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.