Call it the “learning paradox”, the more you struggle and even fail while you're trying to learn new information, the better you're likely to recall and apply that information later.

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　The learning paradox is at the heart of “productive failure”.a phenomenon identified by researcher Manu Kapur. Kapur points out that while the model adopted by many teachers when introducing students to new knowledge―providing lots of structure and guidance early on, until the students show that they can do it on their own―makes intuitive sense, it may not be the best way to promote learning. Rather, it's better to let the learners wrestle with the material on their own for a while, refraining from giving them any assistance at the start. In a paper published recently, Kapur applied the principle of productive failure to mathematical problem solving in three schools.

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　With one group of students, the teacher provided strong “scaffolding”―instructional support—and feedback. With the teacher's help, these pupils were able to find the answers to their set of problems. Meanwhile, a second group was directed to solve the same problems by collaborating with one another, without any prompts from their instructor. These students weren't able to complete the problems correctly. But in the course of trying to do so, they generated a lot of ideas about the nature of the problems and about what potential solutions would look like. And when the two groups were tested on what they'd learned, the second group “significantly out performed” the first. The apparent struggles of the floundering group have what Kapur calls a “hidden efficacy”: they lead people to understand the deep structure of problems, not simply their correct solutions. When these students encounter a new problem of the same type on a test, they're able to transfer the knowledge they've gathered more effectively than those who were the passive recipients of someone else's expertise.

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　In the real world, problems rarely come neatly packaged, so being able to discern their deep structure is key. But, Kapur notes, none of us like to fail, no matter how often Silicon Valley entrepreneurs praise the beneficial effects of an idea that fails or a start-up company that crashes and burns. So we need to “design for productive failure” by building it into the learning process. Kapur has identified three conditions that promote this kind of beneficial struggle. First, choose problems to work on that“challenge but do not frustrate”. Second, provide learners with opportunities to explain and elaborate on what they're doing. Third, give learners the chance to compare and contrast good and bad solutions to the problems. And to those students who protest this tough-love teaching style: you'll thank me later.