Our students needs lots and lots of practice STRUGGLING with novel and challenging problems that they are capable of solving. They need to learn to try, fail, try again, struggle, and ultimately succeed. This is reinforced by a recent commentary noted on the New York Times Opinion Page, which demonstrated that students performed better on tests when given practice problems that were not all of the same type:
When students can’t tell in advance what kind of knowledge or problem-solving strategy will be required to answer a question, their brains have to work harder to come up with the solution, and the result is that students learn the material more thoroughly.
This practice is called interleaving and has proven effective in improving students' performance on tests.
A study published last year in the journal Applied Cognitive Psychology asked fourth-graders to work on solving four types of math problems and then to take a test evaluating how well they had learned. The scores of those whose practice problems were mixed up were more than double the scores of those students who had practiced one kind of problem at a time