I believe the investigations type philosophy is in the right place, but the systems are likely flawed in their execution by being too dogmatic. You can't train creativity or creative problem solving. Forcing a kid to keep guessing at solution approaches until they match the fixed set in the answer guide is a fail.
Frame-worthy. That's the problem in a beautifully-put paragraph.
While you can't TRAIN creative-problem solving (or, for that matter, 'critical thinking skills' either, IMO) using any particular
method...
you
can crush their development in students by stifling exploration. You
can encourage and nurture those things and allow room for them to grow.
But that is
never going to be possible in a system which has ground itself into a corner of testing-testing-testing and preparation for the same, all in the cheery, (but futile) hope that Every Child Can Master Algebra by Adolescence! which assumes that teaching mathematics requires the same approach as teaching arithmetic.
