Yes, but... try asking for a verbal player summary at the end each session and a recap at the beginning of the next.
I've used this technique with my players in several campaigns, ever since it became apparent to me that players will find things interesting that you as the GM did not expect and they will sometimes interpret or recall material differently than you as the GM intended or thought you conveyed. My suggestion is that this is a better solution than asking for their notes.
At the end of each session, ask your players to verbally summarize what occurred during the session. They might find this a little strange at first, but if you just explain to them one time what the purpose is (so that you can audit what information got across from the GM to the players to help improve the player experience) they will, in my experience, buy into it. This helps you prepare for the upcoming session by focusing on what they like.
Then at the start of the next session, ask your players for a verbal recap from last time. They will tend to forget about things that they didn't consider especially interesting or important. Whatever they do recall, it stuck with them enough that you should probably focus on those topics during the current session. Also, if there are important things they fail to recap, you can easily use some simple exposition to remind them of what they may have forgotten. This helps you keep the current session on track and maximize player comprehension.
If they mention things that you already intended for them to pay careful attention to or things that you considered important, then don't bother writing those things down, because you already know them. If they review something that you had not considered important or if they interpreted information or events differently than you did, write down just enough for you to be able to incorporate those ideas into the remainder of the session or into the next session. (And if some players are paranoid and think they've got everything all wrong whenever they see you write something down... take notes no matter what they say, or make it clear that you're not writing down gotchas to try to trip them up later.)
With this technique, you don't need to ask players to show you their notes. In my experience, this makes them feel less like they are being judged or graded on accuracy. It also clearly identifies for you what they thought was important in the grand scheme, not what they might have thought was important when they were jotting it down. In other words, the information they will tell you is a more accurate representation of their intrigue than what their notes include.
To avoid stressing players who don't like this sort of thing, don't make it compulsory to participate in the summary or recap. Make it an optional thing for those sorts of players who enjoy it and want to participate voluntarily.
Depending on the kind of game you're playing, it's easy to incentivize these activities, too, by giving the player who provides the most informative recap some sort of one-use perk or boon for the session, depending on the rules for the system you are playing. For example, in D&D 5e I give Inspiration, in 13th Age I give a free icon relationship re-roll, and in Freeform/Universal or Fate I give hero points. Most games have something equivalent you can provide as a reward to give attentive players a motivation for participating in the summary or recap.