Initially effective early academic interventions often show smaller or no discernible treatment impacts in the years following the end of treatment. This pattern has important implications for theories of children’s mathematical development. In particular, patterns of fadeout can be used to estimate the relative sizes of the effects of prior knowledge and other factors in producing differential stability in children’s mathematics achievement across development. Further, the prevalence of fadeout implies the need for changes to research design and statistical analysis in research on children’s mathematical cognition, such as the need for long follow-up assessment intervals in some experimental research and the need to check causal estimates from non-experimental longitudinal research on mathematical cognition against experimental impacts whenever possible. Finally, fadeout deserves careful consideration by those attempting to translate research on mathematical cognition into interventions intended to produce positive long-term effects on the individuals who receive them. 

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