I went to an event in Washington, D.C. where finalists for teaching jobs had to prepare a five-minute lesson and teach it to a group of fellow applicants. There were eight finalists in the group I observed. All of them were in their 20s, except for one man who was retired and looking for a second career.

The teacher candidates brought all kinds of props for their lessons: read and yellow balloons to teach science; big homemade posters for a literacy lesson; index cards for students to vote on answers.

The lessons were all designed to get the students talking and involved. Except for the older man looking for a second career. He taught a math lesson by standing in front of the class, doing problems on the board. He had no props.

Most people's instinct is to teach the way they were taught, says Harvard professor Susan Moore Johnson. But education researchers and scientists know a lot more now about how people learn than they did thirty years ago. And teaching is changing — or at least it should be, says Johnson.

"The standard math class in my day, in your day, is that the teacher speaks about how to solve a problem, demonstrates that, students get assigned work, and they do it, and then they check their answers," Johnson says. What researchers have discovered, Johnson says, is that students learn math when they understand the concepts of math, not when they just do problems over and over.

"Some of the most interesting research in teaching mathematics has been in classes where teachers explore students' misunderstandings of math, and where [teachers] are far less concerned with the right answer than with the mathematical thinking that's behind that," Johnson says. Students need to talk and ask questions, not just sit quietly listening to a lecture. "It's a very active teaching" style, she says.

And it's hard to do well. "We're asking a lot more of our teachers now," says Heather Hill, one of Johnson's colleagues. "Kids come up with funky ways of doing things. They are wildly inventive. And teachers have to deal with that, " she says. "What kids say to teachers, that's kind of like the raw material of teaching [now]."

Hill and her Harvard graduate students have watched hundreds of hours of video of teachers doing their stuff. "Sometimes you look at the tape and you're like 'what is that child saying?'" she says. The best teachers immediately understand what the child is trying to communicate. "And that's just priceless," says Hill.

Other teachers are terrible at understanding and responding to what students say. "It's like they've got ear muffs on," says Hill. "They're sort of like 'ahh, well next?' They don't process what the kid has just said."

Hill says good teachers deal with curve balls their students throw, and turn the pitches into learning opportunities. She is trying to figure out if this skill results in higher student test scores. But even if there is not a strong correlation between this kind of teaching and test-score improvement, Hill says that probably won't change her mind about this being an effective approach. Instead, it will tell her that the tests are not doing a reliable job measuring what good teachers do.