In the world of design, “ideo” is a prefix that designates the shift, for example, to ideograph, or idea-picture, from mere pictograph, or symbol-picture. An elementary picture of the sun remains a pictograph as long as it represents the thing itself. When the sun picture becomes a symbol for light, day, god, or time, the image moves out of the pictorial realm and into the realm of ideas. The innovative international design team IDEO knew exactly what they were doing when they chose that prefix as a name. And the Cooper-Hewitt gets kudos for choosing IDEO to guest-curate the sixth installment of its wonderful series of small, curious exhibits that highlight specimens from the museum’s permanent collection.

Suggesting childlike curiosity, and somewhere between an acronym and the word “idea,” IDEO sounds like a company that is playful, clever, and serious. The name has that “eureka!” quality that conjures up an image of a light bulb going on in someone’s cartoon head, yet it never loses its core value of rigorous thinking. And the name fittingly separates the company from the many run-of-the-mill design firms out there.

IDEO, formed in 1991 by David Kelley, Bill Moggridge, and Mike Nutall, boasts an impressive and various résumé that suggests the team of more than 500 people can tackle anything. (Has anyone considered sending them to Iraq?) It has been involved with the design of objects as far-a-field as the Palm V, the first Apple mouse, the first notebook-style computer for GRID, and the Handspring Treo, as well as disposable insulin pens, shopping carts, the Oral-B gripper toothbrush, and office cubicles. It doesn’t just make things look good; it rethinks things from the ground up, and it never takes anything for granted. When a company comes to IDEO with a proposal, the design firm often reinvents the wheel, yet it does so not to be different but because it discovers that the way things have been done before may have been wrong from the beginning.

IDEO does not only redesign things, it redesigns concepts and spaces. When Marriott’s extended-stay hotel chain, TownPlace Suites, became a client, IDEO, after a long-term investigation of what hotel guests really need and want, completely changed the design of the hotel rooms and lobbies. Among other innovations, it added large interactive maps to the lobbies and flexible modular wall units to the rooms.

“IDEO Selects,” comprising about 30 objects from the Cooper-Hewitt’s collection, reflects the range of the company’s interests, as well as its respect for empirical design and its interest in generating design awareness in viewers. IDEO’s selection may not be as witty as the grouping of objects Kurt Andersen put together when he was chosen, in 2004, to curate a show in the series. And it may not produce the “ooohs” and “ahhs” that the beautiful grouping of spectacular bird cages did in the recent exhibit selected by artist Yinka Shonibare. Yet it may very well be the most intelligent and cohesive exhibit of the six so far. The show, which includes objects from the 16th century to the present, is organized under the rubric of “design thinking.” Each object is considered in terms of its inspiration, empathy, and intuition, and the exhibit makes you think about how designers think and how they solve unique problems. It includes some giants of industrial and graphic design, as well as a number of innovative or unusual products, but it is geared not to wow you with beautiful things but to provoke you to think about how your world is organized.

Half of the exhibit is devoted to product design, and includes objects such as Ladislav Sutnar’s colorful toy “Build the Town Prototype Block Set With Cars” (1941), René Coulon’s sleek Art Deco glass “Radiator” (c. 1937), Mari Bellini’s mod Olivetti “Calculator Divisumma 18” (1973), and a grouping of 13 flashlights that represents 60 years of innovation and style changes. One of the highlights of the exhibit is the grouping of three chairs, each revolving on a turntable. A compact, comparative representation of period styles and design solutions, the grouping is made up of Charles and Ray Eames’s red, child’s bent-plywood chair with a cutout heart in its back (c. 1944), Hans Coray’s utilitarian aluminum “Landi” chair (1939), and an early 18th-century leather and walnut armchair that includes a candle holder, seat drawer, and adjustable book rest. If straddled, while facing backwards, the chair could be used as a pulpit.

The other half of the show is devoted to the organization of information. Among those objects are Dennis Diderot’s “Encyclopedia” (1751–76), Herbert Bayer’s “World Geographic Atlas” (1953), and the “International Dictionary of Symbols” (1969), designed by Doris Marks Dreyfuss, Henry Dreyfuss, and Alvin R. Tilley.

Other wonderful oddities include Albrecht Durer’s print “Interlaced Cord Pattern With Heart-ShapedCenter”(1506–07), an intricate abstract design based on Leonardo’s diagrams and Hiberno-Saxon religious manuscripts; “The Vernaid Bandage” (early 20th century), a triangular bandana that illustrates, in Boy Scout fashion, how to mend 18 different bone fractures, and the “CaneWithPull-OutMap”(1940), an object that, with a roll-up map of Boston hidden in its body, is a practical and novel solution to the problem of a walking stick that keeps you on track.

If IDEO had been around 60 years ago, I could imagine that that cane could have come out of its studio. Like the exhibit as a whole, the cane focuses on problem solving without losing sight of people’s love of novelty. It relishes fresh ideas and sensible solutions, but it also makes clear that in great design, beauty and intelligence are intertwined.

Until January 13 (2 E. 91st St., between Fifth and Madison avenues, 212-849-8400).