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Metacognitive Strategies in the Math Classroom

By Dr. Lanette Trowery, Sr. Director of Learning at McGraw Hill School and Margaret Bowman, Academic Designer at McGraw Hill School

Metacognition refers to individuals’ knowledge concerning cognitive processes and regulation of these processes in relation to cognitive objectives (Desoete & De Craene, 2019; Flavell, 1976; Jin & Kim, 2018).

In other words, metacognition is the process of thinking about thinking.

Metacognitive strategies, as you can imagine, are teaching and learning practices that encourage students to engage in metacognition, or think about their thinking as they learn new things, explore concepts, and apply knowledge.

Helpful video from the Smithsonian Institute on Metacognition in the classroom

How do metacognitive strategies help students learn?

Strategic metacognitive engagement has been shown to aid in performance in the classroom and overall academic achievement.

💡 Research Spotlight: In one study, students’ problem-solving processes were qualitatively shown to be supported by engaging in metacognitive regulation — the active monitoring and controlling of cognitive processes (Jin & Kim, 2018). Students were able to help monitor and adjust each other’s thinking through their conversations. As students said things like, “This makes no sense” or “I don’t understand this,” other students would respond with, “Let’s try to think of this another way.” Desoete and De Craene (2019) noted that metacognitive skills were associated with mathematical accuracy. Reflection is also linked to social-emotional learning, as students can benefit from reflecting on the thoughts, feelings, and emotional aspects of what they have learned.

How can teachers encourage metacognitive strategies in the classroom?

Metacognitive strategies can be integrated into regular classroom instruction through:

  • Collaborative activities, such as students working in groups while discussing solutions to a given problem (Jin and Kim 2018)
  • Thorough explanation of a topic allows students to reflect on what they know about a topic and connect it to new information they learn (Denton, 2011)
  • Formative assessments (Denton, 2011), such as verbal discussions or written evaluations in which students complete a chart to explain how they feel about their learning.

💡 Research Spotlight: In one study, students were guided to use metacognitive questioning as part of the process of solving math problems. These metacognitive questions included comprehension, connection, strategic and reflection questions (Mevarech & Kramarski, 2003).

Metacognitive Strategies in Math

Why is metacognition important in the math classroom?

Metacognition is a critical skill in K-5 math education because engaging in metacognitive strategies can help students build a conceptual understanding of content and foster student agency.

  • When studying mathematics, metacognitive strategies can play an important role in knowledge acquisition, retention, and application. At the conceptual development stage, when students are first encountering new ideas and skills, thinking about the relationships between their prior knowledge and new knowledge tends to help students have better conceptual understanding (Mevarech & Kramarski, 2003).
  • Giving students the time and space to reflect on their own thinking is critical for fostering student agency. Research shows that agency is time bound, where individuals draw on their patterns, habits, and identity to set goals or outcomes, creating plans or actions toward reaching that goal and evaluating how well the plan and actions are helping meet the goal in the current context or if a new plan is needed (Adie, Willis, & Van der Kleij, 2018; Poon, 2018; Klemencic, 2015). The ability to engage in metacognition allows students to recognize and reflect on how their own thinking helps them reach their goals.
  • Metacognitive skill development is critical for all learners, including those with learning disabilities.

💡 Research Spotlight: Desoete and De Craene (2019) found that metacognitive activities can help students with learning disabilities build computational accuracy and mathematical reasoning.

Helpful Metacognitive Strategies in Math

Here are just a few practical methods that students can use to reflect on their learning and engage in overall metacognition:

Verbalizing and writing the steps to solving a problem helps students reflect on, monitor, and evaluate their problem-solving abilities and strategies. This has been shown to increase conceptual understanding and provides students the opportunity to evaluate their learning (Gray, 1991; Martin, Polly, & Kissel, 2017).

Writing about their thinking contributes to their mathematical learning (Martin et al., 2017). For example, students may write math journal entries to think about what they learned and what they might not yet understand.

Answering prompts about concepts and encourages students to collaboratively reflect, justify their reasoning, and elaborate on their thought processes. Choose prompts that frame math as a as a set of problem-solving strategies instead of an end result.

Reflecting through formative assessment allows them to consider how well they understand the lesson content and engage in thinking about their own thinking and how they feel about their learning

These metacognitive strategies allow learners greater metacognitive insight into their own thinking — connecting intuition, modeling, and conceptual representation — and are at the very heart of the mathematical practices that foster deeper mathematical learning (Hattie, 2017, p. 136). Metacognition also empowers students to drive their own learning, building from the support of a teacher’s modeling and moving toward independent practice of skills and concepts. An added benefit to this approach is that when teachers use strong focusing questions, they are also modeling how to ask clarifying questions in a way that will serve students better in later phases of learning, when they ask themselves those clarifying questions.

For more on the importance of metacognition in mathematics, and how metacognition is practiced through specific instructional elements in Reveal Math K-5, see the full Reveal Math K-5 Research Foundations.

About the Authors

Lanette Trowery, Ph.D. is the Senior Director of the McGraw Hill Learning Research and Strategy Team.

Lanette was in public education for more than 25 years, working as a university professor, site-based mathematics coach, elementary and middle school teacher, mathematics consultant, and a professional learning consultant, before coming to McGraw Hill in 2014. She earned her Master’s and Doctorate from the University of Pennsylvania.

Lanette’s team, Learning Research and Strategy, serves as the center of excellence for teaching and learning best practices. Her team conducts market, effectiveness, and efficacy research into products to provide insights and recommendations to product development. They collaborate across internal teams, external experts, and customers to establish guiding principles and frameworks to move from theory to practice.

Margaret Bowman is an Academic Designer in the Mathematics Department at McGraw Hill.

Margaret earned her Bachelor of Science in Education from Ashland University with a teaching license in Middle Grades Education, and her Master of Education from Tiffin University. She was a middle school Math and Language Arts teacher for six years before joining the middle school team at McGraw Hill in 2012, writing and designing print and digital curriculum.

Margaret is also a Research Associate in the Research Laboratory for Digital Learning at The Ohio State University. She is nearing completion of a PhD in Educational Studies with an emphasis in Learning Technologies. Her past research and journal publications have focused on teachers’ value for using technology in the classroom and technology’s impact on student learning. Her current research examines how students’ use of technology can improve the value they have for mathematics and their expectations that they can succeed.

References

Adie, L., Willis, J., and Van der Kleij, F. (2018). Diverse perspectives on student agency in classroom assessment. The Australian Educational Researcher. 45. 1–12. https://doi.org/10.1007/s13384-018-0262-2

Denton, D. (2011). Reflection and learning: Characteristics, obstacles, and implications. Educational Philosophy and Theory, 43(8), 838–852.

Desoete, A. & De Craene, B. (2019.) Metacognition and mathematics education: an overview. ZDM Mathematics Education, 51(4), 565.

Flavell, J. (1976). Metacognitive aspects of problem-solving. In L. B. Resnick (Ed.), The nature of intelligence. (pp. 231–236). Hillsdale, NJ: Erlbaum.

Gray, S. (1991). Ideas in practice: Metacognition and mathematical problem solving. Journal of Developmental Education, 14(3), 24–26, 28.

Hattie, J. (2017). Visible learning for mathematics, grades K-12: What works best to optimize student learning. Thousand Oaks, CA: Corwin Mathematics.

Jin, Q., & Kim, M. (2018). Metacognitive regulation during elementary students’ collaborative group work. Interchange, 49(2), 263–281.

Klemencic, M. (2015). What is student agency? An ontological exploration in the context of research on student engagement. In Klemencic, Bergan, and Primozic (eds.) Student engagement in Europe: society, higher education and student governance (pp. 11–29). Council of Europe Higher Education Series №20. Strasbourg: Council of Europe Publishing.

Martin, C., Polly, D., Kissel, B. (2017). Exploring the impact of written reflections on learning in the elementary mathematics classroom. The Journal of Educational Research, 110(5), 538–553.

Mevarech, Z. & Kramarski, B. (2003). The effects of metacognitive training versus worked-out examples on students’ mathematical reasoning. British Journal of Educational Psychology, 73, 449–471.

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