[freestyle24147]

If someone is having trouble understanding the absolute most basic part of classical mechanics (masses undergoing acceleration) something tells me they're not going to understand Calculus no matter what lens you view it through. It's not even about the equations, it's simply using it as a backstory for the motivation of the mathematics.

> If you can find an application the student is interested in, then by all means, use that approach. For a general purpose textbook, though, it hinders learning for many students who don't care for the particular choice of application the book decided to use.

This seems absurd. Just because some people will find a particular application less interesting, I don't think the answer is to throw out ALL applications and turn it into a generic boring slog through which no one will be able to see when and how it's useful.

[BeetleB]

> something tells me they're not going to understand Calculus no matter what lens you view it through.

From my experience as a tutor, you are quite wrong in coming to that conclusion. Most people conflate mass and weight all the time, and have a fuzzy understanding of acceleration. It's not because they're thick in the head and incapable, but because they don't care. That doesn't mean they don't care about other applications where math can help.

And standard calculus textbooks go beyond what you are describing. All the ones I encountered would have the integral of force with displacement to get work (which confuses people when they hear it's the same as "energy").

> This seems absurd.

The truth often does seem so.

[crazygringo]

> Most people conflate mass and weight all the time, and have a fuzzy understanding of acceleration.

Conflating mass and weight is generally irrelevant in calculus textbooks, since they're generally giving you the mass, and weight doesn't even come up.

And coming in having a fuzzy understanding of acceleration is fine, because calculus is where you learn what acceleration is.

Learning that velocity and acceleration are the first and second derivatives is the most intuitive way to introduce them to anyone.

If you're taking calculus but you don't want to learn what acceleration is, then I don't know what you're even doing. Even if you're doing it for finance or medicine or something, velocity and acceleration are still the most useful and intuitive ways to introduce derivatives.

[BeetleB]

> And coming in having a fuzzy understanding of acceleration is fine, because calculus is where you learn what acceleration is.

Really? Because I learned what acceleration was a few years before I'd been introduced to calculus.

> If you're taking calculus but you don't want to learn what acceleration is, then I don't know what you're even doing.

Your statement highlights very well the point I'm trying to make.

> Even if you're doing it for finance or medicine or something, velocity and acceleration are still the most useful and intuitive ways to introduce derivatives.

I didn't point it out in my earlier comments, but I learned basic calculus in the 10th grade by two very simple (non-physics) concepts:

The derivative gives you the slope of the tangent (and I had already been taught a year prior that the slope of the tangent is the "point" rate of change). We'd already studied the relevancy to physics (or other applications) of getting the slope of the tangent in prior years (in physics courses, which is where one should be introduced to it). So I definitely did not need a math textbook to give me context.

And the integral gives you the area under the curve. I did not even need a physics application, as I'd done years of geometry up to that point to understand the concept of "area". Again, the application to things like energy was appropriately left to a further physics course.

BTW, I never said providing context in a math book is a bad idea - just that it'll help some people and hurt some people by the book's choice of context. If I were doing 1:1 tutoring, I would definitely try to provide context from the real world. The difference is that I can try to identify the relevant context for the particular student.

That alone was sufficient in motivating me to learn more. Of course, you can go from there to computing volumes, etc.

[crazygringo]

You're speaking from the perspective of how you happened to learn things.

>> If you're taking calculus but you don't want to learn what acceleration is, then I don't know what you're even doing.

> Your statement highlights very well the point I'm trying to make.

But you're missing the point I'm making. Which is that sometimes there is a simply a clearest way to explain a subject regardless of what a student is interested in.

Saying you want to learn calculus but you're not interested in acceleration is like saying you want to learn 20th-century European History but you're not interested in WWII.

I've done my share of teaching. I greatly appreciate that you need to make things relevant to students. But at the same time, you just have to teach what the thing is, using the time-tested analogies that actually work to educate students.

If a student doesn't want to learn calculus because they have no interest in what acceleration is, then I don't think they want to learn calculus at all.

[jbaber]

This is spot on. Everybody has lots of favorite subjects. They're not all the same.

[ordu]

I'm now learning German in Duolingo, and I noticed a correlation between how hard it is for me to learn one more pack of a vocabulary and how this vocabulary is relevant for me.

There is nothing that I cannot understand, but when some words do not relate to my needs I need to make a conscious effort to learn them. When the words are the ones I'd happily use, I'll learn them easily without any effort, I just need to spend enough time with Duolingo.

I believe that people who do not care about physics are having the very same issues with calculus that was explained with references to physics. Probably they can overcome this difficulties, like I can overcome my difficulties with uninteresting words, but it means they need to spend more effort and more time to get the same result.

[VyseofArcadia]

> It's not even about the equations, it's simply using it as a backstory for the motivation of the mathematics.

Bingo. I rarely (if ever) used motivating examples from physics as test or homework problems. This was to ground calculus in reality somewhere. This was after years of wondering how to deal with the common student complaint of, "but why, where does this even come from?"

So I started telling them where it comes from.

[calf]

The alternative is to ground it in philosophy and theoretical mathematics which would be even more abstruse...

[AdamN]

You're missing the part that they may have taken zero classical mechanics classes. Even if it's something you learn in week 3 in that class, if you've never taken it you have no idea where those ideas fit in.

[gowld]

Why is someone studying science in college, if they haven't finished high school?

[acchow]

Most people don’t need or care to learn calculus. They just want to learn how to use calculus

[gowld]

Similar to how most people don’t need or care to learn statistics. They just want to learn how to say statistical words to silence critics of their pseudoscience.