I think you need a good balance. You need problems which are challenging and which teach good math thinking, but you also need to learn the basic arithmetic because like Ania said, it's a tool.

So far our dinner math is usually full of new concepts and problems, but DS5 got lots of very useful drill in Montessori. You see we can and did let him figure out how to add two fractions like 3/5 + 2/3, but after that he needs to practice it. Practice is a big part of math and to be honest DS5 will do much better if he can start from simple problems and move up. He sometimes gets frustrated if he can do the logic but cannot do the arithmetic behind it and I believe there is a place for bunch of 3/4 + 5/6 problems.

I know lots of people who were extremely successful in math, who won prices in math and physics competitions and I hope to mimic the education they got.

LMom