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 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?

On this episode of The Report Card, Nat Malkus discusses these questions, and more, with Jon Star. Nat and Jon discuss conceptual understanding and procedural fluency, whether constructivism has a place in the classroom, the value of worked examples, online curricula and the importance of curricular coherence, what mathematical flexibility is and why it matters, whether students can understand problem-solving strategies more or less well, whether math makes students better problem-solvers more generally, Chinese math education, Jon’s experience teaching middle school math and how being a researcher informs his teaching, whether math education research is sufficiently accessible to teachers, how to improve American math education, and how good American math education could be.

Jon Star is the Carl H. Pforzheimer, Jr. Professor of Teaching and Learning at the Harvard Graduate School of Education and a middle school math teacher.