I’m on a train one day when I overhear several teachers talking about how much they hate grades and how they wish they could throw out their grade books. I chime in, saying how much I agree. For one, even for students at an early age, grades undermine a love for learning and curiosity by imposing external motivators.

But when I explain that I teach at a private school, I receive what has become a familiar, disapproving stare, as though I’m one of those teachers—privileged and misguided, and entirely shameless for even calling himself a teacher. My initial enthusiasm for discussing grading has devolved into an empty, unwelcome feeling, like I’m trespassing on public-school territory and "real teacher" discussions.

As I see the divide, many public-school educators accuse private-school counterparts of hand-picking the easiest, most advantaged students to teach. Public-school teachers maintain that they are the real professionals, boasting not only state certification, something private-school teachers don’t need and few have, but also greater responsibilities—like larger class sizes and an obligation to serve, not turn away, students with all types of needs. They also take pride in the ongoing teacher training they receive, something they say their private-school counterparts lack.

To get a different perspective on this divide, I reached out to John Chubb, president of the National Association of Independent Schools, a nonprofit organization that represents more than 1,400 private schools in the United States. "I think there is some merit to the criticism of independent schools not paying adequate attention to teacher training," he told me. "But teaching any kind of student really well is hard—advantaged, disadvantaged, average, or gifted."

And while many private-school teachers could flourish in inner-city public-school settings, many would struggle, Chubb said. I would likely be one of those teachers, but I’m not at all convinced that this would make me less of a teacher—just a different kind of teacher. I make a difference in my private-school classroom, and I work with students who need and depend on me. The same holds true for my talented and dedicated colleagues who work in every other type of school, public or otherwise.

For their part, I hear many private-school educators lament that public-school educators have little choice when it comes to what they teach and have to focus on preparing students for testing rather than providing meaningful instruction.

A quick Google search shows that the news media have covered the overtesting issue extensively. In writing this article, for example, I came across a PBS NewsHour story, "Is there too much testing in the public schools?" In the segment, Alberto M. Carvalho, the superintendent of Miami-Dade County Public Schools, was quoted as saying, "We need to recalibrate the necessity of so many of these tests, conduct a thorough analysis of the duplicate nature of some of these exams, and have a rapid regression back to reason in terms of what’s appropriate for students and teachers alike."

And private-school educators staunchly object to critics who question their professionalism, acknowledging that though they do have fewer students, they use any extra time to offer their pupils higher-quality feedback and instruction.

I recently reconnected with Mark Barnes, a colleague who recently wrote a book arguing against grading, curious to hear from a celebrated education author and public-school teacher. "My private-school colleagues say they can do things public-school teachers can only dream of," he said, referencing benefits such as more in-depth feedback on their work, fewer lectures, and access to state-of-the-art technology. "Not many public schools do this because of constraints of the Common Core and high-stakes testing."

I can’t help but wonder how much the media have intensified animosity among all types of school personnel—and not just between those in public and private institutions. In 2013, Slate posted a blistering condemnation by one of its senior editors, Allison Benedikt, "If You Send Your Kid to Private School, You Are a Bad Person." With over 70,000 "likes" on Facebook, its bold title also leaves nothing to the imagination: "You are a bad person if you send your children to private school. Not bad like murderer bad—but bad like ruining-one-of-our-nation’s-most-essential-institutions-in-order-to-get-what’s-best-for-your-kid bad. So, pretty bad," Benedikt wrote.

Last September, Diane Ravitch, who served as the U.S. education secretary under President George H.W. Bush, released her latest book, Reign of Error: The Hoax of the Privatization Movement and the Danger to America’s Public Schools. Ravitch derides alternatives to public education as an outright attack on the government’s school system and accuses some reformers of engaging in a "deliberate effort to replace public education with a privately managed, free-market system of schooling."

Then, in October, Christopher A. Lubienksi and Sarah Theule Lubienksi, education professors at the University of Illinois at Urbana-Champaign, released an equally charged book, The Public School Advantage: Why Public Schools Outperform Private Schools. They argue that "[private-school] autonomy is associated with less effective teaching, with schools using their freedom to hang onto outdated methods and to avoid staying current on the professional practices embraced by public schools."

In a Washington Post opinion piece last year about their book, the coauthors also wrote that private schools too often use their autonomy from state regulations to teach in such a way that may please parents but isn’t effective for learning. In the piece, the Lubienskis wrote:

For example, private school students are more likely than their public school counterparts to sit in rows, complete math worksheets and believe that mathematics is 'mostly memorizing facts'—a narrow view that captures neither the breadth of the discipline nor the reasoning that is central to it. In contrast, public schools have moved beyond traditional, repetitive exercises, and more often ask students to solve complex, real-world problems and to learn geometry, data analysis, and early algebra ideas, in addition to basic arithmetic.

Just over a year ago, I reached out to Christopher Lubienski to discuss his book. I asked questions about how he and his wife conducted their research—and to what extent, if any, he thinks private and public schools could or should work together. "Professional collaboration is a wonderful thing with potential benefits for both types of schools and, more importantly, for the students," he replied via email. "But as we put schools into more competitive conditions, opportunities for such collaboration diminish. Moreover, for-profit schools have even less incentive to enter into such relationships."

I’m disappointed by Christopher Lubienski’s book and his generalizations, but I couldn’t agree more with him about the importance of collaboration, not just for enhancing private- and public-school teacher relationships, but also for enhancing student learning in all types of settings—including for-profit and charter institutions, which I know little about. I want to hear fresh ideas from people at any kind of school.

Chubb shares my sentiments about the importance of listening to and learning from others beyond the private-school world. But he told me that "animosity" inaccurately describes how public- and private-school teachers and administrators feel about one another. "What I think is that these worlds are organized to be insular," he said, noting that all types of teachers from all types of schools would benefit from joint professional development and opportunities to learn more about how different schools and classrooms operate.

Last spring, I attended a summit hosted by the National Association of Independent Schools. I came away with a greater understanding and appreciation of how all schools—not just those that are members of the organization—could improve by better embracing education technology.

Fortunately, the National Association of Independent Schools isn’t the only organization working to improve communication among educators from different sectors. I recently came across the Private Schools with a Public Purpose Conference. Now in its eighth year, the organization identifies its goals as to "cultivate, deepen, and strengthen relationships between private schools and the greater community," including public schools. "When you have a professional development session between both public and private educators, they learn a lot from one another," says Carl Ackerman, the co-director of the organization that hosts the conference and a teacher at Punahou School in Honolulu, Hawaii. Ackerman told me how last year’s conference focused on the Hawaii Department of Education’s efforts to work with local private schools and nonprofits to support summer student-enrichment programs.

"By uniting public and private educators, we’re able to make a greater impact on all children, and hence all communities," Ackerman said. "I think it’s a calling in life to promote things like this, because what it really does is level the playing field. We want to give everyone in America a chance."

I don’t need to move to Hawaii to find public- and private-school teachers working together for the benefit of all students. In fact, Peter Gow, one of my former high school history teachers and a longtime private-school educator, co-founded #PubPriBridge, a Twitter chat that fosters dialogue between public- and private-school educators.

In helping to launch #PubPriBridge, Gow wanted to avoid simply giving advice to public schools. "I realized that if we start chirping up and saying, ‘Here's what we know,’ you run directly into a lot of the stereotypes and misunderstandings between the public-school community and public-school educators and independent-school educators," he said. "When people think of independent schools, they have, I think, a stereotype of a very small number of very elite kinds of schools where all of the students are named Chatsworth Osborne, Jr., where the teachers are eccentrics, and everybody has more money than God."

Gow acknowledged that most private schools educate kids whose families are, on the whole, probably a little more affluent than families at many public schools. But "kids are kind of the same," he said. Gow mentioned that many private schools specialize in helping kids with serious learning difficulties, for example, and that those schools could serve as research laboratories for public schools.

When it comes to fostering common ground between public- and private-school teachers, Gow speaks glowingly of Edcamp, an increasingly popular model for professional development. Anybody can attend an Edcamp, a free-of-charge event which never has a set theme or agenda. Before breaking out into sessions, participants post questions or ideas for discussions, often on free-standing boards, about anything to do with learning and teaching that is of interest to them.

To gain some insight into why Edcamp fosters interest and camaraderie among teachers from all types of schools, I recently reached out to its executive director, Hadley Ferguson. "People aren't identified by the type of school that they come from, public, private, charter, parochial," she said. "All are welcome and drawn together by their mutual passion for their work with students. I really do think that the set-up of strangers coming together and having conversations about best practices creates an environment where it’s less about proving that ‘I am right and you are wrong.’ It’s about working together, collaborating to meet the challenges we all face."

Ferguson reminds me of a blog post I read by Chubb last spring, titled "Whoever Has the Best Teachers Wins." "No school, and no school type, has a monopoly on good ideas," he wrote.