@BakersDozen Would you be able to send me your syllabus as well? Thank you! I appreciate it!

We watched this episode this morning - very interesting!

I'll look for that documentary. Thank you for the input and for the examples of calculus applications.

Thank you!

I have AoPS and Saxon on my shelf, along with an ancient college calculus textbook of mine. As easy as CTC was to use from my perspective, I think I'm going to have to switch to a traditional paper and pencil textbook at this point. Thank you all for the help!

I have now shown him a proof, and gone through it with him. When I asked what, exactly, he is stuck on, he says that he still feels like he doesn't understand why anyone thought to do this in the first place. I'm not sure what he means by that. I can't decide if this is teen debating or a genuine question from him!

Thanks for posting that image! AoPS is certainly concise, you're right. What I was trying to say was that I was not looking for an entirely new curriculum to use, just looking for one source for a proof of derivatives, if that makes sense.

I assumed they did, but after you posted the question I asked him and also looked at the CTC lessons. It turns out that no, they don't, not at all. It's pretty plug and chug, which is why he was able to do the math but now he is frustrated that he doesn't understand it. I guess it's a good thing that he is questioning it now.

He wants to know why it works. He has taken a conceptual physics class (not calculus based), and he does seem to understand how calculus is used in practical applications, but he wants to understand why the math of calculus works.

That looks interesting! I haven't seen it before. Thanks!

Hello! My son is doing calculus through CTC math, and it is going well. He completed the differential part of the course in the spring and the plan was to cover integrals this fall. However, coming back to it after the summer, he feels like he wants to understand the "why" behind working the problems. He asked his older brother, who was a math major in college, and was told that he was asking about something that covered two semesters of college classes, lol. My question is what to do to give him some of the theory. Is there anything concise that could possibly provide that for him? I thought about the Art of Problem Solving Calculus book or Calculus Made Easy by Thompson and Gardner, but I'm actually looking for something more concise. Although my son is a strong math student, it is probably his least favorite subject. His quest to understand the theory is suprising me, actually! I would appreciate any input! Thank you!

I have not, but I have a friend who is currently using it for high school. Her oldest child is a sophomore this year. If you have a specific question or concern, I can ask her about it!

I listened to The Black Count this summer as an audiobook and it was fascinating! After reading it, it made me want to read The Count of Monte Cristo so I am doing it as a read aloud this year with my teen. We are calling it his junior year read, haha, as it is so long it may take us the entire year! I highly recommend The Black Count if you can find it!

Aside from the standard application essay requests, the only time any of my older kids were asked for anything like that was as part of honors college applications, which always seem to have their own set of requirements, anyway.

Lantern English offers 8-week writing and literature classes for a range of ages, including several Creative Writing courses. Here is a link to their Creative Writing courses for grades 6-12: https://www.lanternenglish.com/thecreativewriter. They are very affordable, and the quarterly class option is a nice choice. My son did several of their classes last spring as a 10th grader, and overall we were happy with the classes and the feedback he received.