Wow. How exactly does that work? (I am so interested in this because I was very dissatisfied with my public school math education and am determined that when the time comes my children will have exactly the opposite.) Got any links about it? Also be sure to expose them to analytic subjects outside straight "math" such as symbolic logic, computer programming, etc., and when they do calculus make sure they are learning what it means and what it is for, not just how to solve the problems. But you probably don't need to be told that.
I invented the method. We use algebraic operators for all arithmetic problems to break down the problem into easier sub-problems. Engineers use these methods in their heads. We use Saxon only as a source of problems and for drill work. It's archaic.
In our system, all equations for word problems have units, set operations, what we call "truth statements" (such as 1 dozen oranges = 12 oranges), and calculated identities (1 dozen oranges/12 oranges = 1). "We can always multiply any number by one." No hand waving allowed. This rigorous method makes word problems a snap. There is no "borrowing" in subtraction operations. We add another equation that equals zero to adjust the subtrahend. "We can always add zero, can't we?" Any time they apply a principle, axiom, or theorem they are to cite it as if the problem was a proof.
Rigor. It's that simple. Rigorous simple problems makes complex problems easier to do later. This is the necessary preparation that will make chemistry and physics far simpler to learn.
Also be sure to expose them to analytic subjects outside straight "math" such as symbolic logic, computer programming, etc., and when they do calculus make sure they are learning what it means and what it is for, not just how to solve the problems.
Symbolic logic will be taught after the first exposure to calculus (so that we can teach physics) and after an extended period of diagramming sentences. My hope is to teach them to convert sentence structure to mathematics. My goal is that they could do legal analysis with symbolic logic. (That is a skill that would make them truly dangerous.)
I am an engineer. I won't expose them to computer programming until they routinely see science in the world and have mastered paper else paper may too easily bore them. For now, the computer is a word processor. I do not want them thinking that the computer is the world.