Your theory may be viable as a construct of the elite, powers-that-be who dictate what/how/when teachers must teach in the classroom.
However, I am still blessed to work in a public school system that acknowledges me as a professional and allows me to teach. Yes, I am held accountable for teaching the state standards, but my classroom is mine.
I tell my students and parents that there are numerous ways to solve problems. I am elated when parents actually sit down with their children and assist them with assignments. Can’t tell you how many times a problem has been solved in a way I never thought about - I am always learning, too!
BTW ~ I have read many studies that suggest homework has minimal impact upon learning, which is why I assign only 5 homework problems each week. Those problems relate to previously taught skills, and students may turn in their work for me to check, make comments for corrections, and help them to understand when they ask questions. The final work must be turned in each Friday. The majority of my students do not bother... School board policy is that homework can account for no more than 10% of a grade.
One of the movies I have up from IBM Research was done on teaching arithmetic to children. This was Luanne's project, but I directed and guided the video, teaching Luanne to do the actual editing. She used a fascinating approach to offering individual levels of hints at problem solving.
Lyby, don’t forget to tell us the Cheetos and gasoline funny. I know what you mean about your comment “Can’t tell you how many times a problem has been solved in a way I never thought about - I am always learning, too!” Lately I dream more than I ever have with many questions answered. I was mopping the other day and just out of the blue there was an answer I was seeking for a time.