So I encountered a video where they make the proposition that the only reason calculus is hard is that it's different from what we're used to. They then go on to show a lecture where they teach a 5th-grade class the fundamental concepts behind calculus, meanwhile brushing over certain concepts that the children may not have seen up to that point, such as graphs and variables. I actually agree with his point that we probably should be teaching kids more advanced mathematical concepts early, but that's mostly because I was good at math and constantly felt restricted by my classmate's speed growing up. But, I think his video kinda fails to make that point since the kids seem to be pretty out of it the whole time, and mostly seem to be making superficial comments of understanding when he asks them if they understand. I'm not sure this guy is even an elementary teacher. Anyways, take a look at the video if you want to learn calculus really quickly based on the foundation you may have had in the 5th grade. Do you think you could have handled this class in fifth grade?
I would but i still stuck with my nuclear reactor construction lecture. Damn youtube recommendation...
Ah, MIT open courseware... Why am I watching these when I have actual lectures to watch that I paid for and will be graded on?
I never found calculus to be any more difficult than algebra or geometry... Not trying boast but I never found math or science the slightest bit difficult and I'm unable to sympathize with people who struggle with it
mathematic? on 5th grade this cat prefer learnt astronomy~ what is meteor, comet, star, galaxy, blackhole, neutron star, weird stuff ect~ that how you lure children to learn~
The only difficulty I found with it was that my school told me to self study it and just do the tests. I was lazy and did the tests without studying, so I only did alright. Went back later to study it fully before going into uni. Not sure if I could do calculus in elementary though, before doing any algebra.
My 4th grade teacher taught my class basic algebra like x+3 =7 solve for x. I do not recall anyone in class really struggling with it so it stands to reason that if you learn basic algebra in 4th grade, you can learn basic derivatives, like x^2 +2x+1 => 2x +2,in 5th grade. You may not get the kids to understand what it means to take the derivative, but hell, in high school calculus most kids don't understand what it really means either.
I feel like school should probably stop acting like a nursery and maybe allow for kids who are good at math to move through concepts more quickly, but I'm not a teacher, and I was in a small k-12 school so I have no idea what other people experience with school. I do have a mental ideal as to what school should have been for me growing up, but that's probably just me wishing I learned more before university since I'm finding most of the stuff here explained better and simpler then anything growing up.
everyone perceives the world differently when it comes to math I was terrible at it. mostly it was my teachers' fault she had a multiplication chart and without explaining anything to the first graders every morning she made us count the numbers on it little did I know that we were multiplying. it was smart and dumb because she explained nothing and later she would hand out sheets of adding and substracting. In second grade was the start of multiplication, but I was severely distracted to the point that I have no recollection of what in God's name happened in that class. when I mean severely distracted I mean I brought toys to class Power rangers to be exact and when I didn't have toys I would have finger battles and the pencils would be swords or spears. you might as well say I was on 12 liters of vodka drunk cause I don't recall anything that year. 3rd grade my teacher would play multiplications game with index cards every time it was my turn I would get it wrong and end up back of the line and she wouldn't even tell me the answer she would just send me back to the end of the line. I remember she had a daughter who also wanted to be a teacher and she felt bad for me and would always come to sit next to me and try and teach me and even try and fix my godforsaken handwriting. She finally cleared the cloudy sky of multiplication for me she SHINED A LIGHT AND EXPLAINED!!!! This is how she explained it to me; she said 3x3 is just adding 3+3+3 and you do this in a similar way for all numbers and it doesn't matter the order you just need to add that number until you get the answer. 7x4 4x7 will give you the same answer. it was simple, but no one had explained it to me this way nor did I know what multiplication meant and it didn't help that English wasn't my first language nor could I ask for help from my parent they didn't speak English. I was a little kid I was like IMA MARRY THIS GIRL!!!
Calc 3 is killing me rn, but that's because my professor literally teaches his lectures like it's theoretical mathematics instead of trying to teach students who have just come out of calc 2. Math is pretty easy if you take the time I would say. Maybe I could have been learning linear algebra by the time I was in middle school of I had the dedication.
Unfortunately, it wasn't until 12th grade that I finally "got" Algebra while taking, ironically, Calc. Until then, I was failing tests left and right, with the A's only coming from Geometry, the visual component of Math / Calc. Of course, I proceeded to get straight A's on Calc after that. But simple Algebra had been rough until then.
I feel like the methods some teachers use to break algebra into smaller chunks only makes it harder to learn since students never really get the big picture of things, and it all seems pointless.
Sometimes teachers really have to take what they can get. It's pointless to get into the nuances of the "big picture" when the students don't even have a starting point. Like, not knowing what's the difference between a star and a satellite. Then throwing them at the galaxy or universe.
Not really a good comparison, since they are totally different field. I learned cosmology without discussing stars and satellites at all.
My issue was that my high school hadn't bought updated Calculus books for many, many years. So, the books were absolutely awful at explaining the concepts. It was funny because it was the second time I had that particular teacher and I didn't remember her being so bad at teaching. But then I remembered I never paid attention to her last time, since I taught myself using the book. (Looking back, almost half the class would go to me to explain the content. That should have been a red flag... )
I think it somewhat helps because you end up knowing the basics. Factoring, exponents, systems of equations.... But then you get asked to put everything together. And everything just blends together and you don't know where to start. So somewhat helpful, and somewhat not.
And I learned calculus without learning limits. Shall we go smaller into the elements and numbering system?
Never had problems with math, only the physical application of it. Even then, it was just the application, the calculation and the solving was always easy for me. I think two factors allowed me to be "good" at it, one is that I actually enjoyed writing numbers and seeing them all come together in one solution and/or equation, second was that my parents were math geeks. My dad being an engineer and my mom being a math teacher, so they really encouraged me to do what I like, teaching me more advanced lessons as compared to my peers. The education system focuses more on dragging the entire student body down for the sake of those struggling, it's efficient for large populations, but the smart students that are clearly far more advanced are being held down. It's a pity, to be honest, a lot of wasted potential. Also, it can be really hard to explain even simple negatives or positives to some students, since it can sometimes be hard for them to "envision" them in their minds, like, "how do negatives work?" Explaining that with the typical dirt and hole trick is easy, but what about groups? They're concepts with no... physical examples, I guess? Abstract math and all that. But honestly, I think all that can be somewhat solved if kids are taught about it at an earlier age. The sudden change from simple numbers to letters and signs can be hard to adjust with for a lot of kids. There are A LOT of highschool students that can't seem to drill into their heads the rules in subtracting, adding, multiplying, or dividing signs, also substitution. They lack basic foundation, and because of that they keep on getting things wrong, which results in them losing interest in math maybe even hating it.