This research brief from Vanderbilt University that suggests metacognition in math class is interesting to me for a couple of reasons.
The first is that it includes suggestive evidence this practice works and can be implemented at scale. Of course, like most things that are attempted to be used at scale, educators have to understand why it works and adopt the framework behind the practice. They can’t just dogmatically adopt the practice.
The second is that this is a relatively cheap and easy to implement practice that builds on something many, many educators either already do or know they should be doing, which is using exit tickets. Finding out what children have understood from your class is a pretty crucial practice, and this builds on that practice.
But what does metacognition in the math class look like, and why should educators implement this practice?
Metacognition is “an awareness of one’s thought processes and an understanding of the patterns behind them.” (source) In math class, this looks like students thinking about how they solved problems, looking for generalizations they might apply from those solutions, and reflecting on how they can approach mathematics differently in the future.
Amy Lucenta and Grace Kelemanik taught me the power of metacognition through their Routines for Reasoning. Everyone of their instructional routines includes a meta-reflection at the end and is a necessary part of these powerful routines.
[Memory is] the residue of thought, meaning that the more you think about something, the more likely it is that you’ll remember it later.
Dan Willingham, Why Children Don’t Like School
If what we want children to remember is specific problems that they’ll never see again, we should fill all of their time with endless practice. If we want them to be able to generalize and maybe be able to solve problems of a similar type but which they haven’t seen, we should ask them to reflect (for at least a few minutes) on the thought processes they used.
The goal of a metacognition can be for students to generalize from their experiences. A common metacognitive prompt I use is, “What mathematical thing do you want to remember today that you think might be important tomorrow, given you may never see these exact problems again?“
Crucially, metacognition can turn math class from a place where students solve specific mathematical problems into a place where they learn mathematical principles they can apply to solve problems. The difference is in whether students are just learning procedures or if they are also learning concepts.
