Many people might think that in math classrooms the key question is, “What’s the correct answer?” However, Sam Rhodes, a professor of math education, writes that, “Despite the popular belief that mathematics is about memorizing and precisely following algorithms and procedures, mathematics is actually a subject of critical thinking, problem-solving, and creativity. So, “How did you solve the problem?” may be a more productive question to ask of math students. Metacognition is at the root of this line of inquiry.
What is metacognition?
Simply put, metacognition is the “process of thinking about thinking”. However, metacognition is more complex than just taking an interest in our own thoughts. It actually operates on two levels: being aware of and understanding your thought processes and being able to manage and harness them in productive ways.
What does it look like? Psychologist John Flavell, who was among the first to propose the idea of metacognition, offers the following indicators: “I am engaging in metacognition…If I notice that I am having more trouble learning A than B; If it strikes me that I should double-check C before accepting it as a fact; If I sense that I had better make a note of D because I may forget it; If I think to ask someone about E to see if I have it right. Such examples could be multiplied endlessly.”
Why does metacognition matter in the math classroom?
In the context of math instruction, metacognition “involves active learning to help students become aware of, reflect upon, and consciously direct their thinking and problem-solving efforts,” professor Susan S. Gray writes.
A student who tries to solve a problem without metacognitive awareness and regulation - without actively thinking about what they are choosing to do and why - may, as math professor Sam Rhodes observes:
- Rush towards finding a solution without fully analyzing and understanding the problem from the outset.
- Choose the first pathway or procedure that comes to mind and stick to it, without questioning its efficacy.
- Struggle to constructively work through mistakes. If their one strategy doesn’t work, they can’t retrace their steps to find another way and may be more likely to give up.
A student who does apply metacognition as they work through a problem-solving process, on the other hand, can avoid these pitfalls and will be more likely to:
- Pause to assess the problem fully before devising a plan to solve it.
- Show self-awareness and consider, “What do I already know that can help me?” or admit if they are confused.
- Consider multiple approaches and, as they proceed with a plan, question: “Is this approach working, or not?”
- Work through struggles productively. Because they are tracking their decision-making all along the way, they can work backwards from a dead end to understand where they went wrong and map out other ways forward.
- Reflect on the entire problem-solving process and, in doing so, reinforce what they learned and how they learned it.
The impact of metacognition goes beyond simply helping students pursue and persist in specific, discrete math tasks.
- Research has linked metacognition with supporting overall problem-solving skills and mathematical accuracy.
- Studies have also been shown to increase conceptual understanding, which is a crucial element of rigor in math learning and the Common Core.
- Metacognition can also foster student agency. As they hone their metacognitive habits and strategies, John Hattie observes that “students reach the state where they become their own teachers, they can seek out optimal ways to learn new material and ideas, they can seek resources to help them in this learning, and when they can set appropriate and more challenging goals.”
How to promote metacognition in the classroom and with Yup
To support students’ metacognition, teachers can model behaviors in the classroom, like “thinking aloud” as you walk through a problem, demonstrating how you make mistakes and productively work through them, and explicitly asking students to talk together about how they approach and solve problems. Students can also use writing as a tool; through documenting the entire “journey” of solving a problem in math journals, students can reflect while reinforcing what they know and where to grow.
Teachers and Administrators: Yup can support metacognition among your students, too. Yup tutors use a question-based approach and check for understanding all throughout the session. They draw out students’ prior knowledge, use strategies to help make student thinking visible, and prompt students to reflect on their process. Contact partnerships@yup.com to learn more about bringing Yup to your school or district.
