the room.
I mean that actually sounds like great fun to me, reminds me of when I taught myself matrix algebra to be able to mod bullet penetration and ricochets into GMod yeeeeears ago!
Though I think a good bit of what you are describing is beyond the entry level Algebra text book pictured, lol, Fourier is certainly in the realm of Statistics.
But yes, now its time to either fill in multiple choice dot scantron sheets, or fill out your answers to the final in buggy garbage software that often marks a correct answer is incorrect!
Yeah, I enjoyed this also and have written ray tracers for fun and for grades. And you’re right, this isn’t intro to algebra level stuff, I was just trying to capture the way learning can sometimes be simple and straightforward and then you suddenly hit a wall of unexpected complexity you don’t feel ready for.
And you succeeded at that! Was a good, fun comment to read =)
But first, we need to talk about parallel lines
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
So I was taught PEDMAS as a kid instead and it took me an embarrassingly long time to realize what the B stood for…
Barenthesis
Exactly!
Lol.
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).
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?
Yes
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 mean… I can’t understand math? That was what I originally said?
Perhaps you have a writing disability too, or I have a reading disability, but your original comment seems to say that you are completely able to understand math despite having a learning disability.
Go ahead and check. I re-read it several times just to make sure.
Ah, ok. Yes, I meant unable. My mistake. I am just incapable of understanding math even at very basic levels, as I was reminded of again this year after putting my 13-year-old daughter in online school. I barely made it through the math classes I took in high school. College required a single math course and I took the “this is so easy anyone can pass it” one and barely passed it.
Alright then, glad we could clear that up.
I just wanted to clarify because I probably have a learning disability too but I never had any issues with math. It’s always been more about dealing with people.
I’ve taught a class of kids that has various disabilities. Having a disability doesn’t make you stupid.
“Maybe you should have read that book and not the two thousand year old fairytale anthology then.”
Shit I got this. It’s a book you can buy on Amazon. You’re welcome and good luck!
Daddy x and mommy y get together and eventually you get baby z. At least if you’re a god fearing algebrain you do.
If you were a right wing christian republican you wouldn’t tolerate that daddy is X and mommy is Y. That’s against basic biology.
tl;dr: what if numbers were letters and letters were numbers?
then we’ll speak in vocals and consonants.
wait, we already do.
They are in some languages. Like Hebrew. Checkmate, atheists.
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.
Respectfully but strongly disagree. At its very core, math is based on logic which would be valid even without the existence of us or the universe. Things like “if
ais false, andbis false, then the conditionsa and banda or bmust both also be false; but ifais true andbis false, then the condition ofa and bis still false buta or bis true.” Statements like that are what the simplest axioms are derived from, and everything else in math in turn. For example, from the previous statements one can derive that “ifais false andbis false, then bothb and canda and cmust also be false regardless of the value ofc; but ifb or cis true and we know thatbis false, thencmust be true.” Doesn’t take a god to figure that out, it just is. Math tells you nothing about any sort of higher power or creator, nor does it prove the absence of a higher power or creator.Also, math is fundamentally incomplete and never will be complete.
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.
There’s no experimentation involved in the rules of Maths - they are a natural consequence of the way we have defined things to begin with. e.g. 2x3 is shorthand for 2+2+2, hence you must do multiplication before addition or you get the wrong answer. Also equations as we know them - with an equals sign, etc. - have only been around for less than 600 years
