She resigned from the board of the group overseeing the California project, saying she could not support using the tests to evaluate school performance. Last spring, after attending a White House meeting on measuring social-emotional skills, she and a colleague wrote a paper warning that there were no reliable ways to do so. “Our working title was all measures suck, and they all suck in their own way,” she said.

And there is little agreement on what skills matter: Self-control? Empathy? Perseverance? Joy?

“There are so many ways to do this wrong,” said Camille A. Farrington, a researcher at the University of Chicago who is working with a network of schools across the country to measure the development of social-emotional skills. “In education, we have a great track record of finding the wrong way to do stuff.”

Schools began emphasizing social-emotional learning around 2011, after an analysis of 213 school-based programs teaching such skills found that they improved academic achievement by 11 percentile points. A book extolling efforts to teach social-emotional skills in schools such as the KIPP charter network and Riverdale Country School in New York, “How Children Succeed” by Paul Tough, appeared the next year.

Argument still rages about whether schools can or should emphasize these skills. Critics say the approach risks blaming the victim — if only students had more resilience, they could rise above generational poverty and neglected schools — and excuses uninspired teaching by telling students it is on them to develop “zest,” or enthusiasm. Groups that spent decades urging the country toward higher academic standards worry about returning to empty talk of self-esteem, accepting low achievement as long as students feel good.

But teaching social-emotional skills is often seen as a way to move away from a narrow focus on test scores, and to consider instead the whole child. It may seem contradictory, then, to test for those skills. In education, however, the adage is “what’s measured gets treasured”; states give schools money to teach the subjects on which they will be judged.