I just posted the following review on Amazon for Barry Garelick's book Math Education in the US, Still Crazy After All These Years:
A few weeks ago I won this book and the author, whom I know only via blogs, asked me to review it. Here's my review in a nutshell: this is exactly the book *I* would write about the current state of math education if I were but as eloquent as Garelick.
His observations are profound, if simple: "In a world where it doesn't matter when you learn something, because you'll get it eventually, there seem to be few if any critical junctures, no mastery of procedure, no building on what you've learned--no learning." Have you ever been told, "Don't worry if baby doesn't get it (multiplication, fractions, negative numbers) now, he/she'll see it again next year"? That is exactly what Garelick is talking about. "Its substance was shallow, memorization was discouraged, students were kept dependent on mental crutches"--if you've heard a teacher say "Just let them use a calculator; the computation isn't what's important here, it's the higher-level thinking and deep understanding that we're after", then Garelick has told you what's really going on. Are you told that "We don't teach children how to do the problem, we teach them how to think so they can figure out the problem on their own", Garelick again clarifies: "...constructivism taken to extremes can result in students' not knowing what they have discovered, not knowing how to apply it, or, in the worst case, discovering--and taking ownership of--the wrong answer."
What I enjoyed most of all, though, was Garelick's clarification of ideas I've long had. Again, I wish I could state my beliefs as clearly as he does. For example: "That critical thinking cannot occur without something to think critically about--namely facts--is of little concern to ed school gurus", or his entire discussion of working memory/cognitive load theory.
Garelick has his educational history correct. He has his assessment of direct instruction vs. constructivism correct. He has facts and figures and studies, and he quotes top-quality mathematicians. He knows the education world, and he reveals its dirty little secrets. He gets cause and effect correct; for example, "For many students, the 'why' of the procedure is easier to navigate once fluency is developed for the particular procedure." And he adeptly slays the Common Core dragon of writing essays to explain how you got your answer and why it's correct.
I enjoyed this book so much because I share Garelick's fundamental beliefs about math education, where it's been and where it's going. This is an exceptional book for anyone interested in navigating math education today.