{"id":4047,"date":"2019-08-21T23:44:23","date_gmt":"2019-08-21T23:44:23","guid":{"rendered":"https:\/\/www.mathletics.com\/blog\/?p=4047"},"modified":"2023-05-08T07:29:43","modified_gmt":"2023-05-08T07:29:43","slug":"how-the-best-teachers-tackle-problem-solving-and-reasoning","status":"publish","type":"post","link":"https:\/\/www.mathletics.com\/blog\/educators\/how-the-best-teachers-tackle-problem-solving-and-reasoning\/","title":{"rendered":"How the Best Teachers Tackle Problem-Solving and Reasoning"},"content":{"rendered":"<p><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 has-pattern-background has-mask-background nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"background-color: rgba(255,255,255,0);background-position: center center;background-repeat: no-repeat;padding-top:5%;padding-right:0%;padding-bottom:5%;padding-left:0%;margin-bottom: 0px;margin-top: -5%;border-width: 0px 0px 0px 0px;border-color:#eae9e9;border-style:solid;\" ><div class=\"fusion-builder-row fusion-row\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-one-full fusion-column-first fusion-column-last\" style=\"margin-top:0%;margin-bottom:0%;\"><div class=\"fusion-column-wrapper fusion-flex-column-wrapper-legacy\" style=\"background-position:left top;background-repeat:no-repeat;-webkit-background-size:cover;-moz-background-size:cover;-o-background-size:cover;background-size:cover;padding: 0px 0px 0px 0px;\"><div class=\"fusion-text fusion-text-1\"><p>Problem-solving and reasoning (PSR) can be daunting when you\u2019re teaching it for the first or hundredth time.<\/p>\n<p>Teaching PSR is an art, and like any art, there are solid foundation of principles you can follow and expand upon as your confidence grows.<\/p>\n<p>Here\u2019s how the best teachers take PSR to their students:<\/p>\n<\/div><div class=\"fusion-text fusion-text-2\"><h3 style=\"margin-bottom: 16px !important\">1. They get prepared<\/h3>\n<p>Treat PSR lessons like interactive stories and you\u2019ll see where the strengths and gaps are in your lesson. You can try:<\/p>\n<h2>Running a practice lesson<\/h2>\n<p>In your head, in the shower, in front of the most convenient mirror \u2013 wherever suits.<\/p>\n<p>Think about:<\/p>\n<ul>\n<li>How can I introduce the lesson?<\/li>\n<li>How do I begin the activity?<\/li>\n<li>How might students answer the questions?<\/li>\n<li>What do I want them to achieve by the end?<\/li>\n<\/ul>\n<p>Going through these key questions can help you find any stumbling blocks and gives you a good idea of the path you\u2019ll be following from beginning to end. For the middle, you\u2019ll want to make sure you\u2019ve got every student engaged. To do this you can try:<\/p>\n<h2>Finding compelling motivators<\/h2>\n<p>Get students hooked on the problem, and they will follow the entire lesson.<\/p>\n<p>Think about:<\/p>\n<ul>\n<li>How can I spark curiosity?<\/li>\n<li>What is the intrinsic motivator?<\/li>\n<li>Where can I give the class control over the problem?<\/li>\n<li>Am I passionate about the problem?<\/li>\n<\/ul>\n<p>Reaching this level of personal investment is about understanding your students \u2013 what matters to them? It might be a character in the activity you\u2019re trying to help, or the goal of the activity, or the fact they can follow the problem in a way that speaks to them.<\/p>\n<p>Your passion is important. It\u2019s infectious. It\u2019s emotive. It makes the lesson feel more personal.<\/p>\n<p>The closer the activity is to their heart, the more effort they\u2019ll put into finding solutions.<\/p>\n<\/div><div class=\"fusion-text fusion-text-3\"><h3 style=\"margin-bottom: 16px !important\">2. They hone questions into learning experiences<\/h3>\n<p>The best PSR questions aren\u2019t the item in the middle \u2013 they\u2019re the ones that prompt students into action. Give less information, support the strugglers, and scaffold the successful to turn questions into organic learning experiences.<\/p>\n<h2>Use less as more<\/h2>\n<p>You can give information, but you can\u2019t take it away.<\/p>\n<p>Give students enough space to figure things out on their own. This will give you an idea of who\u2019s getting stuck, and who needs scaffolding.<\/p>\n<h2>Support the strugglers<\/h2>\n<p>Have a series of questions up your sleeve that can support understanding \u2013 think about how you can reframe questions, approaches or knowledge of the concepts. Sometimes it\u2019s down to how it\u2019s said rather than what is said.<\/p>\n<h2>Scaffold the successful<\/h2>\n<p>Don\u2019t let them get comfortable!<\/p>\n<p>If they\u2019re flying through, sprinkle in questions that will force them to pause. Try asking them hypotheticals, \u2018what if?\u2019 or \u2018does that always work?\u2019, or throw them a new challenge like \u2018what would it look like as a diagram?\u2019<\/p>\n<h2>And a few other things to keep in mind\u2026<\/h2>\n<ul>\n<li>Again, be prepared! Having a series of prepped questions will create a learning journey you can take your class on.<\/li>\n<li>Resist the urge to give students answers. Let them walk down the path you\u2019ve created in their own way and time.<\/li>\n<li>Confuse students a little \u2013 wrestling with concepts turns general understanding into deeper knowledge.<\/li>\n<li>Group questioning should encourage discussion and debate! This sharing and challenging of ideas show students how different thinking can be between them.<\/li>\n<\/ul>\n<\/div><div class=\"fusion-text fusion-text-4\"><h3 style=\"margin-bottom: 16px !important\">3. They group according to the activity<\/h3>\n<p>Suit your class to the activity. Think through and see if the activity, or what parts of the activity, are best-left solo, or in pairs, or by tables, or by ability levels and so on.<\/p>\n<p>Group activities can inspire a whole new level of creativity with your PSR lesson. You can set each student within groups different roles, tasks or characters if your story-telling is good enough.<\/p>\n<p>One of the best ways to do this is through the <a href=\"\/itali.uq.edu.au\/files\/3077\/Resources-teaching-methods-jigsawtechnique.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Jigsaw Technique<\/a>. It gives students the chance to become temporary experts in a topic before they pass it on to classmates.<\/p>\n<\/div><div class=\"fusion-text fusion-text-5\"><h3 style=\"margin-bottom: 16px !important\">4. They time it just right<\/h3>\n<p>To time PSR lessons, you\u2019ll want to keep three things in mind:<\/p>\n<h2>Know your students<\/h2>\n<p>How long will it take the fastest and slowest students to complete each section? What are the chances of mass distraction breaking out? Having an understanding of how long things might take and when things might go wrong.<\/p>\n<h2>Know your activity<\/h2>\n<p>How long does it take to explain the concepts? How many different ways are you planning to explain questions? How long are they?<\/p>\n<p>Keep a running tally of how long you suspect each part of the lesson might take and use it as a rough guide for your lesson.<\/p>\n<h2>Leave time to reflect<\/h2>\n<p>This is <strong>the most important part <\/strong>of PSR to make time for. Reflecting and giving students the chance to discuss helps them absorb what they\u2019ve just learned.<\/p>\n<\/div><div class=\"fusion-text fusion-text-6\"><h3 style=\"margin-bottom: 16px !important\">5. They reflect themselves<\/h3>\n<p>Now it\u2019s your turn, and immediacy is key.<\/p>\n<p>Get your thoughts on paper make a summary of:<\/p>\n<h2>What worked?<\/h2>\n<p>Note if the lesson:<\/p>\n<ul>\n<li>Sparked interest<\/li>\n<li>Kept them engaged<\/li>\n<li>Was followed the whole way<\/li>\n<\/ul>\n<h2>What didn\u2019t work?<\/h2>\n<p>Note:<\/p>\n<ul>\n<li>Where you might have lost students<\/li>\n<li>If eyes and minds started to wander<\/li>\n<li>If every student was accounted for<\/li>\n<\/ul>\n<h2>What would you like to do next time?<\/h2>\n<p>Take notes on what you\u2019d like to achieve the next time around!<\/p>\n<p>PSR lessons are an iterative process \u2013 you\u2019ll get better from the first to the hundredth time teaching it!<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><\/div><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-2 fusion-flex-container has-pattern-background has-mask-background nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"background-color: rgba(255,255,255,0);background-position: center center;background-repeat: no-repeat;border-width: 0px 0px 0px 0px;border-color:#eae9e9;border-style:solid;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-center\" style=\"max-width:1206.4px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-1 fusion_builder_column_1_1 1_1 fusion-flex-column\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\" style=\"background-position:left top;background-repeat:no-repeat;-webkit-background-size:cover;-moz-background-size:cover;-o-background-size:cover;background-size:cover;border-radius:30px 30px 30px 30px;background-color:#e7f8fe;border-radius:30px 30px 30px 30px;overflow:hidden;padding: 10px 30px 20px 20px;\"><div class=\"fusion-builder-row fusion-builder-row-inner fusion-row fusion-flex-align-items-center\" style=\"width:104% !important;max-width:104% !important;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column_inner fusion-builder-nested-column-0 fusion_builder_column_inner_1_2 1_2 fusion-flex-column fusion-flex-align-self-flex-start\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\" style=\"background-position:left top;background-repeat:no-repeat;-webkit-background-size:cover;-moz-background-size:cover;-o-background-size:cover;background-size:cover;padding: 0px 0px 0px 0px;\"><style type=\"text\/css\">@media only screen and (max-width:1024px) {.fusion-title.fusion-title-1{margin-top:!important; margin-right:0px!important;margin-bottom:!important;margin-left:0px!important;}}@media only screen and (max-width:768px) {.fusion-title.fusion-title-1{margin-top:!important; margin-right:0px!important;margin-bottom:!important; margin-left:0px!important;}}<\/style><div class=\"fusion-title title fusion-title-1 fusion-sep-none fusion-title-text fusion-title-size-six fusion-title-default-margin\" style=\"margin-right:0px;margin-left:0px; margin-top:0px; margin-bottom:0px\"><h6 class=\"title-heading-left fusion-responsive-typography-calculated\" style=\"color:#4f5d67;--fontSize:15;--minFontSize:1em;line-height:1;\"><h2 style=\"text-align: left\">Did you know? Mathletics has 700+ Problem-Solving and Reasoning questions to bring next-level mathematics thinking to your class.<\/h2><\/h6><\/div><div ><style>.fusion-body .fusion-button.button-1 .fusion-button-text,.fusion-body .fusion-button.button-1 i{color:#eef2f5;}.fusion-body .fusion-button.button-1{border-color:#eef2f5;border-radius:30px 30px 30px 30px;background:#efa016;}.fusion-body .fusion-button.button-1:hover .fusion-button-text,.fusion-body .fusion-button.button-1:hover i,.fusion-body .fusion-button.button-1:focus .fusion-button-text,.fusion-body .fusion-button.button-1:focus i,.fusion-body .fusion-button.button-1:active .fusion-button-text,.fusion-body .fusion-button.button-1:active i{color:#efa016;}.fusion-body .fusion-button.button-1:hover,.fusion-body .fusion-button.button-1:active,.fusion-body .fusion-button.button-1:focus{border-color:#efa016;background:#eef2f5;}<\/style><a class=\"fusion-button button-flat fusion-button-default-size button-custom button-1 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screen and (max-width:768px) {.fusion-body .fusion-builder-nested-column-0{width:100% !important;order : 0;}.fusion-builder-nested-column-0 > .fusion-column-wrapper {margin-right : 1.92%;margin-left : 1.92%;}}<\/style><\/div><div class=\"fusion-layout-column fusion_builder_column_inner fusion-builder-nested-column-1 fusion_builder_column_inner_1_2 1_2 fusion-flex-column fusion-flex-align-self-center\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-center fusion-content-layout-column\" style=\"background-position:left top;background-repeat:no-repeat;-webkit-background-size:cover;-moz-background-size:cover;-o-background-size:cover;background-size:cover;padding: 0px 0px 0px 0px;\"><div ><span class=\" fusion-imageframe imageframe-none imageframe-1 hover-type-none\"><img width=\"480\" height=\"375\" alt=\"Problem Solving and Reasoning questions\" title=\"Problem Solving and Reasoning questions\" 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1.92%;}}<\/style><\/div><\/div><\/div><style type=\"text\/css\">.fusion-body .fusion-builder-column-1{width:100% !important;margin-top : 0%;margin-bottom : 0%;}.fusion-builder-column-1 > .fusion-column-wrapper {padding-top : 10px !important;padding-right : 30px !important;margin-right : 1.92%;padding-bottom : 20px !important;padding-left : 20px !important;margin-left : 1.92%;}@media only screen and (max-width:1024px) {.fusion-body .fusion-builder-column-1{width:100% !important;order : 0;}.fusion-builder-column-1 > .fusion-column-wrapper {margin-right : 1.92%;margin-left : 1.92%;}}@media only screen and (max-width:768px) {.fusion-body .fusion-builder-column-1{width:100% !important;order : 0;}.fusion-builder-column-1 > .fusion-column-wrapper {margin-right : 1.92%;margin-left : 1.92%;}}<\/style><\/div><\/div><style type=\"text\/css\">.fusion-body .fusion-flex-container.fusion-builder-row-2{ padding-top : 0px;margin-top : 0px;padding-right : 0%;padding-bottom : 0px;margin-bottom : 0px;padding-left : 0%;}<\/style><\/div>\n<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":22,"featured_media":4049,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[34],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\r\n<title>Problem-solving and Reasoning | How the Best Teachers Tackle Them<\/title>\r\n<meta name=\"description\" content=\"Teaching problem-solving and reasoning effectively relies on these key principles: preparing, honing questions, grouping and timing.\" \/>\r\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\r\n<link rel=\"canonical\" href=\"https:\/\/www.3plearning.com\/blog\/best-teachers-tackle-problem-solving-reasoning\/\" \/>\r\n<meta property=\"og:locale\" content=\"en_US\" \/>\r\n<meta 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