"I can listen and look at the same time"

This is the belief that holds up the others, so it goes first. You can repeat what was just said, so you were listening, so the glance cost nothing.

Repeating the last sentence is a low bar. The words go in whether or not you're attending to them, in the way you can be asked what a song on the radio was and know it. What the person talking wants isn't a record of their words. It's your attention on them, and that's the thing that goes to the screen.

The research here doesn't measure listening. It measures what people get from a conversation with a phone in play, and it's consistent. Ryan Dwyer, Kostadin Kushlev and Elizabeth Dunn had over three hundred people share a meal at a restaurant with friends or family, and assigned some to keep their phones on the table and some to put them away. The people with phones out felt more distracted, and the distraction reduced how much they enjoyed the time. In a second study, people reporting on their days in real time felt more distracted and enjoyed in-person interactions less when they'd used their phone during them.

Kushlev and Dunn then took parents to a science museum with their children and assigned them to use their phones a lot or a little during the visit. The parents told to use their phones more felt more distracted, and through that felt less connected to their children and got less meaning from the time. A week-long diary study found the same shape. Nobody in these studies was told to stop listening. They were told to use the phone, and the distraction came with it.

Adrian Ward and colleagues found something stranger. In two experiments, the mere presence of a person's own phone, not in use, reduced how much attention they had available for a task, and the effect was largest for people who relied on their phones most. If the phone can do that switched off on the desk, it's hard to argue that it does nothing lit up in your hand.

So the half-listen is real, and it's a half. My interpretation is that you keep the words and lose the person, and the person can tell which half they got.