{"id":7322,"date":"2020-06-10T16:41:55","date_gmt":"2020-06-10T16:41:55","guid":{"rendered":"https:\/\/www.mathsweek.ie\/2019\/?page_id=7322"},"modified":"2021-11-26T11:30:43","modified_gmt":"2021-11-26T11:30:43","slug":"encourage-reflective-thinking","status":"publish","type":"page","link":"https:\/\/www.mathsweek.ie\/2025\/encourage-reflective-thinking\/","title":{"rendered":"Encourage Reflective Thinking"},"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\/developing-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\">3. 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\">Next: Problem Solving Skills Session<\/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><\/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-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;\"><div class=\"fusion-text fusion-text-1\"><h2>3. Encouraging Reflective Thinking<\/h2>\n<\/div><div class=\"fusion-text fusion-text-2\"><h4>Reflection is key to developing problem solving skills<\/h4>\n<\/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 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;\"><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-3\"><p><strong>How can we encourage reflective thinking? <\/strong><\/p>\n<p>Reflection is the process of thinking carefully about what is being done and is an important step of problem solving that will enable students to learn. \u201cAs students reflect, use imagery, talk to themselves, and reconcile new ideas with their schema of previous concepts, they gain ways to solve the problem\u201d (McNeal, 1995, Learning not to think in a textbook-based mathematics class. Journal of Mathematical Behavior, 14: 205-234.)<\/p>\n<p>Rather than giving students a list of problem-solving strategies to try out, they will benefit more by discovering these strategies themselves, reflecting on this process and communicating their findings in written and verbal form.<\/p>\n<p>An effective way for students to reflect on the problem-solving strategies that they used is to keep a learning log. In this way students can consciously reflect on and develop some problem-solving strategies that can be used in various situations in their academic and personal lives.<\/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-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-4\"><p>As the parent\/teacher you could ask some of the following questions to inspire deep thinking:<\/p>\n<p>How did you approach this puzzle as a group\/individually?<br \/>\nDid you try many different strategies?<br \/>\nWhat strategies did you try?<br \/>\nDid you try strategies that were not helpful? Why didn\u2019t they help you?<br \/>\nWhen did you realise you had to try another strategy?<br \/>\nWhich strategy worked best for you when solving this puzzle?<br \/>\nHow could you apply this strategy when completing other tasks in school or at home?<br \/>\nWould this strategy be helpful in other types of problems?<br \/>\nWould you be able to teach this strategy to somebody else easily?<br \/>\nWhen did you realise you found the correct approach?<br \/>\nWhat did you find most challenging about this puzzle?<br \/>\nWhat got in the way of your progress if anything?<br \/>\nWhat did you enjoy most about this activity?<br \/>\nHow well did your team communicate with each other?<br \/>\nWhat were some of the ways your teammates helped you to learn or overcome obstacles?<br \/>\nHow did you help your teammates to learn and overcome obstacles?<br \/>\nIs there any way you might have hindered your teams progress?<br \/>\nWhat do you think your greatest strengths are?<br \/>\nIn what areas do you think you have room to improve?<br \/>\nWhat would you personally do differently if you were to approach another puzzle with this group?<br \/>\nHow can you better support and encourage your teammates in future puzzles?<br \/>\nHow can you use what you have learned again in the future?<\/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><\/div><div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-3 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-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\/developing-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\">3. 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\">Next: 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-7322","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>Encourage Reflective Thinking &#8211; MATHS WEEK IRELAND<\/title>\n<meta name=\"description\" content=\"Maths Week will take place from 11 - 19 Oct. 2025. 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