Quizzes after lectures I put together elaborate, very carefully planned out lectures, complete with highly distilled exemplars, student teach-backs, and mid-lecture activities to check for understanding.  I've had feedback that my students really enjoy these lessons and appreciate how much work I put in to making sure that my examples are really clear.  

However, it has come to my attention that, perhaps due to a course structure which gives students lots of chances to re-demonstrate mastery if they initially struggle, a certain number of the students are only half-engaged with my lecture.  Since I realized this, I have spoken to a few of them, and they agree that the lessons are fun, but say that they are stressed by other courses, and sometimes this causes them to work on other things.

On one level, I don't mind this.  Student stress is real, and I have ample evidence to demonstrate to me (or to others!) that the students ultimately master the material that I teach them.  

On another level, however, being lax about this does a disservice to them (as we could progress faster for everyone if kids took the learning opportunity more seriously), and to me, as I have put almost unreasonable amounts of time into distilling rich and complex ideas into explanations that are both beautiful and clear.  

I'm further motivated by the fact that I get evaluated by my administrators, and I have now been dinged twice by having some of the kids off-topic for short bursts.

I'm toying with the idea of adding little, basic quizlets to the ends of my lectures for which students would be immediately responsible.  

The questions would purposefully not be difficult.  They'd be more on the level of, "were you paying attention to what we just did?"  Basic recall, simple factoids, etc.  I already give a difficult test or quiz at the end of the unit, so I don't need this quiz to do much more than (1) give students a chance to dredge up information from memory1 and to help motivate students to take fuller advantage of the lesson opportunities I am giving them.

My question, then, is two-fold: (1) are quizlets a good solution to my problem?  And (2), if they are a good solution, is there any wisdom from the trenches on how to pull these together so that they are effective without bringing on substantially more grading work?  I'd like to make them as useful in the learning process as they can be, but I have to be careful about what I take on.

1 - See points 2, 3, and 4 for how this directly enhances learning.
I have a few thoughts on this topic. One is a couple ideas about how quizzes could be implemented (if you choose to use them), and the other is some more general thoughts on the tactics that I use to solve problems like this.

Quizzes Without Extra Grading

What are your opinions on peer grading or self-grading? I've seen both work nicely for things like this (short, low-pressure quizzes that aren't too hard).

They require a little bit of logistics, since each student needs a normal colored pen and a "grading" pen, and it's easiest if you supply those. Then you require that normal pens are collected before grading starts, and that students do not have their own writing implements out, and it typically goes well.

This would require you to put aside more time during class, since a 5-minute quiz takes at least an additional 5 minutes to grade.

The pro of students grading their own work is that it becomes a way of reflecting and learning from the experience. If they get a question wrong, they get immediate feedback about the correct answer.

Alternatively, you might want to look into giving digital quizzes. They would have to be multiple choice or fill in the blank, but they auto-grade, saving you the time. I know that Google Forms has a method of doing this, and there are a bunch of other platforms too. Your students could take the quizzes on their phones, or computers.

This system tends to be quick and you can integrate it into the entire lesson, not just the end. I had a professor in my undergrad who would lecture for a bit and then pause for us to answer a question or two. Before continuing. It was her way of doing understanding checks. You could easily establish small point values for each question so that they "count."

To Quiz or Not to Quiz

Personally, I've found that increased examination does not tend to increase student attention. I theorize that there are two reasons for this.

First, many quizzes happen "later" - either at the end of class or even several days or weeks later. Most students (especially teenagers, although adult students as well) have trouble remembering potential consequences that seem far off. If the exam is important enough to overcome this problem, then it's probably invoking some level of anxiety or fear, which is a large detractor from student focus and engagement. It may solve your problem of looking like your students are paying attention, but I believe that it's unlikely to actually increase their learning.

My second theory is that people tend to believe that they are better at multitasking than they are. If you gave an anonymous poll to your students and asked if they ever do work for other classes during your lectures and how much attention they pay to your lectures, I would bet quite a bit that they all feel that they are always attentive, even though you know that not to be the case. Thus, saying "Oh, it's very important to pay attention!" seems unlikely to change behavior because they really believe that they are/can pay attention while doing other things.

So, what are the other options? You could do the honest but maybe frowned upon thing of talking to your students and saying "hey guys. I know you're busy. I know you sometimes finish up other homework while in this class. I'm mostly fine with it on occasion; as long as you get your work done and feel like you're learning what you want to learn, I don't really see a problem. But it makes us look bad when a senior teacher/dean/etc. sees you doing that. So we have some options. I can change something about the way the class is structured (quizzes, etc.), or you can keep the distractions to a minimum, especially when we have guests." Whether this will work mostly depends on your students and your relationship with them. It also obviously depends on the institution you teach at.

A Non-Quiz Suggestion

You've mentioned that you're already putting a lot of thought and work into every lesson. So this might not be a solution that seems feasible. But my personal strategy for student engagement is to keep the students active throughout the lesson. I try to talk for 5-10 minute chunks, broken up by having students work through practice problems or explore ideas. Maybe you can take your current activities and spread them out a bit more throughout the lesson? If students are changing tasks frequently, it will be easier for them to stay engaged and harder for them to pull out something else to become involved in.

If you want more concrete information on what this could look like, pick an example lesson and post another question. I'm sure that lots of people will have a wide range of ideas for active learning.

I hope some of these things help. Good luck!