Social influences on the reasoning and rhetorical strategies of 104 fourth graders were examined during 48 small-group discussions. A total of 14,942 lines of discussion transcript were sifted to determine patterns of occurrence of 13 argument stratagems serving several rhetorical functions. The major finding was that the use of argument stratagems snowballs. That is, once a useful stratagem has been used by a child during a discussion, it tends to spread to other children and occur with increasing frequency. After the first appearance of a stratagem, the probability that it will appear again usually rises and remains high. In general, there are fewer and fewer lines of discussion between successive appearances of a stratagem. The snowball phenomenon was more pronounced during discussions with open participation than during discussions with teacher-controlled participation.