31–40 of 102 posts
What do you mean "by hand"? If you mean, you don't have to do things like the product rule, chain rule, etc. then I think this is probably a terrible idea because the "by hand" bits are the foundational concepts behind Calculus.
I may not have understood the question though - can you clarify?
I always thought my calculus 1 & 2 courses focused too much on writing solutions without really understanding concepts. I was pretty lost in calculus 3 and 4.
Yes, it can. The biggest failure in math education is that we spend an inordinate amount of time solving equations without understanding how to apply them to solve real-world problems. Thanks to the calculator we can now spend less time figuring out how to solve x+1=7 and put that time on how to understand when the equation is needed in the real world or how to create an equation that will help solve a real-world pro…
I'm sorry, but if you don't know how to solve x+1=7, you don't actually understand maths.
None of it clicked for me, I stumbled to make any meaning out of any of the hand wavy explanations my poor teachers gave me… until I took my first calculus based physics class and a hundred light bulbs went on as to why any of this stuff needed to exist, but more importantly why.
Yes. I regularly solve (mostly motion control) problems that require integration and differentiation and I absolutely cannot and have never been able to do those things by hand but I understand the concept and with a computer by my side that's plenty. I'm sure there are things that I'm missing out on by having this gap in my knowledge but there's a lot of knowledge out there and I spend most days learning, I may get…
What exactly do you do? Discrete approximations like trapezoidal rule or finite differences? Or do you reach for a symbolic math tool like Maxima?
I always thought my calculus 1 & 2 courses focused too much on writing solutions without really understanding concepts. I was pretty lost in calculus 3 and 4.
curious, what was covered in Calculus 4? Quadruple integrals? More vector valued stuff shading into proper linear algebra? Diff Eq?
Earlier quoted context omitted.
I'm one of those people who find maths really easy. I've also had extensive experience working in mathematics education, from primary to tertiary levels. I've even written policy for our state education department. You are spot on the money. I've seen "progressive" educators who believe that technology, including CAS is the answer to teaching calculus to high school and tertiary students. I think the tech is mostly u…
This is getting offtopic, but back when I was in grad school I TAed some physics labs and the number one thing that annoyed me to no end was students didn’t understand or care about significant digits at all. They had no idea that 2.1cm they measured was in fact (2.1 \pm 0.05)cm, they just put 2.1 in the calculator and wrote down 9.7831m/s^2 the calculator spit out. I would point it out, and next week, same thing. Th…
The question could be changed to a positive. >Can Calculus be taught with differentiating or integrating by hand? And then the answer is yes, as this is how it is done. Now, why would be want to do otherwise? Why would we ever want people to learn less?
Dunno if I agree with this, just sounding it out seeing how it feels. >>Can literacy be taught with hitting students with a stick when they err? >And then the answer is yes, as this is how it is done. (19th century). >Now, why would be want to do otherwise? Why would we ever want people to learn less? Maybe you don't learn less by not being hit? Even if my grandparents all had vastly better handwriting than myself. P…
I preface this by saying I find math very difficult. However, it is the struggle to understand in mathematics that leads me to understand the concepts. It often seems too hard, but I found that if I stuck at it I actually started to understand what was going on.
Not popular advise, I realise, but those who can stick with it seem to find maths almost fun, despite the pain.
Yes, it can. The biggest failure in math education is that we spend an inordinate amount of time solving equations without understanding how to apply them to solve real-world problems. Thanks to the calculator we can now spend less time figuring out how to solve x+1=7 and put that time on how to understand when the equation is needed in the real world or how to create an equation that will help solve a real-world pro…
The vast majority of so called real world problems aren’t things people who use math in their jobs actually do.
Imho, the better question is should calculus be taught without physics? None of it clicked for me, I stumbled to make any meaning out of any of the hand wavy explanations my poor teachers gave me… until I took my first calculus based physics class and a hundred light bulbs went on as to why any of this stuff needed to exist, but more importantly why.