For decades, the prevailing wisdom in education was that high self-esteem would lead to high achievement. The theory led to an avalanche of daily affirmations, awards ceremonies and attendance certificates — but few, if any, academic gains.

Now, an increasing number of teachers are weaning themselves from what some call empty praise. Drawing on psychology and brain research, these educators aim to articulate a more precise, and scientific, vocabulary for praise that will push children to work through mistakes and take on more challenging assignments. Consider teacher Shar Hellie’s new approach in Montgomery County.

To get students through the shaky first steps of Spanish grammar, Hellie spent many years trying to boost their confidence. If someone couldn’t answer a question easily, she would coach him, whisper the first few words, then follow up with a booming “¡Muy bien!”

But on a January morning at Rocky Hill Middle School in Clarksburg, the smiling grandmother gave nothing away. One seventh-grade boy returned to the overhead projector three times to rewrite a sentence, hesitating each time, while his classmates squirmed in silence.

“You like that?” Hellie asked when he settled on an answer. He nodded. Finally, she beamed and praised the progress he was making — in his cerebral cortex.

“You have a whole different set of neurons popping up there!” she told him.

A growing body of research over three decades shows that easy, unearned praise does not help students but instead interferes with significant learning opportunities. As schools ratchet up academic standards for all students, new buzzwords are “persistence,” “risk-taking” and “resilience” — each implying more sweat and strain than fuzzy, warm feelings.

“We used to think we could hand children self-esteem on a platter,” Stanford University psychologist Carol Dweck said. “That has backfired.”

Dweck’s studies, embraced in Montgomery schools and elsewhere, have found that praising children for intelligence — “You’re so clever!” — also backfires. In study after study, children rewarded for being smart become more likely to shy away from hard assignments that might tarnish their star reputations.

But children praised for trying hard or taking risks tend to enjoy challenges and find greater success. Children also perform better in the long term when they believe that their intellect is not a birthright but something that grows and develops as they learn new things.

Brain imaging shows how this is true, how connections between nerve cells in the cortex multiply and grow stronger as people learn and practice new skills. This bit of science has proved to be motivating to struggling students because it gives them a sense of control over their success.

It’s also helpful for students on an accelerated track, the ones often told how “smart” they are, who are vulnerable to coasting or easily frustrated when they don’t succeed.

That’s how teachers at Rocky Hill Middle started talking about “neuroplasticity” and “dendritic branching” during training sessions. They also started the school year by giving all 1,100 students a mini-course in brain development.

“This is the most important thing you are going to learn this year,” Hellie said she told her students before playing a YouTube video that explains how brains grow. “It has to do with the way you are going to live the rest of your life — whether you will continue to learn, be curious, have an active, growing brain or whether you are going to sit and let things happen to you.”

An online curriculum called Brainology developed by Dweck and another researcher in 2009 has been used in 300 schools. Joshua P. Starr, the new Montgomery schools superintendent, selected Dweck’s book, “Mindset,” for the inaugural session of a book club he created to introduce his education philosophy.

Dweck’s work builds on other research about motivation and the malleability of intelligence that has stirred significant changes in curriculum, teacher training and gifted instruction in many school districts.

In Fairfax County, for example, students are no longer labeled “gifted” but considered on a spectrum of “novice” to “expert” in each subject — the kind of language that is seeping into teacher praise, said Carol Horn, coordinator of advanced academic programs for Fairfax schools.

Education experts have long warned about the dark side of praise.

Alfie Kohn, author of the book “Punished by Rewards,” has said most praise, even for effort, encourages children to be “praise junkies” dependent on outside feedback rather than cultivating their own judgment and motivation to learn.

Michelle A. Rhee, the former D.C. schools chancellor, often recounts a story about how her daughters’ many soccer trophies are warping their sense of their athletic abilities. Her daughters “suck at soccer,” she said in a radio interview for Marketplace last January.

“We’ve become so obsessed with making kids feel good about themselves that we’ve lost sight of building the skills they need to actually be good at things,” Rhee said.

Underlying the praise backlash is a hard seed of anxiety — a sense that American students are not working hard enough to compete with students from overseas for future jobs.

In an oft-cited 2006 study by the Brown Center on Education Policy at the Brookings Institution, U.S. eighth-graders had only a middling performance on an international math exam, but they registered high levels of confidence. They were more likely than higher performing students from other countries, such as Singapore and South Korea, to report that they “usually do well in mathematics.”

Praise should be relevant to objective standards, said Chester E. Finn Jr., president of the Thomas B. Fordham Institute, an education think tank. Whether it’s given to make children feel good or because “at least they tried,” it’s not helpful if students are still “50 yards from proficient,” he said.

“Winning or losing also matters in the real world,” Finn said. “You either beat the enemy or you don’t. You either get the gold medal or you get the silver.”

Dweck said it is important to be clear with children about what proficient or gold-medal performance looks like so they know what to strive for. (Unhelpful: “You were robbed! Those judges must be blind!”)

But she stresses the importance of using praise to encourage risk-taking and learning from failure in the classroom, experiences that make way for invention, creativity and resilience.

“Does the teacher say: ‘Who’s having a fantastic struggle? Show me your struggle.’ That is something that should be rewarded,” she said. “Does the teacher make it clear that the fastest answer isn’t always the best answer? [That] a mistake-free paper isn’t always the best paper?”

Changing the language of praise can be difficult for adults who grew up thinking that an “A for effort” was a consolation prize.

During his book club, Starr recounted how his 3-year-old son recently discovered that the word “brown” starts with B.

“My wife says, ‘You are so smart,’ ” he recalled. When he discouraged her from praising his intelligence, Starr said, “she looked at me like I was crazy.”

Typically, young children don’t second-guess praise. But teenagers understand when feedback is useful and authentic. “Great job!” doesn’t tell them what was great about what they did, experts say.

“They know that everything they do isn’t ‘Magnificent!’ ” Hellie said.

And so her class is becoming accustomed to awkward silence.

The same January morning, another seventh-grade boy struggled to figure out what was wrong with this sentence: Un chico soy inteligente.

One classmate started to answer, but Hellie stopped her. Another classmate volunteered, in newly acquired vocabulary, why the boy needed to persist on his own. “He’s trying to connect pathways in his brain or whatever,” she said.

Finally, the boy understood.

“Soy un chico inteligente,” he said.

“What does it mean?” the teacher asked.

“I am an intelligent boy?”

The class broke into applause.