I really think that targeting this toward parents or teachers of gifted kids is barking up the wrong tree. Gifted kids typically grasp things like the associative and commutative properties of addition and multiplication the first time they are taught them. They are not typically the kids who are applying an algorithm without understanding why it works. If they make mistakes on word problems, it is usually because either they over-complicate them, or because they are being asked to do 10 or 20 or 50 problems of a type they know how to solve, and that are essentially identical, and they lose interest halfway through, so they don't notice when one of the problems switches things around.
My son glanced at your page with the first chapter excerpts. His immediate response: "He hasn't really thought this through. His rules don't work for every case. Let's say that you have a problem where someone gave you half of a zebra, and someone else gave you another half of a zebra. That would be (1/2 * 1 zebra) + (1/2 * 1 zebra) by his rules. So according to him, that would be equal to 2*(1 zebra/2)= 1 zebra. And that method would be correct if you were talking about liters of water. But you aren't, you are talking about zebras. Just because you have two halves of a zebra, that doesn't mean that you have a whole zebra. You might have two right halves. You might have half of a male zebra and half of a female. And even if you had two halves of a single individual, that still wouldn't give you a whole zebra without an awful lot of repair work."
When gifted kids have issues with word problems, it is not generally because they can't figure out what the words mean, or how that should translate into an equation, but because they can see too well what they mean.
