Children's preference for mixed‐ versus fixed‐ratio schedules of reinforcement: A translational study of risky choice
Kids choose to do more math when the first reinforcer comes after one problem, even if later ratios are larger.
01Research in Context
What this study did
Four elementary kids did math problems for tokens. They could pick between two reward rules.
Rule one: every 5th problem gave a token (fixed-ratio 5). Rule two: a mix—first token after 1 problem, then after 9 more (mixed-ratio 1,9).
The class used an ABAB reversal design. Kids switched rules across days so the team could see real choice patterns.
What they found
All four kids chose the mixed schedule most of the time. They did more problems when a single quick win started the chain.
Even when the mix got leaner (1,11), three kids still picked it. The tiny first ratio kept them hooked.
How this fits with other research
Fantino (1967) first saw this with pigeons. Birds also pecked more when a small ratio led the mix. Mullane moves the same rule from lab cages to classroom desks.
Mellott et al. (2023) swapped ratio for time. Kids picked mixed-duration over fixed-duration and finished more work. Together the papers say “mix beats fixed” in both ratio and time worlds.
Iwata et al. (1990) showed toddlers already work harder under ratio than interval schedules. The new data say older kids will also chase a mixed ratio if it starts small.
Why it matters
You can boost math work right now by giving the first token after only one problem, then spacing the rest. The tiny front-loaded win pulls the child in and keeps the momentum going. Try it during independent seat-work or fluency drills—no extra tokens needed, just smarter timing.
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Start your token board with a single-problem token, then return to your usual ratio.
02At a glance
03Original abstract
Laboratory research has shown that when subjects are given a choice between fixed-ratio and bi-valued mixed-ratio schedules of reinforcement, preference typically emerges for the mixed-ratio schedule even with a larger ratio requirement. The current study sought to replicate and extend these findings to children's math problem completion. Using an ABCBC reversal design, four fourth-grade students were given the choice of completing addition problems reinforced on either a fixed-ratio 5 schedule or one of three mixed-ratio schedules; an equivalent mixed-ratio (1, 9) schedule, a mixed-ratio (1, 11) schedule with a 20% larger ratio requirement, and an equally lean mixed-ratio (5, 7) schedule without the small fixed-ratio 1 component. This was followed by a reversal back to the preceding phase in which preference for the mixed-ratio schedule had been observed, and a final reversal back to the mixed-ratio (5, 7) phase. Findings were consistent with previous research in that all children preferred the mixed-ratio (1, 9) schedule over the equivalent fixed-ratio 5 schedule. Preference persisted for the leaner mixed-ratio (1, 11) schedule for three of the four children. Indifference or preference for the fixed-ratio 5 alternative was observed in phases containing the mixed-ratio (5, 7) schedule. These results extend previous research on risky choice to children's math problem completion and highlight the importance of a small ratio component in the emergence of preference for bi-valued mixed-ratio schedules. Implications of these results for arranging reinforcement to increase children's academic responding are discussed.
Journal of the Experimental Analysis of Behavior, 2017 · doi:10.1002/jeab.234