Symmetries, commutativity, associativity, transitivity, basic algebra/equation solving, some geometry, etc.

Teaching these ideas gives children a language to describe the world they're in and make sense of the ideas and concepts that bombard them - they're perhaps even more useful than numbers in this regard. The problem is that most elementary teachers aren't up to explaining these more advanced math concepts (lots of them have trouble with advanced middle school level math), and instead focus on just basic arithmetic.

This does a huge disservice to our children, because kids soak these topics up when well explained, and seem to really enjoy the learning (which is often hands on). I spent a fair bit of time in university (where I studied math) volunteering along with a professor to teach lectures to young children (1st-4th grade in the US) about math.

I honestly wish we could just accept that mathematics is as much of a specialized language/topic as foreign languages, and get specialist teachers starting early on.