TCS Math Specialist Tom Pittard explains metacognition and math
ARITHMETACOGNITION. Yes! It is a term I made up. But stay with me for a just a few paragraphs, and I think I might just convince you of its importance.
Metacognition is generally thought of as “thinking about one’s own thinking”. So, by extension … if we want students to think about their math thinking, couldn’t we refer to it as ARITHMETACOGNITION? I think so. But why bother having students think about their math thinking, anyway?
Beyond “thinking about thinking,”metacognition can be broken into a few different subcategories, all of which are crucial to a math student’s success.When a child tells someone that they know a lot about dinosaurs or that they can sing all the songs from “Frozen,” they are demonstrating declarative metacognitive knowledge. When your son or daughter tells you what they did to get themselves ready for school, they are using their procedural metacognitive knowledge. The somewhat more complex skill of identifying when they are no longer working on the task they should (playing with the water instead of brushing their teeth) or asking themselves if an answer makes sense is referred to as regulatory metacognitive behavior and, as you might expect, takes a bit longer to fully develop. Children’s ability to reflect in these ways varies widely and develops at different times for different types of self thought. Evidence is strong that all types can be taught and strengthened through practice in all areas of learning and growth.
Math instruction in the Singapore method builds in time and activities to develop these types of reflective thoughts by asking students to explain more than just their answer. They are required to describe their thinking from the beginning to the end of a process to answer a question or solve a problem. Having students coach each other on the next step in a procedure and check their own work for reasonableness also serve to grow these skills.
Even more important to math students’ success is their self confidence around math (according to many studies). “I stink at math!” versus “I’m good at math” is actually a better predictor of success in math class than any skills measure that we can give. The types of metacognition that work together to help a student develop their self concept as a math student are the person, task, and strategy categories of metacognitive knowledge. These have to do with task analyses, strategy application and feelings about the student’s own ability to be successful.
Here are some sample questions that can get students thinking about their math thinking in constructive ways:
- How do I feel about this task in front of me?
- What strategies can I think of that might help me?
- Have I ever done something like this before?
- Which parts do I know, recognize or recall?
- What’s the next step?
- Why should I do that?
- Is that answer even possible?
- Could I have done that in a different / more efficient way?
- How confident am I about the work I just did?
Interested in learning more about metacognition and its impact on learning math? Check out some of these resources.
http://singteach.nie.edu.sg/issue29-mathed/
http://singteach.nie.edu.sg/issue54-research02/
http://www.sciencedirect.com/science/article/pii/S0883035599000154
https://opus4.kobv.de/opus4-bamberg/files/7364/SchneiderMetacogse_A3b.pdf
https://eric.ed.gov/?id=ED474273
https://www.sciencenews.org/article/math-anxious-brains-tackle-simple-problems-differently
“You better think! … “
ALSO: I hope you can make it to the upcoming Singapore Math Night May 17, 6:30 – 8:00 p.m. You can RSVP here.
AND: Don’t forget to check in on the Singapore Math Resource page on the TCS-University page.
Tom
TCS Math Specialist
@tompitttcs
