Don't know the Bridges curriculum myself, but the principle behind varied approaches to problem solving with fluid decision making seems like an important skillset. If the only object is to teach addition, subtraction, multiplicate, etc. then a single algorithmic approach seems ok.
But the fluidity, diverse approaches, etc. is great, the small quick decision in approach can really payoff. However, I doubt you can put in a box and sell it en piece. First criterion should be that the teacher has the fluid, creative problem solving in their own natural toolbox.
I read the link Kelly had, and oddly it is very similar to how I explain problems or talk through them with my son. Except any particular explanation is dependent on the problem. 168 + 32... oh hey look two and eight make a ten, so you can do it as 170 + 30. Or 26 * 12 oh a five is close, let's start with 25 which is a quarter so one fourth of 12 is 3, a couple of tens in there, so 300 and add the 12 back for the lonely 1 we dropped earlier to get 312...
Ultimately, I'm feeling skeptical that you can teach creativity dogmatically.
