Barry Garelick is a long-time math instruction analyst and current middle-school math teacher. For years he has done yeoman’s work carefully analyzing Common Core math and showing precisely how it affects students, down to the level of individual math problems, approaches, and specific mandates.
He recently responded to criticism of some of his work discussing why requiring students to overly explain their answers in math actually harms their learning.
Understanding, critical thinking, problem solving come when students can draw on a strong foundation of domain content relevant to the topic currently being learned. As students find their feet and establish a larger repertoire of mastered knowledge and methods, the more articulate they can become in explanations. Put in neuroscience terms … the pre-frontal cortex (where critical thinking takes place) is underdeveloped in early & middle years. It undergoes rapid development through teen years (where self-concept is growing) and this is where students should be challenged to more sophisticated reasoning, explanation of meaning and so on. It is not fully developed until one reaches early adulthood, sometime in one’s 20s. When a small child is asked to engage in critical thinking about abstract ideas, they will produce a response that may look like independent reasoning to an untrained adult, but it will involve more of a limbic response. That is, they are responding emotionally and intuitively, not logically and with ‘understanding’. That may be behaviorally interesting, but it is not mathematical development and it leaves them behind in the development of their fundamental skills.
There’s more, if you’re interested. One last comment: This of course also fits well with the classical method, which emphasizes concrete instruction in the early years that gradually transitions to more abstract, advanced thinking as students mature. It’s impossible to put the cart before the horse, you see. The horse doesn’t like it, and the cart ultimately goes nowhere.