Tucked in a 64 year old book is a mathematical formula that gives clues about grouping procedures. Bossard1 points out that the number of people in a group may increase by simple mathematical progression, but the increase of relationships comes through geometric progression.

Two variables are defined. Let Y equal the number of persons in the group, and X the number of personal relationships between the members. Then using the formula X = (Y2 – Y)/2 (that is, X equals Y squared minus Y all divided by 2), as Bossard1 has, we find that the larger the group, the more disproportionate the increase in personal relationships.

Size of group: 2 3 4  5   8   12   15  35
Relationships: 1 3 6 10  28  66 105 595

Note how radically the number of relationships increases with the addition of one or two people. What does this do to the individual in terms of communication, understanding, and ability to participate without pressure or frustrations?

Hundreds or thousands may be spectators. Working, interacting groups seem to do best when composed of five to eight members. If the group is larger, some become performers and others spectators. At age six, spontaneous groups seldom exceed three or four children. Sizes now accepted for school classes are much too large for good cooperative work.2

If the mathematical formula is a hang-up, try drawing the relationships on a page of paper to convince yourself of the truth of this work. See the example at the end of this blog.

What implications do such formulas have for those of us who work with small groups in education or church leadership? How might we be excluding people in some of our educational contexts? We talk a lot about being communities of believers or communities of learners but this information suggests that members could easily be left on the fringe and never truly feel part of the group. The person who can entertain a large group of 1000 people may not be the best person to teach people to care for others or interact with others. Some of the goals we seek to accomplish in school or church cannot be accomplished in the size of groups we seek to use. We would be better served to restructure some of our groups so that peer learning can happen in groups of twos and threes. Neil Cole has some further insight on group dynamics in his book Cultivating a Life For God: Multiplying Disciples Through Life Transformation Groups.3 It may well be worth another look.

1 James H. S. Bossard. The Sociology of Child Development. New York: Harper and Brother, 1948. p. 146.
2 This whole section is adapted from an article by Mary Margaret Scobey, entitled “Developing and Using Classroom Groups,” 1960. See http://ascd.com/ASCD/pdf/journals/ed_lead/el_196312_scobey.pdf.
3 Cole, Neil. Cultivating a Life For God: Multiplying Disciples Through Life Transformation Groups. Carol Stream: ChurchSmart Resources, 1999.

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