What is “critical thinking” and how private schools do better teaching it?

At approximately 1000 meetings on standardized testing (not always a great measure of critical thinking, but still) it has been brought up that home environment (aka parental input) is the single largest factor in determining the general level (advanced, average etc). But that when you measure from one year to the next the teacher is the single largest factor determining growth. Goes back to the question that the Sec of Ed struggled with- are you looking for achievement, or growth?