In an article published in 2005, Patricia Clark Kenschaft, a professor of mathematics at Montclair State University, described her experiences of going into elementary schools and talking with teachers about math. In one visit to a K-6 elementary school in New Jersey she discovered that not a single teacher, out of the fifty that she met with, knew how to find the area of a rectangle. They taught multiplication, but none of them knew that multiplication is used to find the area of a rectangle. Their most common guess was that you add the length and the width to get the area. Their excuse for not knowing was that they did not need to teach about areas of rectangles; that came later in the curriculum. But the fact that they couldn't figure out that multiplication is used to find the area was evidence to Kenschaft that they didn't really know what multiplication is or what it is for. She also found that although the teachers knew and taught the algorithm for multiplying one two-digit number by another, none of them could explain why that algorithm works.Holy god, that is insane. I have a hard time imagining anyone being unable to find the area of a rectangle, never mind school staff actually teaching arithmetic, to say nothing of going 0-for-50 in a survey on the subject. I mean... unbelievable! Maybe I should take a poll of students in one of my own classes. Is it possible that people had just forgotten what the word "area" meant?
Just to complete the progression in the article:
The school that Kenschaft visited happened to be in a very poor district, with mostly African American kids, so at first she figured that the worst teachers must have been assigned to that school, and she theorized that this was why African Americans do even more poorly than white Americans on math tests. But then she went into some schools in wealthy districts, with mostly white kids, and found that the mathematics knowledge of teachers there was equally pathetic. She concluded that nobody could be learning much math in school and, "It appears that the higher scores of the affluent districts are not due to superior teaching but to the supplementary informal ‘home schooling' of children."On the larger thesis of the article, that current math instruction in K-6 is doing more damage than good, and could and has been dropped successfully at least once... you know what? I can potentially believe that. It's possible. If the quality of math instruction is truly that atrocious, I wouldn't want children subjected to it -- of course the only consistent result would be crippling lifelong math anxiety (per Dijkstra's, "as potential programmers they are mentally mutilated beyond hope of regeneration," and all that).
But far more important than my own best-guesses would be: This would take a lot more research before going forward with a plan of that nature. And no way in hell would we either get (1) the research approved, or (2) the program implemented here in the USA (what with the READING AND MATH UBER ALLES!! approach to education that comes down from the political wing these days).