Barry Garelick writes about discovery learning in math at the Nonpartisan Education Review.
Students given well-defined problems that draw upon prior knowledge . . . are doing much more than simply memorizing algorithmic procedures. They are developing the procedural fluency and understanding that are so essential to mathematics; and they are developing the habits of mind that will continue to serve them well in more advanced, college level mathematics courses. Poorly-posed problems with multiple “right” answers turn mathematics into a frustrating guessing game. Similarly, problems for which students are expected to discover what they need to know in the process of solving it do little more than confuse.
Lefty stands accused of “widening the achievement gap” by running an extracurricular Continental Math League club for students who enjoy math. The principal wants a club for kids who aren’t doing well in math. Sounds like fun! Lefty suggests a better math curriculum so fewer kids are confused and struggling.