Paying Attention During Team Stand Ups Vs. Working Through Them

I'm on a team of 10 people, including my manager. During our weekly meetings, I struggle to pay attention to what's happening when other people give their updates. I only work closely with 2 of my 8 coworkers. For those 2 coworkers, I already have a weekly sync with our manager on a different day. For the time being, I don't have much to do with the other 6 people on my team.

I have 2 questions:

1. Should I try paying attention to others' updates or should I try and reclaim this time and do work during the meeting? One can make an argument that long-term, it's beneficial for me to know what's happening with the other people on my team, but in general, I'm under the impression that the greedy (short-term) approach is best.
2. If I should try and pay attention to others, does anyone have tips for doing so? I'm not sure how normal/abnormal I am in being able to pay attention to people, but I've always been a big day-dreamer. In elementary and high school, I was a good student in spite of day-dreaming during class because school was pretty easy and I was self-motivated to learn from the textbook. In university, I was still a big day-dreamer, but I was no longer a good student because school was hard and I couldn't just learn from the textbook. Now, post-school, I am motivated to pay attention to things that really count. e.g. when my boss wants me to do something, you better believe I'm motivated to pay attention closely to what he says. But by default, my mind doesn't want pay attention to anything unless it knows I need to do it. I can try taking notes, but often times there's so much additional knowledge and context the people working on the tickets have that my notes are kinda useless.

Ultimately, this team meeting is only a half hour per week, so it's a huge deal either way, but I'm leaning towards trying to continue working on my tickets during them (i.e. what I know counts).