{"id":7319,"date":"2020-06-10T16:38:23","date_gmt":"2020-06-10T16:38:23","guid":{"rendered":"https:\/\/www.mathsweek.ie\/2019\/?page_id=7319"},"modified":"2021-11-26T11:30:11","modified_gmt":"2021-11-26T11:30:11","slug":"developing-problem-solving-skills","status":"publish","type":"page","link":"https:\/\/www.mathsweek.ie\/2025\/developing-problem-solving-skills\/","title":{"rendered":"Developing Problem Solving Skills"},"content":{"rendered":"<p><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 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:0px;padding-right:0px;padding-bottom:0px;padding-left:0px;margin-bottom: 0px;margin-top: 0px;border-width: 0px 0px 0px 0px;border-color:#eaeaea;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_4 1_4 fusion-one-fourth fusion-column-first\" style=\"width:25%;width:calc(25% - ( ( 4% + 4% + 4% ) * 0.25 ) );margin-right: 4%;margin-top:0px;margin-bottom:20px;\"><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-align-block\"><style type=\"text\/css\">.fusion-button.button-1 {border-radius:2px;}<\/style><a class=\"fusion-button button-flat fusion-button-default-size button-default button-1 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.mathsweek.ie\/2025\/problem-solving-skills\/\"><span class=\"fusion-button-text\">1. Problem Solving Introduction<\/span><\/a><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-1 fusion_builder_column_1_4 1_4 fusion-one-fourth\" style=\"width:25%;width:calc(25% - ( ( 4% + 4% + 4% ) * 0.25 ) );margin-right: 4%;margin-top:0px;margin-bottom:20px;\"><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-align-block\"><style type=\"text\/css\">.fusion-button.button-2 {border-radius:2px;}<\/style><a class=\"fusion-button button-flat fusion-button-default-size button-default button-2 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.mathsweek.ie\/2025\/developing-problem-solving-skills\/\"><span class=\"fusion-button-text\">2. Developing Problem Solving Skills<\/span><\/a><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-2 fusion_builder_column_1_4 1_4 fusion-one-fourth\" style=\"width:25%;width:calc(25% - ( ( 4% + 4% + 4% ) * 0.25 ) );margin-right: 4%;margin-top:0px;margin-bottom:20px;\"><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-align-block\"><style type=\"text\/css\">.fusion-button.button-3 {border-radius:2px;}<\/style><a class=\"fusion-button button-flat fusion-button-default-size button-default button-3 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.mathsweek.ie\/2025\/encourage-reflective-thinking\/\"><span class=\"fusion-button-text\">Next: Encouraging Reflective Thinking<\/span><\/a><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-3 fusion_builder_column_1_4 1_4 fusion-one-fourth fusion-column-last\" style=\"width:25%;width:calc(25% - ( ( 4% + 4% + 4% ) * 0.25 ) );margin-top:0px;margin-bottom:20px;\"><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-align-block\"><style type=\"text\/css\">.fusion-button.button-4 {border-radius:2px;}<\/style><a class=\"fusion-button button-flat fusion-button-default-size button-default button-4 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.mathsweek.ie\/2025\/problem-solving-skills-session\/\"><span class=\"fusion-button-text\">4. Problem Solving Skills Section<\/span><\/a><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-4 fusion_builder_column_1_1 1_1 fusion-one-full fusion-column-first fusion-column-last\" style=\"margin-top:0px;margin-bottom:20px;\"><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-sep-clear\"><\/div><div class=\"fusion-separator fusion-full-width-sep\" style=\"margin-left: auto;margin-right: auto;width:100%;\"><div class=\"fusion-separator-border sep-double\" style=\"border-color:#eaeaea;border-top-width:1px;border-bottom-width:1px;\"><\/div><\/div><div class=\"fusion-sep-clear\"><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-5 fusion_builder_column_1_2 1_2 fusion-one-half fusion-column-first\" style=\"width:50%;width:calc(50% - ( ( 4% ) * 0.5 ) );margin-right: 4%;margin-top:0px;margin-bottom:20px;\"><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;\"><style type=\"text\/css\"><\/style><div class=\"fusion-title title fusion-title-1 fusion-title-text fusion-title-size-one\" style=\"margin-top:0%;margin-right:0px;margin-bottom:30px;margin-left:0px;\"><h1 class=\"title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:50;line-height:1.2;\"><h2>2. Developing Problem Solving Skills<\/h2><\/h1><div class=\"title-sep-container\"><div class=\"title-sep sep-single sep-solid\" style=\"border-color:#eaeaea;\"><\/div><\/div><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-6 fusion_builder_column_1_2 1_2 fusion-one-half fusion-column-last\" style=\"width:50%;width:calc(50% - ( ( 4% ) * 0.5 ) );margin-top:0px;margin-bottom:20px;\"><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;\"><span class=\" fusion-imageframe imageframe-none imageframe-1 hover-type-none\"><img decoding=\"async\" width=\"400\" height=\"400\" title=\"Problem Solving\" src=\"https:\/\/www.mathsweek.ie\/2025\/wp-content\/uploads\/2021\/11\/Problem-Solving.png\" class=\"img-responsive wp-image-11119\" srcset=\"https:\/\/www.mathsweek.ie\/2025\/wp-content\/uploads\/2021\/11\/Problem-Solving-200x200.png 200w, https:\/\/www.mathsweek.ie\/2025\/wp-content\/uploads\/2021\/11\/Problem-Solving.png 400w\" sizes=\"(max-width: 800px) 100vw, 400px\" \/><\/span><div class=\"fusion-clearfix\"><\/div><\/div><\/div><\/div><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-2 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:0px;padding-right:0px;padding-bottom:0px;padding-left:0px;margin-bottom: 0px;margin-top: 0px;border-width: 0px 0px 0px 0px;border-color:#eaeaea;border-style:solid;\" ><div class=\"fusion-builder-row fusion-row\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-7 fusion_builder_column_1_2 1_2 fusion-one-half fusion-column-first\" style=\"width:50%;width:calc(50% - ( ( 4% ) * 0.5 ) );margin-right: 4%;margin-top:0px;margin-bottom:20px;\"><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;\"><style type=\"text\/css\"><\/style><div class=\"fusion-title title fusion-title-2 fusion-title-text fusion-title-size-one\" style=\"margin-top:0%;margin-right:0px;margin-bottom:30px;margin-left:0px;\"><h1 class=\"title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:50;line-height:1.2;\"><h4>Problems and Puzzles: Using puzzles to develop problem solving skills<\/h4><\/h1><div class=\"title-sep-container\"><div class=\"title-sep sep-single sep-solid\" style=\"border-color:#eaeaea;\"><\/div><\/div><\/div><div class=\"fusion-sep-clear\"><\/div><div class=\"fusion-separator fusion-full-width-sep\" style=\"margin-left: auto;margin-right: auto;width:100%;\"><div class=\"fusion-separator-border sep-double\" style=\"border-color:#eaeaea;border-top-width:1px;border-bottom-width:1px;\"><\/div><\/div><div class=\"fusion-sep-clear\"><\/div><div class=\"fusion-text fusion-text-1\"><p><strong>What is Problem Solving?<\/strong><\/p>\n<p>Problem Solving is defined as \u201cthe process of finding solutions to difficult or complex issues\u201d. In a more mathematical sense problem solving is \u201cthe ability to analyse mathematical situations; to plan, monitor and evaluate solutions; to apply strategies; and to demonstrate creativity and self-reliance in using mathematics\u201d (Irish Primary School Curriculum Mathematics 1999, p.8).<\/p>\n<p>Problem Solving is not only limited to solving equations or finding the solutions to mathematical questions. Problem Solving is much more \u2013 we all solve problems daily when are going shopping or deciding what to wear. Sometimes we might not even be aware of it.<\/p>\n<\/div><div class=\"fusion-text fusion-text-2\"><p><strong>Problems vs exercises:<\/strong><\/p>\n<p>An <strong>exercise<\/strong> is a challenge where you know the method and you are given practice using the method or slight variations on the method.<\/p>\n<p>A <strong>problem<\/strong> is a challenge where it is not immediately obvious to one how to proceed. It is important to solve problems of increasing difficulty, only then is learning activated \u2013 if you keep solving problems of the same difficulty, they simply become routine exercises.<\/p>\n<p>A <strong>puzzle<\/strong> is a problem specifically designed to challenge the solver. It may have purposeful misdirection or pitfalls built in by the puzzle maker. Puzzles have a recreational purpose and often include a contrived and amusing situation.<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-8 fusion_builder_column_1_2 1_2 fusion-one-half fusion-column-last\" style=\"width:50%;width:calc(50% - ( ( 4% ) * 0.5 ) );margin-top:0px;margin-bottom:20px;\"><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-3\"><p><strong>Why we use puzzles?<\/strong><\/p>\n<p>Puzzles act as a fun educational tool that can boost self-confidence and self-esteem. By including puzzles into teaching and learning at home, it offers a great opportunity for families to work together as they pool their knowledge, skills, and efforts to reach a solution. Once that solution has been reached the sense of achievement and satisfaction is gratifying and uplifting.<\/p>\n<p>Puzzles can strengthen skills such as lateral thinking, innovation, deductive reasoning, open mindedness, and attention to detail; all these skills are easily transferred into the maths class and beyond as students become more adaptable and creative problem solvers.<\/p>\n<\/div><div class=\"fusion-text fusion-text-4\"><p>Strategies that are often applied to solve problems are:<\/p>\n<ul>\n<li>Trial and error<\/li>\n<li>Change your point of view<\/li>\n<li>Work backwards<\/li>\n<li>Find intermediate points, work step by step<\/li>\n<li>Eliminate what is impossible<\/li>\n<li>Work with simplifications<\/li>\n<li>Look for patterns, symmetry<\/li>\n<li>Make a list or prepare a table of data<\/li>\n<li>Draw a picture<\/li>\n<li>Make a physical model<\/li>\n<\/ul>\n<p>This list is by no means exhaustive but can be a starting point. Several of these may be applied to the same problem individually or sequentially.<\/p>\n<p>Our philosophy is to guide the students to \u201cdiscovering\u201d these strategies themselves rather than handing them a toolkit. A reflective discussion should be facilitated so that students can explore and discover the many strategies used by the different groups of students.<\/p>\n<p>In this way they<\/p>\n<ul>\n<li>Better appreciate and remember the strategies<\/li>\n<li>Build confidence<\/li>\n<li>Develop the habit of reflecting<\/li>\n<\/ul>\n<p>It is important to emphasise the ultimate aim is not to solve the puzzles, but to develop a toolkit of strategies that will be useful with other problems.<\/p>\n<p>Pupils that are fast at solving problems and are in the habit of tossing them aside once they have solved them may miss the opportunity to develop their skills.<\/p>\n<p>It is perseverance and reflection that are important in becoming a great problem solver.<\/p>\n<\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-9 fusion_builder_column_1_1 1_1 fusion-one-full fusion-column-first fusion-column-last\" style=\"margin-top:0px;margin-bottom:20px;\"><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-sep-clear\"><\/div><div class=\"fusion-separator fusion-full-width-sep\" style=\"margin-left: auto;margin-right: auto;width:100%;\"><div class=\"fusion-separator-border sep-double\" style=\"border-color:#eaeaea;border-top-width:1px;border-bottom-width:1px;\"><\/div><\/div><div class=\"fusion-sep-clear\"><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-10 fusion_builder_column_1_4 1_4 fusion-one-fourth fusion-column-first\" style=\"width:25%;width:calc(25% - ( ( 4% + 4% + 4% ) * 0.25 ) );margin-right: 4%;margin-top:0px;margin-bottom:20px;\"><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-align-block\"><style type=\"text\/css\">.fusion-button.button-5 {border-radius:2px;}<\/style><a class=\"fusion-button button-flat fusion-button-default-size button-default button-5 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.mathsweek.ie\/2025\/problem-solving-skills\/\"><span class=\"fusion-button-text\">1. Problem Solving Introduction<\/span><\/a><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-11 fusion_builder_column_1_4 1_4 fusion-one-fourth\" style=\"width:25%;width:calc(25% - ( ( 4% + 4% + 4% ) * 0.25 ) );margin-right: 4%;margin-top:0px;margin-bottom:20px;\"><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-align-block\"><style type=\"text\/css\">.fusion-button.button-6 {border-radius:2px;}<\/style><a class=\"fusion-button button-flat fusion-button-default-size button-default button-6 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.mathsweek.ie\/2025\/developing-problem-solving-skills\/\"><span class=\"fusion-button-text\">2. Developing Problem Solving Skills<\/span><\/a><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-12 fusion_builder_column_1_4 1_4 fusion-one-fourth\" style=\"width:25%;width:calc(25% - ( ( 4% + 4% + 4% ) * 0.25 ) );margin-right: 4%;margin-top:0px;margin-bottom:20px;\"><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-align-block\"><style type=\"text\/css\">.fusion-button.button-7 {border-radius:2px;}<\/style><a class=\"fusion-button button-flat fusion-button-default-size button-default button-7 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.mathsweek.ie\/2025\/encourage-reflective-thinking\/\"><span class=\"fusion-button-text\">Next: Encouraging Reflective Thinking<\/span><\/a><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-13 fusion_builder_column_1_4 1_4 fusion-one-fourth fusion-column-last\" style=\"width:25%;width:calc(25% - ( ( 4% + 4% + 4% ) * 0.25 ) );margin-top:0px;margin-bottom:20px;\"><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-align-block\"><style type=\"text\/css\">.fusion-button.button-8 {border-radius:2px;}<\/style><a class=\"fusion-button button-flat fusion-button-default-size button-default button-8 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.mathsweek.ie\/2025\/problem-solving-skills-session\/\"><span class=\"fusion-button-text\">4. Problem Solving Skills Session<\/span><\/a><\/div><div class=\"fusion-clearfix\"><\/div><\/div><\/div><\/div><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"class_list":["post-7319","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Developing Problem Solving Skills &#8211; MATHS WEEK IRELAND<\/title>\n<meta name=\"description\" content=\"Maths Week will take place from 11 - 19 Oct. 2025. We will have events and activities for all the family. 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