The Power of Metacognition in Learning

What is the role of active versus passive learning for math? How would data science become an avenue of math study for high school students and why isn’t it already? Where does change in math education start? At the college level or before?

Jo Boaler is a professor of mathematics education at Stanford University and also the author of a number of books, including Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics, Limitless Mind: Learn, Lead, and Live Without Barriers, and Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching.

Greg and Jo discuss creativity, diversity, and meaning in math education. Their conversation identifies certain flaws in current math teaching methods, the resistance to educational change, and the importance of metacognition, visual learning, and collaborative problem-solving. Jo shares insights from her journey as a math educator, including her experiences with educational reform and the implications of neuroscience on learning math. They also examine the role of active versus passive learning, the potential of data science in education, and the impact of AI on future teaching practices.

*unSILOed Podcast is produced by University FM.*

Episode Quotes:

How conjectures ignite mathematical thinking

17:00: When we ask kids to reason about maths and to come up with their own conjectures, we like to share that word with kids. This is a word that all mathematicians use—a conjecture for an idea they have that you need to test out. It's like a hypothesis in science, but kids have never heard of that word, which is, you know, means there's a reason for that. But anyway, we teach our kids to come up with conjectures and then to reason about them and prove it to each other. And they get these great discussions where they're reasoning and being skeptical with each other. And that's what sparks their interest. They actually feel like they're discovering new things. And it's, like, really engaging for the kids to get into these discussions about the meanings of why these things work in maths. So it's a great route in, not only to engage kids, but have them understand what they're doing. Yeah, it's not that common.

Why every kid should learn data science

31:02: Data science is really something all kids should be learning in school, before they leave school, and developing a data literacy and a comfort with data and being able to read and analyze data, to some extent, is an important life skill. And it probably is really important to say, if a democracy, as a lot of misinformation is shared now, and if kids aren't leaving able to make sense of and separate fact and fiction, they will be left vulnerable to those misinformation campaigns. So, it's important just to be an everyday citizen.

Why estimation is really important

34:48: The idea of Math-ish is, estimation is really important. There's a lot of research evidence that we should be getting kids to estimate, but I know that kids in schools hate to estimate, and they resist it, and they will work things out precisely and round them up to make them look like an estimate. But you ask them, what's your ish number? And something magical happens. Like, suddenly they're willing to share their thinking, but it doesn't happen enough.

The problem with teaching everything every year

14:28: In the US, we have this system of teaching everything every year. So, you start learning fractions in maybe grade three, but you also learn them again in grade four and grade five and grade six. And at the end of that, kids don't understand fractions and everything else. Everything is taught every year. Whereas if you look at very successful countries like Japan, they don't teach in that way. Fractions is taught in one year—one year group—deeply, well, conceptually. So this is why you see kids going around in these massive textbooks that they can hardly carry, because it has all this content. And, of course, when you try and teach everything every year, often kids don't learn any of it well.

Show Links:

Recommended Resources:

• Randomized Controlled Trial
• Metacognition
• Compression as a unifying principle in human learning
• Carol Dweck

Guest Profile:

• Faculty Profile at Stanford GSE
• Profile on Wikipedia
• YouCubed
• Social Profile on Instagram
• Social Profile on X

Her Work:

• Amazon Author Page
• Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics
• Limitless Mind: Learn, Lead, and Live Without Barriers
• What's Math Got to Do with It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success
• Data Minds: How Today’s Teachers Can Prepare Students for Tomorrow’s World
• Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching