{"id":2025,"date":"2023-12-07T16:14:54","date_gmt":"2023-12-08T00:14:54","guid":{"rendered":"https:\/\/theothermath.com\/?p=2025"},"modified":"2024-05-03T07:24:57","modified_gmt":"2024-05-03T14:24:57","slug":"inserting-productive-failure-into-your-mathematics-lessons","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2023\/12\/07\/inserting-productive-failure-into-your-mathematics-lessons\/","title":{"rendered":"Inserting Productive Failure into your Mathematics Lessons"},"content":{"rendered":"<p align=\"left\">Check this out! <a href=\"https:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/10508406.2011.591717\"><img loading=\"lazy\" class=\"alignright wp-image-2026\" src=\"https:\/\/www.theothermath.com\/wp-content\/uploads\/2023\/12\/struggle.png\" alt=\"\" width=\"352\" height=\"543\" srcset=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/12\/struggle.png 900w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/12\/struggle-194x300.png 194w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/12\/struggle-663x1024.png 663w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/12\/struggle-768x1185.png 768w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><\/a><\/p>\n<p align=\"left\">Students were randomly assigned to experience 1 of 2 conditions:<\/p>\n<ul>\n<li>Productive Failure (PF), in which students collaboratively solved complex problems\u00a0without\u00a0any instructional support or scaffolds; or<\/li>\n<li>Direct Instruction (DI), in which the teacher provided strong instructional support, scaffolding, and feedback.<\/li>\n<\/ul>\n<p align=\"left\">Findings showed that although PF students generated pictorial representations and methods for solving the problems, they were ultimately unsuccessful in their problem-solving efforts. Yet despite seemingly failing in their initial problem-solving efforts, PF students significantly outperformed DI students on the posttest.<\/p>\n<p align=\"left\">PF students also demonstrated greater representation flexibility in solving problems involving graphical representations, a representation that was not targeted during instruction.<\/p>\n<p align=\"left\">The 2nd and 3rd studies, conducted in schools with students of significantly lower mathematical ability, largely replicated the findings of the 1st study.<\/p>\n<p align=\"left\">More recently, <a href=\"https:\/\/drive.google.com\/file\/d\/1nHY4jf3cYMjE3kYmuosnZwq01BEH-YFz\/view?usp=sharing\" target=\"_blank\" rel=\"noopener\"><strong>additional studies<\/strong><\/a> suggest the benefits of PF over DI extends to students at the elementary grades as well.<\/p>\n<h3 align=\"left\">So how do you design your math lessons to take advantage of this new evidence?<\/h3>\n<p align=\"left\">Here are some discrete steps for you to try:<\/p>\n<ol>\n<li>Introduce the story problem to students<\/li>\n<li>Students work independently on the problem at their desks.\n<ul>\n<li>Students may use manipulatives, pictures, and\/or number sentences to represent the problem.<\/li>\n<li>While students are working, teacher &#8220;teaches between the seats&#8221; to support students as needed<\/li>\n<li>(REMEMBER: it is not important for every student to be successful with this problem.)<\/li>\n<\/ul>\n<\/li>\n<li>Select two or three students to share their thinking.\n<ul>\n<li>Strategically sequence the order in which the two or three students will share.<\/li>\n<li>Arrange the student solution methods from left to right on the whiteboard.<\/li>\n<li>Allow the class some time to compare and contrast between the various solution methods<\/li>\n<\/ul>\n<\/li>\n<li>The teacher now teaches a mini-lesson to show students what they will try to do in the NEXT problem.\n<ul>\n<li>Connect the student-generated solution methods to the lesson objective<\/li>\n<li>Be explicit about what you want students to try on the next problem.<\/li>\n<\/ul>\n<\/li>\n<li>Introduce Problem #2 for students to work on.\n<ul>\n<li>This cycle continues for Problem #2 and possibly Problem #3 (if needed):<br \/>\nIntroduce problem \u2192 Students work independently \u2192 Students share \u2192 Teach mini-lesson<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p align=\"left\"><img loading=\"lazy\" class=\"alignnone \" src=\"https:\/\/docs.google.com\/drawings\/d\/e\/2PACX-1vRwWoass-lrMsI__sNOPHtGrYe7mXfYoTE78S799JqPDdsM4cMaH4sJopJLsGqdtgR5dXrJd9KIIehY\/pub?w=1442&amp;h=1008\" width=\"757\" height=\"529\" \/><\/p>\n<p align=\"left\">Do you want to learn more about how can you teach YOUR students through Productive Failure?\u00a0\u00a0You can read more about it <strong><a href=\"https:\/\/theothermath.com\/index.php\/2017\/12\/04\/infinite-insights-episode-9-pisa-question-1\" target=\"_blank\" rel=\"noopener\">here<\/a><\/strong>\u00a0and\u00a0<strong><a href=\"https:\/\/theothermath.com\/index.php\/2022\/10\/17\/flipping-the-script-you-do-we-do-i-do\" target=\"_blank\" rel=\"noopener\">here<\/a><\/strong>\u00a0and\u00a0<strong><a href=\"https:\/\/theothermath.com\/index.php\/2023\/09\/05\/a-formula-for-inquiry-and-direct-instruction\" target=\"_blank\" rel=\"noopener\">here<\/a><\/strong>\u00a0and\u00a0<strong><a href=\"https:\/\/theothermath.com\/index.php\/2023\/09\/12\/planning-a-bansho-lesson\" target=\"_blank\" rel=\"noopener\">here<\/a><\/strong>.<\/p>\n<p align=\"left\"><a href=\"mailto:dhabecker@mcoe.org\" target=\"_blank\" rel=\"noopener\">Contact us<\/a>\u00a0if you want to learn more!<\/p>\n<p align=\"left\">.<\/p>\n<p align=\"left\">.<\/p>\n<p align=\"left\">.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Check this out! Students were randomly assigned to experience 1 of 2 conditions: Productive Failure (PF), in which students collaboratively solved complex problems\u00a0without\u00a0any instructional support or scaffolds; or Direct Instruction (DI), in which the teacher provided strong instructional support, scaffolding, and feedback. Findings showed that although PF students generated pictorial representations and methods for solving [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2031,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[87,97,46,99,98],"_links":{"self":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/2025"}],"collection":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/comments?post=2025"}],"version-history":[{"count":5,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/2025\/revisions"}],"predecessor-version":[{"id":2032,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/2025\/revisions\/2032"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media\/2031"}],"wp:attachment":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media?parent=2025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/categories?post=2025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/tags?post=2025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}