The problem with your comment is that busywork is not (and never has been) mathematical weight lifting. You don't gain thinking skills by memorizing multiplicat

The problem with your comment is that busywork is not (and never has been) mathematical weight lifting. You don't gain thinking skills by memorizing multiplication tables or practicing adding fractions, you gain it by solving problems you don't know how to solve. Of course it's not enough to state something, but making the students reiterate what you've stated a hundred times is only marginally better. Another problem is that no student really learns ANYTHING until they need to use it to do something else. No student learns fractions until they need to use it to do algebra, and they don't learn algebra until they need it to do calculus. And they don't learn calculus until they need it to do engineering/physics or higher mathematics (real analysis, which they don't really learn until they do measure theory...).