I've figured out why we have so much trouble with mathematics education here in the United States. It's because for years teachers of mathematics have been teaching their students that 0.9 is greater than 0.1. I'll even sheepishly admit that I've taught it that way in my classes as well.
But I have incontrovertible proof that it's actually the other way around. What's my proof? Well, in thousands of staff meetings and PLC's around the country this time of year, teachers are being told that 0.1 is greater than 0.9. Let me illustrate.
Picture two students who take the same state-mandated, standards-based test. One student scores a 2.0 and the other scores a 2.9. Based on the scale that has been setup, both those students are grouped in the "Partially Proficient" category. In order to be considered "Proficient," students must score a 3.0 or higher. This is where the faculty meetings, PLC's, and the mathematics comes in. Teachers are being told how important it is to get the 2.9 student up to a 3.0; how we should be focusing on those students who are really close to the Proficient level (often referred to, lovingly of course, as "bubble kids") and developing strategies to nudge them up over the 3.0 barrier.
The student who scored 2.0, however, well that's a tougher sell. You see, to move that student from the Partially Proficient to the Proficient category would require an increase of 1.0 and that's really, really difficult to do. We could raise that student's score by a dramatic 0.9 and it still wouldn't do us (I mean them, of course I mean them) any good because they'd still be Partially Proficient. Increasing the 2.9 student by 0.1 is greater than increasing the 2.0 student by 0.9.
Now, I know what you're thinking. You're thinking that the actual impact on the 2.9 student's life from moving her to 3.0 is probably non-existent (and also probably statistically suspect), whereas the impact on a 2.0 student's life of advancing her to a 2.9 could be significant (assuming, of course, that standard is worth improving on for that student's needs and interests).
But you'd be missing the point. Or at least 0.8 of the point.