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Calculus For The People

geogebra.org

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Re: Calculus For The People

#21

Post by [deleted] »

kstenerud wrote: post #14
maxmunzel wrote: post #13

Earlier quoted context omitted.

Actually I think that GeoGebra is by far the most intuitive and for-the-people that a math toolbox can be. When I picked it up in Highschool, I didn’t need to google a thing about it, contrary to the CAS Systems I use nowadays... (Maybe not a fair comparison)

Except that there's no "I don't understand" button where you can tell the author what you don't understand. So it's basically a one-way textbook with no feedback mechanism for the author to discover his assumptions and clarify them.

[deleted]

Re: Calculus For The People

#22

Post by gregpetrics »

kstenerud wrote: post #2

"You might notice that when h is very close to 0, the slope of the line very closely matches the graph of f(x)" Huh? "and therefore, the slope of the line very closely matches the growth rate of the function as well." Growth rate? What's that? "Notice that as h gets close to zero, the secant line almost perfectly matches the growth of f at point A. " Not sure what this means... "For instance, in this situation we can…

Good point. Thanks. I do think that limit is obvious and equal to 4. The point tends to 4.

That said, I also agree the "growth rate" thing is coming in a little too quickly there. It's meant to foreshadow derivatives in the next chapter, but it seems like maybe it's introducing confusion to the reader.

I went ahead and made some revisions to try to ease that connection of the "slope of a secant line" as an estimate of "growth rate" of a function.

That said, no matter what I do, this is one of those "object equivalencies" in calculus that there's no way to really make for someone. At the end of the day "slope of secant line" and "growth rate" are two different objects that in the context of a mathematical model are equivalent, but in a mathematical vacuum, are not. I write about this a little bit at the end of the book here: https://www.geogebra.org/m/x39ys4d7#material/fxpkwpt7

Sadly, the resolution for you isn't really very concrete. To get another person to "learn" an object equivalence is a challenging thing. There's really only two options: 1. tell them. 2. put evidence in front of them and hope they make it themselves. I went for option 1 after sprinkling in a bit of option 2. I've tried to slow it down a bit more, but of course, every learner will be different on when they're ready to make this important connection.

So at some point or another, this speed-bump needs to get hit.

If you have more thoughts let me know!

Re: Calculus For The People

#23

Post by gregpetrics »

kstenerud wrote: post #11
tannrckb wrote: post #10

Earlier quoted context omitted.

If it's a curve, that means that the growth rate of the function is itself changing. And using the approach of finding slopes of lines incrementally closer to the tangent line through a point, you can naturally identify the value that the slopes approach. This is the most basic way to demonstrate taking a limit

But if the growth rate is changing, then how could a line be equivalent to the growth rate? Actually, what does growth rate even mean?

Hiya. I wrote a more detailed response above. Thanks for sharing your struggle.

Re: Calculus For The People

#25

Post by gregpetrics »

kstenerud wrote: post #7

A common failing of these "for the people" guides is that they fail the most basic UX test: User observation. When you build a UI, at some point you have to test it on actual people, observing them as they try to use it. Without fail, you'll discover a whole bunch of assumptions you'd made without even realizing it. It's only natural, since you've been working on this project for months and have intimate understandin…

Good point. I've put in a request with Geogebra for the feature.

In the meantime, I'm thinking of how I might hack it with what I have now by just using URLs attached to text like "Help me! I don't understand!" to out-of-book auxiliary resources to provide another perspective on some of the slipperiest topics (like "growth rate" vis-a-vis derivatives).

I really would like to know where people stumble with these activities... and then fix it. So that feature would be really helpful. Or if someone wants to copy this and change it themselves, go for it! I put this up on Geogebra because it is a fully open platform.

Which brings me to another reason for going with Geogebra: your point.

Geogebra books are a nice balance of free hosting, wide distribution, and a reasonably friendly UX format. That said, it's hardly perfect. But it offers me what I think is my best chance to fail fast, get feedback, and make changes with the approach to teaching calculus that I present in this book. But I want to fully acknowledge your point regarding UX. I absolutely agree. The "Geogebra Book" format has its limitations and introduced new assumptions along the way that make it harder for users. If nothing else, it's A BOOK. There is an inherent "one-way-ness" to it. I don't see that being as much of an issue as you, but I agree some of it needs to be broken down. How else will revisions make it into the book? That's the whole point of it being open.

As a sidenote: I also want to point out that I have tested these activities as best I can in a variety of LMSs and in a variety of classrooms from Ivy League students gunning for top marks to adult learners who "can't do math" and gave up on Calculus 20 years ago, but due to some reason or another now need to know it. This book is sort of the "least common denominator" of all these testings, and is itself a testing.

So... you're right! Thanks. Want to work together to test it more?

I've already changed it just from reading these comments, and I'd be really interested in continued revisions!

Re: Calculus For The People

#28

Post by strikelaserclaw »

master_yoda_1 wrote: post #19

For which people? Who does not go to school?

" It was written for people who think they can't understand calculus." Even many people who went to school or are going to school think they can't understand calculus. I think most math from undergrad is understandable by a lot of people provided they get rid of "math fear" and put in the work.

Re: Calculus For The People

#29

Post by oneepic »

A lot of people are just linking out to their favorite calc intro instead of commenting on this one. I like it so far, but I already did 2 years of calculus a few years ago, so I'm not learning much.

I do appreciate the growing trend of presenting material in a more down-to-earth way, maybe with less-formal language and showing the reader it's not as scary as they might've thought previously. Kudos to the author, this is cool.

Re: Calculus For The People

#30

Post by aj7 »

“Most people think calculus is absolutely impossible no matter how hard they think.“ This is how people who KNOW calculus think. In fact, it is INDEED impossible for people weak in algebra and trigonometry, which is virtually the ENTIRE set of people who wash out of calculus.
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