What it notices
The gap between what is claimed and what was shown. Critical thinking notices when a measure has been swapped for the thing it stands in for, when an assumption is carrying the argument and when two sources that seem to disagree are answering different questions.
What it cannot see
Anything that has not yet been claimed. Critical thinking needs something to evaluate, so it is weak at the start of a problem and at generating options. It can also make a group very good at finding flaws in every proposal and very slow at making one.
It sees arguments more clearly than it sees structures. A set of individually sound decisions can still add up to a bad pattern, and no amount of scrutinising each decision will reveal it.
What it asks of teachers and students
Knowledge first. Willingham’s argument is that critical thinking cannot be taught as a general skill cut loose from content, because what counts as good evidence differs between history and chemistry. Teachers need to teach it inside their subject. Students need to be allowed to reach conclusions, not only to find faults.
Good work names what evidence would change the writer’s mind. Weak work lists objections to every side and settles on none.
Where the values sit
Behind the question of what to measure. In the day above, critical thinking cleared away the false disagreement and then stopped at the real one: whether the school cares more about what students can show in a project or in a subject test. That is a question about purpose. The Delphi Report’s experts included fair-mindedness among the dispositions of a critical thinker, which is an admission that the method needs values it cannot supply.
How it gets hollowed out
The hollow version is a poster of question stems and a generalised scepticism that treats every claim as equally doubtful. It teaches students to say "but what about bias?" about everything. That is a verbal habit, and it can make a class more confident and less accurate at the same time.