Concepts vs. Procedures – the Great Math Debate

In last week's post—read it before you read this one—I presented evidence of deep math concept deficits in four 5^th graders in inner-city Brooklyn. Math is America's weakest subject, according to the results of international exams,^[1] and it's traditionally the most feared and hated among students. There's a lot of debate as to why that is, and as with so many other issues, that debate tends to polarize around two camps. For years, I have found myself torn between those camps, but I believe the evidence that I presented last week offers a glimpse of an elusive middle-ground and a more nuanced approach to math education.

The Confusion Beneath Confusion: Brief Glimpses of Number and Quantity

For the past few months, I’ve been spending a couple hours each week teaching remedial math to four fifth-graders in inner-city Brooklyn. My assignment: help my students to develop a conceptual grasp of numbers and elementary mathematics.

Over the course of my first week or two with my charges, I gauged my students’ knowledge and understanding—or so I thought. In fact, I had discerned only the superficial: their addition tables were shaky, but they could perform two-digit column-addition; they could carry but were prone to mistakes; three of them could borrow, but again with errors; they could name the place values of two- and in some cases three-digit numbers; they could quickly add multiples of ten in their heads.

It took me several weeks to realize what should have been obvious: that that was a procedural assessment, not a conceptual one. Beneath those weak basic skills were fundamental gaps in my students’ understanding of number and quantity.

Finland (Part 2)

Last week, I posted an article about the demographic causes of Finland’s preeminence on the 2009 Programme for International Student Assessments (PISA) exams. My purpose in that post was to show that a simple comparison between countries is impossible—but this is not to say that we can learn nothing from international comparisons. We can learn a lot, but only through careful and detailed examination of the data. I’ve spent much of the past two weeks sifting through that data, and I’ve come up with some interesting leads.

Finland (part 1)

Every time I get into a conversation about education lately, someone drops a side-comment about Finland, like it's the Valhalla of public schooling. In the past few months, the success of Finnish students on international exams has been widely touted and press-ganged into the service of various arguments about what we do and don't need more of in America. Most notably, perhaps, in the documentary Waiting for "Superman", Davis Guggenheim cites Finland's success as proof that you can have a good public school system without spending any more money per pupil than we do currently.

I don't know much about the Finnish school system—I'm sure it's a good one—but to give teachers, schools, and school-systems the sole blame and credit for differences in test scores is one of the most common misuses of data in the study of education.

Why Poor Kids Have To Memorize

I want to clarify something from my last post: when we talk about rigid, test-driven instruction that leaves students without the tools or confidence to think critically or solve unfamiliar problems, we’re talking about a phenomenon occurring primarily and maybe exclusively in poor neighborhoods. There are two main reasons for this, in my view. (Note well this “in my view.” I normally try to ground these posts in established fact and concrete data, but in this case that is impossible. As noted in my last post, this entire discussion is a foray into the realm of the unquantified, because it deals with precisely those qualities of mind and education not measured on the exams. The evidence behind this post is anecdotal—largely my own experience.) The first reason has to do with differences in academic achievement, the second with differences in behavior and school funding.

The New Age of Testing

My brother forwarded me this Times article about Shael Polakow-Suransky, the soon-to-be second in command of the NYC public school system. The focus of the article is Mr. Polakow-Suransky's approach to assessment: despite a progressive pedigree—he attended an extremely progressive highschool and studied under Ted Sizer at Brown—he's for more testing and better testing. Strange as it sounds, that may be the only viable position for a contemporary progressive educator, working at the policy level; and though some will probably call it a softening of ideals, Mr. P-S's position represents not so much a compromise as an adaptation of old principles to new circumstances.

Organizational Mediocrity

Why is it that mediocrity is a pervasive rather than an isolated trait in a company? Riding the 3 back to Brooklyn a couple weeks ago, I was struck by a flashy-looking ad campaign for Delta Airlines that took up half my car. The tag lines ranged from meaningless ("The only way up is up") to impenetrable ("Sleep is not a perk") to baffling ("Our newest international destination: California") to downright alarming ("An ounce of humanity can outweigh five hundred tons of metal," over a close-up of a jet engine during take-off—don't they realize that when you read "five hundred tons of metal" the first thing you think of is five hundred tons of metal falling out of the sky? Don't they realize that people contemplating trips through the heavens in giant combustion machines don't want to think about humanity being measured in ounces?!)