My sons are both in college now, but during the K-12 years I took the approach that I could not try to "accelerate" other than by offering help with homework. T

My sons are both in college now, but during the K-12 years I took the approach that I could not try to "accelerate" other than by offering help with homework. That is, I didn't introduce any concepts that would arrive later in their curriculum. Instead, I introduced concepts (verbally, while driving to school and so on) that would never be covered at the HS level. These included: the idea that some things are provably unprovable (e.g. halting problem), that some things are provably impossible (e.g. constructibility of polygons), that everything in mathematics has a history around why it was invented, and a story as to what it's useful for, that generally doesn't get taught but can be very helpful in appreciating why you might want to learn about it.