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 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 cooperating with one another，without any hints 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 outperformed"the first． The apparent struggles of the second 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 meet with 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． 59．Why does the author call the learning process a paradox？　 　 A．Pains do not necessarily lead to gains． B．What is learned is rarely applicable in life． C．Failure more often than not breeds success． D．The more is taught，the less is learned． 60．What does Kapur disapprove of in teaching？　 　 A．Asking students to find and solve problems on their own． B．Developing students ability to apply what they learn． C．Giving students detailed guidance and instruction． D．Allowing students a free hand in problem solving． 61．What kind of problem should be given to students to solve according to Kapur？　 　 A．It should be able to encourage collaborative learning． B．It should be easy enough so as not to frustrate students． C．It should be solvable by average students with ease． D．It should be difficult enough but still within their reach． 62．What can be expected of this tough﹣love teaching style？　 　 A．Students will be grateful in the long run． B．Teachers will meet with a lot of resistance． C．Parents will think it too harsh on their kids． D．It may not be able to yield the desired results．

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 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 cooperating with one another，without any hints 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 outperformed"the first．

The apparent struggles of the second 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 meet with 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．

59．Why does the author call the learning process a paradox？　   　

A．Pains do not necessarily lead to gains．

B．What is learned is rarely applicable in life．

C．Failure more often than not breeds success．

D．The more is taught，the less is learned．

60．What does Kapur disapprove of in teaching？　   　

A．Asking students to find and solve problems on their own．

B．Developing students ability to apply what they learn．

C．Giving students detailed guidance and instruction．

D．Allowing students a free hand in problem solving．

61．What kind of problem should be given to students to solve according to Kapur？　   　

A．It should be able to encourage collaborative learning．

B．It should be easy enough so as not to frustrate students．

C．It should be solvable by average students with ease．

D．It should be difficult enough but still within their reach．

62．What can be expected of this tough﹣love teaching style？　   　

A．Students will be grateful in the long run．

B．Teachers will meet with a lot of resistance．

C．Parents will think it too harsh on their kids．

D．It may not be able to yield the desired results．