Simplifying and Refactoring Introductory Calculus (2018)
1–10 of 88 posts
Re: Simplifying and Refactoring Introductory Calculus (2018)
#2[flagged]
Re: Simplifying and Refactoring Introductory Calculus (2018)
#3where I heard of this from : https://youtu.be/4ZB2PNUYR1Y
Re: Simplifying and Refactoring Introductory Calculus (2018)
#4[deleted]
Re: Simplifying and Refactoring Introductory Calculus (2018)
#5Looks like this came out nearly 8 years ago, so… how’d it work out? Given the way job titles work these days I guess we could have some Senior Engineers here who learned calculus from this paper…
Re: Simplifying and Refactoring Introductory Calculus (2018)
#6This guy has an interesting publication history, programming books and what looks like evolutionary biology from a creationist perspective.
Re: Simplifying and Refactoring Introductory Calculus (2018)
#7Got to the place where he says "As you can see, this is identical to the d/dx() operation except that the result is not divided by dx."
What does it mean with his d() operator to "divide by dx"? All of a sudden it seems like he has changed dy/dx from unfortunate notation that sort of looks like a division into something that actually is dividing two meaningful things, dy and dx? And so what the hell are dy and dx?
Re: Simplifying and Refactoring Introductory Calculus (2018)
#8Eh. I think that the standard calculus approach is mostly fine, but just needs tweaking.
The only major change that I'd like to make is the removal of sequences and all the associated theorems from the introductory calculus. Instead, start with limits of functions and the notion of continuity.
It immediately leads to the notion of the derivative. And after that, it's just a lot of building blocks.
Re: Simplifying and Refactoring Introductory Calculus (2018)
#9> Again, by using differentials instead of derivatives, we have transformed a number of processes that students find unintuitive
into a single process where the intuition is supplied by the student’s knowledge of algebra.
Ah yes. Algebra. The subject all students love dearly. If only we could get students to love and appreciate calculus as much they love algebra!
I have a hard time even imagining an article that is more disconnected from the reality of teaching calculus to tiny humans.
Re: Simplifying and Refactoring Introductory Calculus (2018)
#10Got to the place where he says "As you can see, this is identical to the d/dx() operation except that the result is not divided by dx." What does it mean with his d() operator to "divide by dx"? All of a sudden it seems like he has changed dy/dx from unfortunate notation that sort of looks like a division into something that actually is dividing two meaningful things, dy and dx? And so what the hell are dy and dx?
They are differentials. https://en.wikipedia.org/wiki/Differential_(mathematics) has some info but is not great as a beginning introduction. dx is an infinitesimal bit of x, and dy is an infinitesimal bit of y. dx here is the same dx as in an integral, which you can think of as the width of one of the infinite infinitesimally thin rectangles whose areas are being added up to find the area under the curve: https://en.wikipedia.org/wiki/Riemann_integral