Welcome to the report card with Nat Malchus, the Education Policy podcast from the American Enterprise Institute.

Math is one of the subjects that gets the most attention in American education.

But how well do we actually understand what good math instruction should look like?

Should math classes mainly consist of students solving problem after problem? Or should math classes

also include opportunities for discussion and group

work? Should students learn a topic and then move on to the next topic after they have achieved

competency? Or should teachers strive to teach each topic deeply, giving students many different

strategies for solving problems. And if math education

in America were dramatically improved, just how good could it be? To discuss these questions and

more, I invited John Starr onto the podcast. John Starr is the Carl H. Fortzheimer Jr., professor of teaching and learning at the Harvard

Graduate School of Education and a middle school math teacher. John Starr, welcome to the report card.

Thanks, Nat. It's my pleasure to be here. Looking forward to the conversation.

John, in conversations about math education, people often will contrast

conceptual understanding with procedural fluency. Are those two things separate in your mind?

So yes and no, they are separate because in mathematics, there really is a distinction between

the things that we know, like principles and ideas versus procedures or algorithms or

strategies that we execute.

So there is a difference between those ideas and things we do.

They just feel like fundamentally different things.

But at the same time, they're closely tied to each other in the way we think about math

working or what we want students to know.

So for example, there might be a procedure that I know and I know how to execute it,

...