[betaclass]

'I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it.' I think that's a bit of a straw man.

The challenge is that simply getting the right answer, especially in terms of arithmetic (one small piece of math), can mask how well a student understands the underlying concepts and whether s/he can flexibly apply the concepts.

Here's a great video on that topic:

    https://www.youtube.com/watch?v=_ofQ_WnQiZ4

And here's a great video that shows what a participatory classroom with a great teacher can achieve:

    https://www.youtube.com/watch?v=BlvKWEvKSi8