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Two randomized\u2010controlled studies found that both methods lead to high levels of procedural knowledge. However, students who engaged in problem solving before being taught demonstrated significantly greater conceptual understanding and ability to transfer to novel problems than those who were taught first. The second study further showed that when given an opportunity to learn from the failed problem\u2010solving attempts of their peers, students outperformed those who were taught first, but not those who engaged in problem solving first. Process findings showed that the number of student\u2010generated solutions significantly predicted learning outcomes. These results challenge the conventional practice of direct instruction to teach new math concepts and procedures, and propose the possibility of learning from one's own failed problem\u2010solving attempts or those of others before receiving instruction as alternatives for better math learning.<\/jats:p>","DOI":"10.1111\/cogs.12107","type":"journal-article","created":{"date-parts":[[2014,3,14]],"date-time":"2014-03-14T05:51:00Z","timestamp":1394776260000},"page":"1008-1022","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":337,"title":["Productive Failure in Learning Math"],"prefix":"10.1111","volume":"38","author":[{"given":"Manu","family":"Kapur","sequence":"first","affiliation":[{"name":"National Institute of Education Nanyang Technological University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2014,3,14]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cognition.2010.10.001"},{"key":"e_1_2_7_3_1","volume-title":"How people learn: Brain, mind, experience and school","author":"Bransford J. 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