The latest study asks a few big questions.

First: Do teachers have an impact on students’ attitudes and behavior, as measured by student surveys? Here, the answer is convincingly yes, consistent with the emerging research.

Second: Are the statistical estimates—often called value-added measures—of teacher impacts on test scores and non-cognitive skills accurate? The study examined this by comparing the statistical estimates to the results from from random assignment, and it found that the answer varies. Value-added measures are quite accurate for predicting test scores—an important finding in light of the charged debate on whether to judge teachers by these metrics. But it concludes that the statistical models are often biased for measuring impact on student attitudes, suggesting that attempting to evaluate teachers in this regard may be misguided.

Finally: Is a teacher’s performance, measured by test scores, similar to performance according to other measures? This question is especially important because it’s key for understanding how to think about teacher quality and how to evaluate it.

The study concludes there was only a weak relationship between test score performance and student behavior and feeling of efficacy in math. But when it came to student happiness, there was a moderate negative association—on average, greater test score gains meant less happy students.

What explains this potentially surprising inverse relationship?

It could be that teachers who were less demanding were more popular because their instruction was less likely to promote learning—but more enjoyable for students. Maybe those teachers just popped in a video on many days; perhaps they never gave homework.

Blazar, for his part, is skeptical of this theory.

“I’m not sure that’s a likely explanation in large part because teachers’ emotional support for students … seems to be really predictive of how happy students are in class,” he said. “Building an emotionally supportive classroom environment is something that educators and researchers have cared about for a long time.”

Another interpretation, then, is that measures of teacher effectiveness based on test scores leave out important dimensions of what makes a good teacher—such as caring for students, something that might show up in happiness surveys.

Blazar emphasizes that while the correlation was negative and statistically significant it was not strong in size, meaning that there were certainly teachers who succeeded in improving both test scores and happiness.

Past research has generally shown that test-based measures capture some, but not all, of the components of effective teaching. Test score results tend to be only modestly related to other measures of performance, like classroom observations or effects on student attendance.

On the other hand, teachers’ impacts on tests have rarely been negatively related to other measures. In fact, there is usually a small positive association, including with regards to student surveys. Moreover, a number of studies have linked teachers’ and schools’ test score impacts to longer-term results, including adult income and college success.