From an article about the Russian Math School:
“Meanwhile, Hilary Kreisberg, director of the Center for Math Achievement at Lesley University and a former fifth-grade teacher turned math coach, says her experiences with RSM students have led her to question the claim that Russian Math focuses more on developing a deep understanding of math instead of memorization. In fact, she has seen the opposite. “From what I’ve seen, they come in well above their grade-level standards in terms of memorization, but not in terms of content understanding,” she says. “Many of them very quickly get to an answer or can compute in a fast way, but they can’t necessarily explain to me what they’re doing or why they’re doing it.” And explanations, she says, are a critical component of mathematics. “In public school teaching, we are very strictly taught that the goal is not to accelerate,” Kreisberg says. “The goal is not to extend their thinking into another grade level, but to go deeper with the current grade-level standards because there’s always more you could learn about a topic.” “
There is no discussion in the article, or from the experts proclaiming math zombie-ism, of levels of understanding and how that figures into the novice/expert spectrum. The general excuse given for programs like RSM that are successful is “Well the kids are good at memorizing procedures but there is no deeper understanding.” The unanswered question is how deep is the understanding of the students who are supposedly benefiting from the “deeper understanding” approach the math reformers seem to think works so well? More to the point, how many of those in the “deeper understanding” category have to take remedial math in college compared to those from the RSM program?
And why is it that the US is lagging behind other nations (who used traditional techniques or those used by RSM) with all the “deeper understanding” the US students supposedly have? In articles I’ve read about reform methods, a common answer is “We’re just not doing reform math correctly.” (See in particular this article, which received criticism for its inaccuracies.)
These are questions that need further delving. In my opinion, what passes for “deeper understanding” in the educationists’ realm, frequently amounts to “rote understanding.”