A May 29, 2018 article about Common Core from the Yale Tribune, references another article that appeared in the Washington Post and Chicago Tribune by Jessica Lahey. It summarizes her views about the bad rap she and others feel is being given to Common Core’s math standards:
She believes that the gap between parents and students does not necessarily lie on the Common Core itself, but on the flawed approach of conventional math education where students were taught to memorize and dutifully accept axioms and mathematical rules without completely understanding its application and the principles at work.
This view is shared by many and has become the hobby horse of the math reform movement that gained significant traction with the National Council of Teachers of Mathematics’ (NCTM’s) math standards, first published in 1989 and subsequently revised in 2000.
I have written about the mischaracterization of conventional –or traditional–math many times. My main message is that the underlying concepts were in fact taught, and students were then given practice applying the various algorithms and problem solving procedures. I have provided evidence of such explanations in excerpts from the math textbooks in use in the 20’s through the 60’s. Yes, the books required practice of the procedures, but they also showed the alternatives to the standard algorithms. These were presented after mastery of the standard algorithms as a side dish to the main course. These alternative methods are by and large the same methods that are taught today under the rubric of “Common Core Math”. The difference is that the alternatives are generally taught before the standard algorithm in the belief that teaching the standard algorithm first eclipses the understanding of the “why and how” of the procedures. Delaying the teaching of the standard algorithm by requiring students to use inefficient and often confusing techniques (in the name of “understanding”) can result in a confusion of what is the side dish and what is the main dish. The beauty and simplicity of the standard algorithm is lost among a smorgasbord of techniques that leave students more confused than enlightened.
In short, the ideas expressed in the two articles referenced above represent the groupthink that pervades education schools and other forms of the education establishment. The prevailing mode of thought views drills, practice and the learning of procedures as “rote learning” and prevents true “understanding”. If students “understand”, then everything else follows–the corollary of which is that understanding must come before procedure.
What is left out of such pronouncements is the difference between novice and experts. There are levels of understanding as one goes through school, and depending where one is on the spectrum between novice and expert, the level of understanding may be deep, shallow, or in between. Procedural understanding is a level of understanding, but students who are at such level are sometimes referred to as “math zombies”. This term is is relatively current but is what Lahey and others think is the end result of “conventional math.” And unfortunately, their view seems to rule the roost.