In today’s 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 “work” 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 “messy middle” 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.
The Research on Metacognition
In the context of mathematics, metacognition is an awareness and understanding of one’s thought process during problem-solving. Cognitive science research 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 “why” are stuck in surface-level learning.
A recent meta-analysis 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.
Connecting Metacognition to Educational Goals
- Metacognition and Social-Emotional Learning
Self-awareness is one of the five competencies in CASEL’s framework 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 SELf Question Set for Academic Problem Solving to provide students a structured framework for self-assessing their progress before, during, and after engaging in mathematical tasks.
- Metacognition and Habits of Mind
Thinking About Your Thinking is one of the 16 Habits of Mind 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’s thinking by focusing on setting, monitoring progress towards goals, and using past knowledge to weigh options that aid in problem-solving. Consider incorporating this collection of quotes curated by the Habits of Mind Institute into instructional conversations and activities.
- Metacognition and Standards for Mathematical Practice
Metacognitive strategies can enhance the implementation of Common Core Standards for Mathematical Practice (SMP), specifically SMP 1: “Make sense of problems and persevere in solving them.” This standard highlights metacognition by describing how mathematically proficient students engage in deliberate self-monitoring and self-regulation throughout the problem-solving process. 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, “Am I making progress?,” builds students’ awareness and control over their learning. This Exploring the Core blog post offers several suggestions for supporting the Standards of Mathematical Practice through a metacognitive lens. - Metacognition and Growth Mindset
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, MATH-ish (HarperOne, 2024), Dr. Jo Boaler, a Professor of Education at Stanford University, describes metacognition as “learning how to learn and learning to be effective in life” (25). She lays out an extensive set of metacognitive strategies in the book and also offers several free handouts on the Math-ish blog that can help students adopt metacognitive ways of thinking.
Practical Implementation Strategies
Daily Routines that Build Metacognition:
- 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 (reviewed here), where students can share their reflections. Alternatively, have students use Book Creator (reviewed here) to build a digital math journal where they can use multimedia tools to store their reflections and document their strategies.
- 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 (reviewed here) to narrate their thinking while solving problems on a digital whiteboard like Whiteboard.chat (reviewed here). Alternatively, leverage the AI tool Snorkl (reviewed here) to let students receive personalized AI-generated feedback on their responses.
- Utilize the Think-Pair-Share protocol as an opportunity for students to share problem-solving strategies. Consider using the silent Think-Pair-Share adaptation mentioned in this article, where students post their strategies on an online collaboration space such as Figjam (reviewed here) and their peers silently annotate each other’s problem-solving approach to a task.
Assessment Modifications that Push Metacognition
- Extend questions to include an “explain your thinking” component. Teachers can create traditional multiple-choice or open-response questions using a digital assessment builder tool like Formative (reviewed here), 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 (reviewed here), includes an “ask students to explain their thinking” 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’ responses.
- 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 (reviewed here) or Padlet TA (reviewed here).
- Add an opportunity for student self-assessment before you provide teacher-driven feedback. Consider having students submit a Google Form (reviewed here) to reflect
Magnifying metacognitive strategies within math instruction slows answer-getting to help students focus on sense-making. It enhances students’ 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.
How have you prioritized student reflection and thinking about thinking in your instruction? Let’s build a collaborative vision of what a metacognitive-focused math classroom can look like!