Rote memorisation is the main educational method in primary schools. Children learn by repetition and are tested by simply being asked to regurgitate information learned in class. Little, if any, time is spent on critical or creative thinking. This is what philosophy can add to the curriculum. Philosophically-driven pedagogy allows the teacher to step back and assume the role of facilitator rather than educator. The class is then encouraged to engage with each other and discuss philosophical principles such as ethics, knowledge, logic, and language. The pupils can then lead the discussion, proffering their own arguments and opinions. This teaches children how to think and not what to think.
There is a misconception about philosophy; that it is outdated or replaced by science. It’s certainly true that empirical, descriptive questions about the world are now answered by science (where once upon a time they would have been in the domain of philosophers). However, these sorts of questions are not the only sorts of questions, and (more often than not) we should look to the philosophical tradition to think seriously about the others. Teaching philosophy at a young age will help children to understand the value and approach of philosophy, inoculating them against philistinism as they grow older.
Reason and logic are invaluable tools, often neglected in favour of slogans and passion (and I am no exception, of course). Understanding that logically valid arguments can lead to false conclusions, or that we can reason about the hypothetical without holding that the contingent is not identical to the actual are particularly strong additions to the arsenal of a budding thinker.
Learning to listen to others arguments (rather than dismissing their position because you are certain that it is false, or simply because you don’t like it) is also dying art in the age of angry Twitter campaigns, heavily moderated comment sections, and interested political disagreements. I’ve argued the value of this elsewhere.
Finally, I think there’s a lovely complement to learning the art of critical thinking: computer programming. If you can write a program such that it successfully compiles, you will have had to have thought about it in a methodical, logical manner. I think this could provide a great practical application for the skills gained learning critical thinking and logic. They will have to understand why their program has a bug, in the same way they will have to try to figure out why someone else’s argument is unconvincing. They will do this by going back through each line of code (or premise), and carefully evaluating whether or not it it is flawed, and whether or not their desired output (or conclusion) inevitably follows.