At any given moment, there are artists — significant artists — working against what fashion dictates. “High Times, Hard Times: New York Painting 1967–1975,” which opens at the National Academy Museum on February 15, examines abstract painting in a period most often associated with minimalism, conceptualism, and performance art. But the New York art world of late 1960s and ’70s was much more diverse than art history texts suggest. The show’s curator, Katy Siegel, begins her catalog essay by asking, “What is possible?” and answers, “Another history is possible.”

The National Academy Museum is a surprising venue for a show about experimental abstraction that reflects the art, politics, and culture of the late 1960s. The artists to be included would seem more suited to P.S.1 or the Whitney.

Of the 37 artists to be included in the show, only three are members of the National Academy: Joan Snyder, Dorothea Rockburne, and Elizabeth Murray (an “NA-elect”). “High Times, Hard Times” is essentially an attempt to rewrite and expand recent art history. Is the idea of painting’s larger role in this period still so problematic that the National Academicians — mostly painters themselves — are the only ones willing to present it?

Ms. Siegel groups the included artists into five categories. First are those reflecting the psychedelic optimism of the mid-’60s, using spray paint or intense color like Dan Christensen and Ralph Humphrey. Next are those who take painting apart, bringing it off its supports, onto the floor or midair, such as Richard Tuttle, Howardena Pindell, Joe Overstreet, and Lee Lozano. In the third group, performance and installation play a major part in paintings by Ms. Rockburne, Harmony Hammond, Yayoi Kusama, Carolee Scheeman, Mel Bochner, and others. Film and video inform a fourth group that includes Lawrence Stafford, Michael Venezia, and Roy Colmer. The final group is those that play with traditional structures of painting, some using shaped canvases, such as Ron Gorchov, Ms. Murray, and Ms. Snyder.

If you don’t recognize the names of some of the artists on exhibit, you are not alone. Some have had prominent careers, but many are little-known, and some rarely exhibited. As the first-person artist accounts reproduced in the catalog make especially clear, painting was up against fierce challenges in the late ’60s, when minimalism, conceptualism, and performance art questioned painting’s continued relevance. Artist Guy Goodwin, in interview with abstract painter and exhibition advisor David Reed says in the catalog, “Painting was thought to be a waste of time, a joke.”

Faced with such art world opposition, the question became: How does one paint? The experimental modes these artists introduced were a solution. “High Times, Hard Times,” by emphasizing technical solutions such as Jack Whitten’s poured and raked acrylic paintings, underscores the conceptual and performance aspects of how to make a painting.

Short catalog essays suggest why the stories of these painters have gone largely untold. Robert Pincus-Witten blames it on October, the leftist art journal founded in 1976 that frames art, above all, in terms of its political discourse. Marcia Tucker writes about trustee and corporate interference in museum programming. Ms. Siegel, by not including major figures of the period such as Brice Marden, Larry Poons, and Robert Ryman, suggests that market streamlining may also have had something to do with eliminating many of the artists here from our attention.

The first-person catalog accounts and Mr. Reed’s position as consultant lend the exhibition a sense of place and time not often present in museum surveys. Mary Heilmann, in her statement, recalls that as she left California for New York, “I was on a quest. I looked forward to meeting my heroes: Carl Andre, Donald Judd … Andy Warhol … I thought I would see some of them at Max’s Kansas City, the bar I’d heard about.” In school, Ms. Heilmann had studied sculpture and felt little in common with the painting students. However, even though she “looked askance at the culture of painting,” she writes, she “chose it as a practice to have arguments with people like Robert Smithson.”

Ms. Heilmann’s polemical choice reminded me of Fairfield Porter, another painter who was active during the same years in New York. Porter’s decision to be a figurative painter was fueled by a similar refusal to do what he was supposed to. In a 1968 interview with Paul Cummings for the Archives of American Art oral history project, Porter recalled witnessing an exchange between the critic Clement Greenberg and Willem de Kooning in the 1950s. Greenberg said to de Kooning, who was working on his series “Women,” “You can’t paint figuratively today.” Porter recalls that upon hearing this, “I thought, if that’s what he says, I will do just exactly what he says I can’t do.”

February 15 until April 22 (1083 Fifth Ave. at 89th Street, 212-369-4880).