Originally Posted by
spopepro
I'll do my best. One of the things that's hard about knowing facts of education is that the gold standard, double-blind, clinical, replicable studies can't really be done with real kids and real classrooms. So often the best we can do is conduct loads of observational studies, and later gather them all up in a metaanalysis and identify consistent trends. Therefore we as practitioners largely depend on our professional orginizations (like the National Council of Teachers of Mathematics) to provide us with advisory and position papers based on quality metaanalysis of loads of observational studies. Why am I saying this? Because there isn't any solid proof of what I'm about to say. It's our best understanding, and our understanding is always being advanced and amended.
Mathematics, when done correctly, is a challenging topic because it's about making meaning out of abstract ideas. When I was in my PhD program we would say "all of mathematics is either impossible or trivial" and that's true at all levels. There is little "ramp" as you build knowledge like in other areas. Math doesn't make any sense, you don't know what to do, you don't know how to get started, and then all of a sudden it clicks and you don't know how anyone couldn't understand. Note: this is about math, not arithmetic or computation. Computation is easy and fastest to teach by rote practice, but is largely unimportant because of calculators and computer solvers. Yes, know how to do it, and why it works, but the important parts are defining the problem, using the correct informations, setting up the problem, knowing your answer is accurate, and justifying your method to someone else. Second note: this is really what the common core standards in math attempt to do.
So... since this is about making meaning and problem solving the best way to do so is through exploring problems, writing and taking about the problems, and then applying ideas to a variety of situations. The most effective problems and activities have multiple methods and multiple solutions. This makes small groups of students working collaboratively (not cooperatively, there's a difference) a really effective way for students to learn. These collaborative work times are most valuable when there's a large diversity of ideas to stimulate rich discussion. This is why a wide range of abilities and experiences lifts the quality of learning for all students in a math classroom.
The studies that have been conducted generally support this. High performing students in heterogeneous classrooms perform the same to very slightly worse. The rest of the students perform better to significantly better. There's also the issue of isolating groups of students. In our district, which is 35% Hispanic or Latino, the grade level math classes were 41% Hispanic or Latino and with the new process these classes are now 60% Hispanic or Latino. It's generally not good to have official policies that help concentrate racial isolation, whether intended or not.
Now all that said (and holy crap am I rambling) this is all kind of predicated on teachers being able to correctly teach. If they are reverting to algorithmic, computational methods, then tracking and separating will probably end up being better. But industry and universities (and the general public) have said over and over again that our students need to learn to think, solve problems, collaborate, and communicate. If I'm being honest... we don't yet have the talent in our teaching ranks to consistently do this well. And as such all these "best practices" might all be for naught. What I'm trying to do is to provide training and support to improve the professional capacity of teachers, provide the right classroom structures and schedules to give all students the best learning environment collectively, and not stomp on anyone's civil rights.
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