It’s hard to understand exactly why the tradeoff between achievement and student engagement exists. One theory is that “drill and kill” style rote repetition might be effective in helping students do well on tests but make class dreadfully dull. The researchers watched hours of videotaped lessons of these teachers in classrooms, but they didn’t find statistical evidence that teachers who spent more class time on test prep produced higher test scores. High achievement didn’t seem to be associated with rote instruction.

Instead, it was teachers who had delivered more cognitively demanding lessons, going beyond procedural calculations to complex understandings, who tended to produce higher math scores. The researchers admitted it was “worrisome” that the kind of cognitively demanding instruction that we want to see “can simultaneously result in decreased student engagement.”

Other researchers and educators have noted that learning is hard work. It often doesn’t feel good for students when they’re making mistakes and struggling to figure things out. It can feel frustrating during the moments when students are learning the most.

It was rare, but the researchers managed to find six teachers among the 53 in the study that could do both types of good teaching simultaneously. Teachers who incorporated a lot of hands-on, active learning received high marks from students and raised test scores. These teachers often had students working together collaboratively in pairs or groups, using tactile objects to solve problems or play games. For example, one teacher had students use egg cartons and counters to find equivalent fractions.

These doubly “good” teachers had another thing in common: they maintained orderly classrooms that were chock full of routines. Though strict discipline and punishing kids for bad behavior has fallen out of fashion, the researchers noticed that these teachers were proactive in setting up clear behavioral rules at the start of each class. “Teachers appeared quite thoughtful and sophisticated in their use of routines to maintain efficiency and order across the classroom,” the researchers wrote. “The time that teachers did spend on student behavior typically involved short redirections that did not interrupt the flow of the lesson.”

These teachers also had a good sense of pacing and understood the limits of children’s attention spans. Some used timers. One teacher used songs to measure time. “The teachers seemed intentional about the amount of time spent on activities,” the researchers noted.

Given that it’s not common or easy to engage students and get them to learn math, Blazar was curious to learn which teachers were ultimately better for students in the long run. This experiment actually took place a decade ago in 2012, and the students were tracked afterward. Blazar is currently looking at how these students were doing five and six years later. In his preliminary calculations, he’s finding that the students who had more engaging elementary school teachers subsequently had higher math and reading achievement scores and fewer absences in high school. The students who had teachers who were more effective in raising achievement were generally doing better in high school too, but the long-run benefits faded out somewhat. Though we all want children to learn to multiply and divide, it may be that engaging instruction is ultimately more beneficial.

Researchers like Blazar dream of developing a “science of teaching,” so that schools of education and school coaches can better train teachers to teach well. But first we need to agree what we want teachers to do and what we want students to achieve.

*This story about* *good teaching* *was written by Jill Barshay and produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the **Hechinger newsletter.*