Making Math Risky: A Translational Study on Preference for Mixed- Versus Fixed-Ratio Schedules during Problem Completion

Date of Award


Degree Type


Degree Name

Master of Science (MS)




Brian K. Martens


Math problem completion, Ratio schedules, Risky choice

Subject Categories

Social and Behavioral Sciences


Basic research has demonstrated that when given a choice between a reinforcement schedule that requires a fixed number of responses or one that requires a mixed number of responses, preference typically emerges for the mixed option even when it requires a larger response requirement. The current study attempted to replicate and extend these findings to math problem completion by fourth-grade students. Across 5 phases, 4 students chose either to complete 5 addition problems per trial (fixed-ratio schedule) or a mixed number of addition problems per trial (mixed-ratio schedule). The first mixed schedule examined required either 1 or 9 problems per trial. The number of math problems in the mixed schedule was increased by 20% (1 or 11 problems per trial) in the subsequent phase. The third phase featured a mixed schedule requiring 5 or 7 problems per trial. This was followed by a reversal to the preceding phase in which preference for the mixed schedule had been observed and a final reversal back to the phase featuring a mixed schedule requiring 5 or 7 problems per trial. Findings were consistent with previous research in that preference emerged for the mixed schedules that required only 1 problem on some trials, but did not when the mixed option required 5 or 7 problems. Results highlight the importance of small work requirements in the emergence of preference for mixed schedules and offer implications for future studies aimed at encouraging students to choose lengthier assignments.


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