I'm left wondering why this would be a problem.
I've often had the pain of dealing with people who try to do it all in their head. Sure, one or two are good enough where it's not a problem. The rest of them? They keep getting confused and making mistakes. For things that are not very complex. If they had only written it out or drawn on paper/board, they would not get confused.
It's most obvious when I try explaining some code's algorithm to them. They'll begin with understanding, and then 70% of the way through they'll keep getting confused because they couldn't hold it all in their head.
I've often had to tell these people "Don't try to do it in your head!"
If that doesn't work, get him a rubber ducky [] and tell him to go talk to it if he's not willing to compromise on communication styles.
I had a lot of success with asking him if I could think about the problem and we could schedule a meeting in half an hour or so. He was much happier with that result because I had thought through the problem and was now able to give him the back and forth he needed. I was also much happier because I was no longer expected to come up with insight on problems I had no time to chew on.
You don't have to just accept doing your mutual conversation exactly as he likes it.
In my work experience I don't remember ever having to do that. I'd look at code & investigate a problem independently, then talk to someone about it afterward. I think that should be considered at valid approach to the interview.
In other words, from my perspective, you're not actually in disagreement with their method. They weren't saying "narrate in real time as you're first having [thoughts]". Practically nobody does that ever, or is expected to do it, except in other practices like mindfulness or therapy and what have you. They were saying they ask them to understand it, explain it, and then talk about improving it. OP's problem was with the candidates whom couldn't understand the code, and weren't even willing to talk about the state of their understanding so that the interviewer might help them walk through things further...
I don't have any source but from my experience mathematical/computer minded people are more likely to be introverted/talk less then arts people.
I think you are right about that, but that just means that if they want to be effective members of a team in an organization, they need to work on their communication skills. Ability to communicate is something you can learn to do better.
I know this for a fact. I used to teach public speaking, and students came out far better at it than they came in. The same is true for many other communication skills. See for instance Marshall Rosenberg's book Nonviolent Communication, which is great for interpersonal conflict situations.
In fact, I think a lot of introversion is at least in part due to poor communication skills that could be improved with training and practice.
As for programmers - same thing. If they are any good they are more than able to talk the talk.
Effective communication doesn't necessarily mean you talk a lot or are extroverted. It means that you say things that matter when they matter, and that is a crucial skill to have in almost any work environment.
If they sat there for a bit thinking about the problem and then provided a solution, I'm sure that would be fine. But that's not the situation he was describing.
(a) discussing an open problem with a colleague, and
(b) explaining what's going on in my mind as I'm attempting to solve the problem single-handed.
I'm very effective at (a), and it's a skill that I've used many times as a software developer and/or grad student.
But (b) is more typical in psychoanalysis sessions.
I often have to explain a problem to my coworker and vice versa. It's also really helpful when pair programming. Just curious about your experience.