This past semester, I did an online course related to this (link):
and I learned things I will use in my math classes. Of course I waited until the last minute to finish the course and was then furiously reading/skimming the online tests (since I had done the physical copy reading but had to click things for credit) before the district mandated deadline, but I digress.
I highly recommend it (not the last minute stuff, but the book). Unlike some other PD that speaks a good game of, "oh yes, you can use this for any school subject. Math? Of course!" and then proceeds to not provide useful examples of ideas or validation that it has been used effectively in math, this book actually had genuine math examples of various HS subjects.
One of the sections involved Top-Down Topic Webs. Quotes:
"Teaching students to organize ideas in a systematic, visual graph improves their ability to remember what they read."
"Many students become overwhelmed by too much information, focus excessively on details, and lose sight of the big picture when they read."
"Students often have difficulty connecting material taught from day to day and week to week."
This all is confirmed by me when I recall various things my kids said about calculus:
"Oh, why didn't they just call the class derivatives and integrals?"
"Wait, I get mixed up on the difference between ...."
So with all this in mind, I created a Concept Map for AP Calculus AB:
I'm sure I will edit it somehow, but for now I'm happy with it. I plan on handing it out the first week and continually referring back to it, so the students always have a clear idea of the big picture. Now maybe I'm the last person on this knowledge boat and maybe everyone is already doing this. If so, then it is a well-kept tidbit, and I don't know the secret hand-shake.
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