> We'd need someone who is informed on the developmental process of math skill to comment on "times tables".

(I feel somewhat qualified...)

It is a mistake to make the kids memorize the times tables before they intuitively understand that multiplication is a repeated addition (or visually, that multiplication is a rectangle). The right moment to memorize comes a few weeks or months after they can calculate the result without memorizing. I think it is safer to wait, because many parents would be tempted to make it prematurely, in order "not to waste time".

Generally: understanding first, memorizing later. If you memorize first... many kids won't even try to understand, because "they already know it". The problem is, if you remember without understanding, there is nothing to correct you if you make a mistake. An incorrectly remembered fact feels exactly the same way as a correctly remembered fact, and you have no alternative way to check.

Also, memorizing instead of understanding is a strategy that works well in short term and terribly in long term, because memorizing a small thing for a few days is easy, but then you forget it (kids famously lose a lot of what they learned at school over summer holidays), and when the memorized things accumulate, it becomes too much and you start confusing them. Actual understanding takes more time, but it can survive the summer holidays, and already understanding many things makes understanding an additional thing easier.

(But when the day comes to memorize the times tables, spaced repetition is your friend.)

I'm guessing the advice stems from school being boring already and being ahead of your class makes it even more boring.

Though reading should be something teachers are equipped to handle very wide range of competency.

montessori does advanced math in kindergarten (advanced compared to regular kindergarten). i haven't heard anything about that leading to problems when those kids go to regular primary schools after that.