Very strange usage of 、. Or maybe I would just expect ときに instead of ときの and because of that I don’t like the comma there. :)

Japanese speakers very often put a comma in a strange place.

This comma seems to be an attempt to show that ときの doesn't modify 学生 (or 思考), but after reading it twenty times, I still haven't get it's structure. It seems that ときの modifies 選択および活用方法 (Does it mean "選択 & 活用方法" or "選択方法 & 活用方法"?). I understand that you choose メディア教材 during your 授業設計, but I think you use them rather during your 授業, not during your 授業設計...

Anyway, I believe this sentence was taken from a real syllabus. It looks very natural in some way.

In a real situation, you'll often face this kind of sentence, and you'll have to simply pretend to understand it.

By the way, ときの should modify a noun.
If it were ときに, it should modify a verb (or an adjective). But neither 授業設計をするときに学生の思考を触発する nor 授業設計をするときに～理解する makes sense to me.

Let's just stop thinking about this sentence. It's obviously not worth it.

Well, at least I am not the only one who finds this sentence strange. After reading your insights I think I finally realized how its pieces are related and why it means what it means. It’s actually more understandable than it looked like at the first (and twentieth) glance. Thanks for prodding me in a right direction! Worth it or not, 大成功だ!

Now rather leave it quickly before I start to be unsure again. :D