Just read about ability-grouping vs. mixed-ability classes.
Of course, when you first think about it, grouping the students by their ability levels in mathematics and placing them in classes with those who display similar achievement seems like the most logical approach. It would allow teachers to teach at one pace and everyone would be able to keep up. However, America uses this ability-grouping approach on a widespread level, and the mathematical achievement of American students is at 19th out of 38 countries according to the latest TIMSS assessment in 2007 (according to Boaler, the author of this book I am reading). The countries that scored highest, including Finland and Korea, used mixed-ability approaches. The evidence that the mixed-ability approach of teaching mathematics (where open-ended problems are used so students can work together on complex problems, allowing them to work up to their own levels of the problem) is the most effective is overwhelming. Throughout Boaler's longitudinal studies, she has uncovered that students who were taught in mixed-ability classes are much more successful in life.
You probably didn't read all of this, but it just seems so clear to me since I have been in this class: mathematics education in the United States needs to be changed drastically. Students are put into groups from the beginning, based on their very early signs of understanding, and these groups will continue to limit them for the rest of their lives, determining which math classes they will take, and ultimately closing doors for them in terms of where they will be able to go to college, what they will choose to study, and so forth. The system of mathematics teaching in America honestly makes students hate math. America will never improve their rankings in mathematical success among other countries if they do not change the system they use to educate.
