{"id":12151,"date":"2025-07-03T07:30:00","date_gmt":"2025-07-03T11:30:00","guid":{"rendered":"https:\/\/teachersfirst.com\/blog\/?p=12151"},"modified":"2025-07-02T22:12:51","modified_gmt":"2025-07-03T02:12:51","slug":"magnifying-metacognition-reclaiming-the-messy-middle-in-math-instruction","status":"publish","type":"post","link":"https:\/\/teachersfirst.org\/blog\/2025\/07\/magnifying-metacognition-reclaiming-the-messy-middle-in-math-instruction\/","title":{"rendered":"Magnifying Metacognition:\u00a0Reclaiming the \u201cMessy Middle\u201d in Math Instruction"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">In today\u2019s fast-paced age of technology, students often prioritize finding immediate answers rather than focusing on thinking to grow their understanding. With ever-growing access to AI, students can turn to chatbots as personal assistants who can even give them the \u201cwork\u201d their teacher requested to support their answers. But math teachers will tell you that math is about the process rather than the product. The problem with this instant availability of information is that students lose the \u201cmessy middle\u201d of the learning process. Highlighting metacognition can serve as a pathway to helping students reframe learning math as an opportunity to build strategies and discover tools that will help them solve novel problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The Research on Metacognition<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In the context of mathematics, metacognition is an awareness and understanding of one\u2019s thought process during problem-solving. <a href=\"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/cogs.13048\" target=\"_blank\" rel=\"noreferrer noopener\">Cognitive science research<\/a> supports the idea that metacognitive processes are pivotal in non-routine problem-solving, especially when procedural understanding is insufficient. Students who can explain their mathematical reasoning have a stronger conceptual understanding, whereas students who memorize steps to solve a problem without understanding the \u201cwhy\u201d are stuck in surface-level learning.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A <a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0001691824003639\" target=\"_blank\" rel=\"noreferrer noopener\">recent meta-analysis<\/a> confirms that metacognition is positively associated with academic achievement in mathematics. Metacognitive strategies prompt deeper engagement with mathematical concepts and can help students see patterns and connections across different problem types. If students regularly engage in strategic problem solving, they can develop the ability to monitor their progress and catch and correct their own mistakes, improving accuracy on performance measures.\u00a0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Connecting Metacognition to Educational Goals<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em>Metacognition and Social-Emotional Learning<\/em><br><\/strong>Self-awareness is one of the five competencies in <a href=\"https:\/\/casel.org\/fundamentals-of-sel\/what-is-the-casel-framework\/#self-awareness\" target=\"_blank\" rel=\"noreferrer noopener\">CASEL\u2019s framework<\/a> for integrating social-emotional learning into learning environments. Self-awareness helps individuals experience a stronger sense of self-efficacy and develop a sense of purpose as learners. Students who can evaluate their understanding honestly will build confidence based on genuine competence. They will also be able to monitor their understanding to better recognize when they need help or additional practice. Use the <a href=\"https:\/\/cloudfront-s3.solutiontree.com\/pdfs\/Reproducibles_TMS\/figure1.1thetwostructuredself-questionsets.pdf?_ga=2.257056587.1551993222.1709424849-949657863.1709424849\" target=\"_blank\" rel=\"noreferrer noopener\">SELf Question Set for Academic Problem Solving<\/a> to provide students a structured framework for self-assessing their progress before, during, and after engaging in mathematical tasks.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-medium\"><a href=\"https:\/\/teachersfirst.com\/blog\/wp-content\/uploads\/2025\/07\/2025_JUN_12_ran_JUL_3_Magnifying_Metacognition_Hedetniemi.png\"><img loading=\"lazy\" decoding=\"async\" width=\"200\" height=\"300\" src=\"https:\/\/teachersfirst.com\/blog\/wp-content\/uploads\/2025\/07\/2025_JUN_12_ran_JUL_3_Magnifying_Metacognition_Hedetniemi-200x300.png\" alt=\"\" class=\"wp-image-12271\" srcset=\"https:\/\/teachersfirst.org\/blog\/wp-content\/uploads\/2025\/07\/2025_JUN_12_ran_JUL_3_Magnifying_Metacognition_Hedetniemi-200x300.png 200w, https:\/\/teachersfirst.org\/blog\/wp-content\/uploads\/2025\/07\/2025_JUN_12_ran_JUL_3_Magnifying_Metacognition_Hedetniemi-683x1024.png 683w, https:\/\/teachersfirst.org\/blog\/wp-content\/uploads\/2025\/07\/2025_JUN_12_ran_JUL_3_Magnifying_Metacognition_Hedetniemi.png 735w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a><\/figure>\n<\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em>Metacognition and Habits of Mind<\/em><br><\/strong><em>Thinking About Your Thinking<\/em> is one of the <a href=\"https:\/\/www.habitsofmindinstitute.org\/what-are-habits-of-mind\/\" target=\"_blank\" rel=\"noreferrer noopener\">16 Habits of Mind<\/a> created by Art Costa, Bena Kallick, and Allison Zmuda. It aims to build efficacious thinkers who can apply their learning in unfamiliar situations. It encourages using a strategic cycle to improve one\u2019s thinking by focusing on setting, monitoring progress towards goals, and using past knowledge to weigh options that aid in problem-solving. Consider incorporating <a href=\"https:\/\/www.habitsofmindinstitute.org\/resources\/hom-quotes\/5-thinking-thinking-metacognition\/\" target=\"_blank\" rel=\"noreferrer noopener\">this collection of quotes<\/a> curated by the Habits of Mind Institute into instructional conversations and activities.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em>Metacognition and Standards for Mathematical Practice<\/em><\/strong><br>Metacognitive strategies can enhance the implementation of <a href=\"https:\/\/corestandards.org\/wp-content\/uploads\/2023\/09\/Math_Standards1.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Common Core Standards for Mathematical Practice<\/a> (SMP), specifically SMP 1: \u201cMake sense of problems and persevere in solving them.\u201d This standard highlights metacognition by describing how mathematically proficient students engage in deliberate self-monitoring and self-regulation throughout the problem-solving process.\u00a0 Instead of jumping to a solution, students analyze the problem, plan their approach, monitor their progress, and adapt their strategies as needed. This process of continual reflection, including asking, \u201cAm I making progress?,\u201d builds students\u2019 awareness and control over their learning. This <a href=\"https:\/\/www.exploringthecore.com\/post\/k12-math-metacognitive-constructivism\" target=\"_blank\" rel=\"noreferrer noopener\">Exploring the Core blog post<\/a> offers several suggestions for supporting the Standards of Mathematical Practice through a metacognitive lens.<br><\/li>\n\n\n\n<li><strong><em>Metacognition and Growth Mindset<\/em><\/strong><br>Students who engage in metacognition can begin to track their thinking development over time and recognize their growing mathematical achievement. Framing that achievement as the process of learning from our mistakes cultivates a growth mindset. In her latest book, <em>MATH-ish <\/em>(HarperOne, 2024), Dr. Jo Boaler, a Professor of Education at Stanford University, describes metacognition as \u201clearning how to learn and learning to be effective in life\u201d (25). She lays out an extensive set of metacognitive strategies in the book and also offers several free handouts on the <a href=\"https:\/\/www.mathish.org\/activities\" target=\"_blank\" rel=\"noreferrer noopener\">Math-ish blog<\/a> that can help students adopt metacognitive ways of thinking.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Practical Implementation Strategies<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Daily Routines that Build Metacognition:<\/em><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Regularly incorporate reflection opportunities into instruction. Provide sentence starters for students to use when completing entrance tickets. Consider adding these sentence starters as pinned posts on Padlet (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=10007\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>), where students can share their reflections. Alternatively, have students use Book Creator (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=17988\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>) to build a digital math journal where they can use multimedia tools to store their reflections and document their strategies.<\/li>\n\n\n\n<li>Assign students mathematical tasks that move beyond finding a solution and require them to document their thinking process. Students can utilize screen recording tools such as Screencastify (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=15569\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>) to narrate their thinking while solving problems on a digital whiteboard like Whiteboard.chat (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=19238\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>). Alternatively, leverage the AI tool Snorkl (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=20132\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>) to let students receive personalized AI-generated feedback on their responses.<\/li>\n\n\n\n<li>Utilize the Think-Pair-Share protocol as an opportunity for students to share problem-solving strategies. Consider using the <a href=\"https:\/\/www.edutopia.org\/article\/think-pair-share-variations-16-ways-up-your-game\/\" target=\"_blank\" rel=\"noreferrer noopener\">silent Think-Pair-Share adaptation<\/a> mentioned in this article, where students post their strategies on an online collaboration space such as Figjam (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=20133\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>) and their peers silently annotate each other\u2019s problem-solving approach to a task.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Assessment Modifications that Push Metacognition<\/em><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Extend questions to include an \u201cexplain your thinking\u201d component. Teachers can create traditional multiple-choice or open-response questions using a digital assessment builder tool like Formative (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=16556\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>), followed by whiteboard or audio response option where students explain their thinking on the content question. The activity builder in Amplify Desmos Math, formerly Desmos Classroom (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=17800\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>), includes an \u201cask students to explain their thinking\u201d option teachers can check to allow multiple response types. In action, students will provide their answer and then be prompted with a follow-up response box to explain their thinking. There is also an option to then show students their classmates\u2019 responses.<\/li>\n\n\n\n<li>Include process-focused rubrics alongside content-focused ones on performance-based tasks. Consider leveraging a rubric generator in an AI tool such as Magic School (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=19888\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>) or Padlet TA (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=21314\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>).<\/li>\n\n\n\n<li>Add an opportunity for student self-assessment before you provide teacher-driven feedback. Consider having students submit a Google Form (<a href=\"http:\/\/www.teachersfirst.com\/single.cfm?id=17867\" target=\"_blank\" rel=\"noreferrer noopener\">reviewed here<\/a>) to reflect<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Magnifying metacognitive strategies within math instruction slows answer-getting to help students focus on sense-making. It enhances students\u2019 conceptual understanding and empowers them to grow as mathematical thinkers. While building confidence in their academic abilities, students also increase their self-awareness and problem-solving ability outside the classroom.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">How have you prioritized student reflection and thinking about thinking in your instruction? Let\u2019s build a collaborative vision of what a metacognitive-focused math classroom can look like!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In today\u2019s fast-paced age of technology, students often prioritize finding immediate answers rather than focusing on thinking to grow their understanding. With ever-growing access to AI, students can turn to chatbots as personal assistants who can even give them the \u201cwork\u201d their teacher requested to support their answers. But math teachers will tell you that &hellip; <a href=\"https:\/\/teachersfirst.org\/blog\/2025\/07\/magnifying-metacognition-reclaiming-the-messy-middle-in-math-instruction\/\" class=\"more-link\">read more &raquo;<\/a><\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[27],"tags":[14,50,350,22],"class_list":["post-12151","post","type-post","status-publish","format-standard","hentry","category-classroom-application","tag-edtech","tag-instructional-strategies","tag-metacognition","tag-stem"],"modified_by":null,"_links":{"self":[{"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/posts\/12151","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/comments?post=12151"}],"version-history":[{"count":18,"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/posts\/12151\/revisions"}],"predecessor-version":[{"id":12257,"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/posts\/12151\/revisions\/12257"}],"wp:attachment":[{"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/media?parent=12151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/categories?post=12151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/teachersfirst.org\/blog\/wp-json\/wp\/v2\/tags?post=12151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}