On-Sets: The Game of Set Theory

This collection of games and puzzles taught some of the basic ideas of set theory, one of the topics of the New Math, an abstract approach to teaching mathematics that was introduced in American primary and secondary schools during the 1960s. On-Sets was developed by Layman E. Allen, of Yale University Law School, in collaboration with Peter Kugel and Martin F. Owens, of Technical Operations, Inc., located in Burlington, Vermont. They developed the game while Allen was director of the ALL (Accelerated Learning of Logic) Project that developed mathematical games under a grant from the Carnegie Corporation of New York. A trademark for On-Sets was registered in February 1968 but was later canceled. The game sold from about 1966.
The set includes eighteen wooden cubes—eight have colored dots on all faces and three have numbers on all faces. The remaining seven cubes have set theory symbols on them: four have symbols representing union, intersection, difference, and complementation; and three have symbols representing set equality, set inclusion, the universal set, and the empty set. There are also sixteen cards with colored dots on them.
The set also includes a timer, playing mats, a sheet listing “GAMES for THINKERS” that were available from WFF ‘N PROOF Publishers, a postcard offering a free one-year subscription to the WFF ‘N PROOF Newsletter, and a 1971 edition of an instruction book first written in 1969 by Allen, Kugel, and Owens, ON-SETS: The Game of Set Theory, that was published by AIM (Autotelic Instructional Materials) Publishers. The instruction book includes various games, and a few puzzles, with the method of play given for each game describing the interaction between the different types of cubes and the cards. In the simplest games the only cubes used were those with dots or numbers. All the materials related to this set are stored in an orange plastic case that is marked on the cover: on-sets (/) The Game of Set Theory.
In 1968 Allen moved from Yale to the University of Michigan with a joint appointment in the Law School and the Mental Health Research Institute, where he continued his work on instructional games. Over the years the name and location of the distributor of On-Sets changed, although the phrase “Games For Thinkers” has been associated with it from before Allen’s move to Ann Arbor. Price lists in the WFF ‘N PROOF Newsletters (part of the documentation in accession 317891) indicate that at first the game was distributed by WFF ‘N PROOF in New Haven, Connecticut, and sold for $4.00. In 1970 the price was raised to $5.00 and in 1971 the game was distributed by WFF ‘N PROOF through Maple Packers in Turtle Creek, Pennsylvania. A firm called Learning Games Associates of Ann Arbor later took over distribution of the game and donated this example to the Smithsonian in 1975. The Accelerated Learning Foundation of Fairfield, Iowa, then became the distributor.
Games For Thinkers Website.
Currently not on view
date made
ca 1971
Allen, Layman E.
Kugel, Peter
Owens, Martin
Learning Games Associates
place made
United States: Michigan, Ann Arbor
Physical Description
plastic (overall material)
wood (overall material)
paper (overall material)
overall: 2.5 cm x 15.25 cm x 12.5 cm; 31/32 in x 6 in x 4 29/32 in
ID Number
accession number
catalog number
Credit Line
Gift of Learning Games Associates
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Mathematical Recreations
Data Source
National Museum of American History


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