POOR ANNELISE ELSE FRIEDA FLEISCHMANN. Born a century ago into a mercantile German-Jewish home, she, like so many before and after, thought she could detour from the well-trodden path of mother and homemaker and become an artist. So the gaunt Berlin teenager took a portrait of her mother to Oskar Kokoschka, who asked dismissively: “Why do you paint?” Undaunted, she responded to a leaflet for a new art school, was rejected, and then applied again, successfully, to Weimar's socially idealistic Bauhaus.

But ideals rarely free themselves entirely from the pervasive ignorance of their moment, and so the eager student found that she and her fellow females were relegated to the haus part of Bauhaus, where they were urged away from sharp and erect pursuits (“We are fundamentally opposed to the education of women as architects,” Walter Gropius wrote in 1920) and toward the more accommodating fields of bookbinding, pottery, and textiles. Anni would have been happy to work with glass, but enrollment in that class was already filled—with a single student, Josef Albers. So in 1923 she slunk, resigned, into Gunta Stölzl's weaving workshop (“fate put into my hands limp threads”) and stuck with fabric for the rest of her life.

Anni married the older Josef in 1925. That same year, the Bauhaus moved from Weimar to Dessau, also shifting emphasis from handwork to production. In 1929, now adept at spinning, dyeing, weaving, and fabric design, she unraveled a cunning crocheted cap made of cellophane that she had bought in Italy and fashioned similar fiber to create an auditorium wall covering that would dampen sound yet reflect light. The product, unveiled in Bernau, Germany, in 1930, worked splendidly and won Albers her Bauhaus degree, as well as awards and outside attention from aestheticians and engineers.

A swatch of this cotton-and-cellophane fabric—one side beige, the other silvery black—was on view, along with many other samples and full hanging pieces, in this centenary show organized by the Josef and Anni Albers Foundation and the Peggy Guggenheim Collection, Venice (where the show originated). Although it is wonderful to see so much of Albers's work in one place (why has it taken so long to mount a retrospective of such a pivotal artist?), the show has a small but disturbing problem.

Forget the usual difficulties attached to most fabric shows: How are single woven works distinguished from fabrics designed for production, the endless yards of cloth whose composition and weave, in comparison, show them as idea-centered, almost conceptual? Should labels include the details of warp, weft, and loom that doom weaving to the category of artless craft? The telling difficulty here is a room of ephemera—“grandma” snapshots, professional and personal letters, and, it seems, whatever else could be dragged out of the Albers archive—collaged on the walls as if the gallery were a sentimental mantelpiece. This display is almost as large as the rest of the show and adds virtually nothing to a viewer's understanding of Albers's unique place in modern art.

Would the same have been done for Josef? You know the answer. The other Albers is undoubtedly an art artist, not a craft artist, and, as we know, art stands alone. It need not be placed in the world of domestic and financial concerns. What is more, despite an excellent chronology and informative addenda about weaving methods, the exhibition catalogue inadvertently diminishes Anni Albers's achievement with a long, chatty reminiscence and a short, tentative critical analysis.

This is a shame, because Albers was the first artist of the Western world to bring the full focus of modernism to the art of weaving—to make weaving modern art—and her influence can be seen today in the work of Trude Guermonprez, Sheila Hicks, Ed Rossbach, Lenore Tawney, Claire Zeisler, and Magdalena Abakanowicz. Her tenets were the same as those of many of her Bauhaus teachers and comrades, especially Paul Klee—who taught a weaving workshop himself. All her working life, Albers weighed practical and accessible usefulness against the surprising and lasting qualities of beauty and meaning that seemed to her to be the most important “use” of fine art. She was looking for an achievable middle ground.

Her weaving, which began the usual Bauhaus way, by using handwork as a template for industrial production, divided later into machine-made designs and individual handmade pieces, usually hangings. Albers believed in truth to materials—hence her subtle, often muted, palette—but she scoured industry for brand-new material truths, unafraid of the promise of plastic. Her fascination with materials extended easily during the early '40s into making jewelry (with student Alex Reed) from paper clips, washers, strainers. Obviously, Albers did not limit herself to fiber; she just preferred it.

She also liked to look back to Central and South American weaving, especially of the Andean masters, for inspiration not only with regard to technique but also with regard to result. Albers knew that knotting and raised designs were a form of preliterate record keeping, and she tried, with limited success, to rope the eyes into reading the suggestive curled and jumping calligraphic script lines that cover the surface of her later pictorial weavings. In this way, by dividing these works into background and foreground, into pattern atop surface, she again found herself in the Bauhaus world of planar art—of painting—that she never ceased to admire. But ultimately her art's message was always her medium—and it was this that made Albers the modern innovator she was.

Jeff Weinstein is fine arts editor of the Philadelphia Enquirer