That is the question. Are you more concerned with making sure your child learns the techniques and tools within that big box we call math? Or, are you more interested in making sure your child learns to think independently and use math as a tool to solve problems?
Here is the problem, though. You cannot use a tool before you know how to use it or even how it works. Imagine baking in the kitchen without knowing what the ingredients are or how even to use the oven.
The fundamental problem with learning math is that you must learn the techniques and tools, and also learn to think independently. The independent thinking part of the equation becomes most important when your child begins to learn algebra.
In past decades, algebra was taught only as a set of techniques and tools. No independent thinking needed. Just grab the formula and practice using it. Repeat the process that you see on the board. Get the right answer and move on. Finish the course, get a good grade, and promptly forget absolutely everything about algebra. It was like learning fine art by practicing brushstrokes but never actually creating a painting.
These children, me included, could pass the tests and get the grades but never learned how to apply algebra to the real world and add it to our toolbelts for future use. Why? Because we never had the chance to think on our own, independently about a situation and apply the tools and techniques of algebra to it.
By the point your child is ready for algebra, she will have the basic math techniques under her belt. She will know adding and subtracting, multiplying and dividing large and small numbers, and even likely understand powers and roots. Those are the basic tools. The best way to learn algebra is to bite off a chunk of a technique, and then use that new technique to solve a problem. One chunk at a time. This cycle really should continue throughout an algebra curriculum, continually using the tools your child knows, those he recently learned, and adding one new technique at a time in order to solve a real-world problem that requires independent thinking.