I've found that most traditional textbooks oversimplify and isolate concepts, and yet, are still too difficult for non-readers to use. They don't generally push students to think, but offer repetitive, and boring, practice.
My primary goal as a teacher is to help my students understand the reasoning behind math rules and procedures. I have several core beliefs about this: (1) Understanding is constructed by the learner, not passively received from the teacher. (2) Understanding is built by making connections between as many strands of knowledge as possible. (3) Understanding is galvanized through communication. (4) Understanding is only valuable when you reflect on it and question it.
My sequence and pace are set by a long-term plan that I have designed to catch the students up on second-, third- and fourth-grade material as well as introduce every single D.C. public schools fifth-grade standard by testing time. I model my word problems after the eighth-grade text that I used in Louisiana because those problems require the level of understanding that I am looking for. I focus on non-traditional problems so that students are forced to think.
She even issues a less-effective kind of praise:
You're brilliant! I can't stand it.
One indication that things might be amiss is:
although Suben's students improved markedly on the nationally standardized test, that was not enough to meet the first-year federal target for No Child Left Behind when they took the new and unusually rigorous D.C. Comprehensive Assessment System test.
but, state tests are often so awful that they are not fair indicators of student knowledge. The D.C. test may be such a test.
I know performance gains of this magnitude in fifth grade math are possible in inner city schools. See the fifth grade performance (pdf) of the City Springs School in Baltimore. But, in one year? In City Springs in took the 2003 fifth grade cohort five years of good teaching to hit this level, using a curriculum that's been tested, retested and revised over the course of thirty years.
In any event, I am having trouble suspending disbelief when I hear things like this
What's the key. It's not that my lessons are so dramatically better than anyone else's lessons. It's just that we, the students and I, own our lessons.
No one who really knows how to teach math effectively says things like that. But, maybe it's just youth speaking. Or, maybe there's a massive disconnect between the rhetoric and the actual teaching.