Meaning of "so" in the following context

The passage is saying that children get ideas from outside the classroom – from the popular media. But not all this information is correct. Some schools don't allow children to express these ideas in the classroom. The result is that false ideas are not challenged or corrected.

The grammatical purpose of so is a conjunction

so
CONJUNCTION

2 (so that) With the aim that; in order that.
they whisper to each other so that no one else can hear

The last sentence

It seems schools may not be providing an opportunity for children to re-express their ideas and so have them tested and refined by teachers and their peers.

can be broken down like this

It seems – it is believed [that]
schools may not be providing an opportunity for – schools don't allow
children to re-express their ideas – children to talk freely
and so – with the aim
have them tested and refined – of [those ideas] being corrected
by teachers and their peers. – by the teachers and other children.

It seems schools may not be providing an opportunity for children to re-express their ideas and so have them tested and refined by teachers and their peers.

Here, 'so' is used as a short form of 'in doing so'.