When I was writing in the 1980s about the startling success of low-income students in Advanced Placement calculus at Garfield High School in East Los Angeles, many otherwise smart and well-educated people tried to convince me that the deep learning I was seeing with my own eyes couldn’t be real.

They said Garfield must have let only students with college-educated parents into those difficult classes. Nope. Only 35 of the 109 calculus students I surveyed had even one parent with a high school diploma.

They suggested the students memorized a few formulas to score high on the AP exams but could not attain the conceptual understanding of suburban calculus students. Engineering professors I consulted who knew what the Garfield grads were doing in college laughed at that.

That was my introduction to the widespread belief that impoverished children can’t do well in school. A new study by the nonprofit research firm RTI International shows that such assumptions still bedevil our education system, but also identifies a unique way to weaken their grip.

The researchers interviewed 175 teachers and parents participating in the Parent Teacher Home Visits program, a network of more than 450 communities in 20 states. The study was funded by the D.C.- and Puerto Rico-based Flamboyan Foundation, which promotes great teaching and family engagement in schools.

The Sacramento-based program has shown that the visits give parents a clearer idea of how to support their children’s studies, and they help teachers learn more about students’ interests and how to motivate them in class.

But the RTI study also discovered that educators often have “implicit biases” that lower their expectations for students. Many told the researchers their understanding of the families they visited changed when they saw that low-income parents could be just as supportive of learning as affluent parents.

It took me many years to learn that lesson. Most teachers are wonderful people who would do anything for their kids. But when visiting schools, I found their basic humanity often prevented them from helping their students reach higher levels. Many told me they feared that putting a student in an AP course would be too stressful, and harm rather than help their academic development.

I realized then how important the unusual background of Jaime Escalante, the leading calculus teacher at Garfield, had been to his success as a motivator. He began teaching in his native Bolivia. When he arrived at Garfield at age 44, he was convinced that the impoverished Hispanic kids at that school were just like the ones he had in La Paz. They were not incapable of learning higher math. He thought they were just lazy and undisciplined, like teenagers around the world.

He and his colleague Ben Jimenez gave students more time for their studies by keeping them after school and bringing them in on weekends and during the summer. The results were spectacular. In 1987, Garfield produced 26 percent of all Mexican Americans in the country who passed an AP Calculus exam.

The RTI report, “Mindset Shifts and Parent Teacher Home Visits,” said “decades of research shows that students of color and those from low-income households are often treated differently from white and middle- and upper-class students.”

Many educators told the researchers that as a result of the twice-a-year visits to homes that volunteer for the program, they “recognized that previous deficit assumptions about families and students were unfounded.” They said they were wrong to assume many parents did not care about education. The teachers’ attitude moved “from thinking students lack motivation or interest in school to recognizing students’ capabilities,” the report said.

“Focusing on hopes and dreams for the first visit, rather than on academics and/or student performance, is a particularly powerful practice for decreasing implicit biases as it builds understanding and trust [and] reduces anxiety and stress,” the report said.

The researchers admitted, however, that some educators still held on to wrong assumptions that lowered their expectations. It will take more time for the many teachers who now teach like Escalante to show it is the worst form of kindness to hold students back because they just don’t seem strong enough to succeed.