An effective preschool mathematics curriculum (Building Blocks, evaluated in the TRIAD cluster-randomized trial) produces large immediate achievement gains that largely fade over elementary school. A matched-subgroup decomposition attributed about 72% of this fadeout to stable pre-existing differences between treatment and control children with equal post-test achievement, but could not identify which specific differences (prior mathematics achievement, literacy and language, family socioeconomic resources, domain-general cognition, motivation, home conditions, time-varying family change) causally drive the catch-up, and could not test whether better-aligned or substantially higher-quality subsequent schooling would change the magnitude or mechanism of fadeout. The open problem is a causal account of this fadeout: identifying the pre-existing differences that cause matched control children to outlearn matched treatment children, and determining whether intentionally aligned, cumulative instruction or school quality beyond the observed range makes early intervention effects persist.

Background

A robust finding across early-childhood education research is that the achievement gains produced by preschool interventions shrink or disappear over the elementary-school years, a phenomenon called fadeout: control children who never received the intervention gradually catch up to treated children. The best-studied case is the Building Blocks preschool mathematics curriculum (a research-based curriculum built around learning trajectories—descriptions of the levels of thinking children pass through when mastering a mathematical concept), evaluated in the TRIAD study (Technology-enhanced, Research-based, Instruction, Assessment, and professional Development). In that evaluation 42 low-resource schools across two U.S. sites were rank-ordered into blocks by school-wide mathematics scores and randomly assigned within block to one of three conditions: a pre-kindergarten-only treatment, a pre-kindergarten-to-first-grade treatment whose teachers received professional development for a follow-through curriculum designed to build on the preschool content, or a control condition (Clements, Sarama, Spitler, Lange, and Wolfe, 2011; Clements, Sarama, Wolfe, and Spitler, 2013). The intervention produced a large immediate effect on mathematics achievement that diminished in the following years, although a small advantage persisted in the follow-through condition through the third year.

Two hypotheses compete to explain such fadeout. The constraining content hypothesis holds that elementary instruction offers too little advanced content for the boosted children, so equally skilled control children converge with them. The pre-existing differences hypothesis holds that a control child who reaches the same post-test level as a treated child without the intervention must be advantaged on stable, unboosted characteristics—prior skills, family resources, home environment—and will therefore outlearn the matched treated child thereafter. Bailey, Nguyen, Jenkins, Domina, Clements, and Sarama (2016) tested these hypotheses by matching each treated child to a control child with a nearly identical post-test score (Rasch-scaled, meaning scores from different assessment waves are placed on a single equal-interval scale by a psychometric item-response model, so they are comparable across years) and comparing their subsequent trajectories. Matched control children outscored matched treated children a year later, and this difference accounted for roughly 72% of the total fadeout; the matched-group difference was fully statistically attenuated by measures of prior academic achievement (literacy, language, and earlier mathematics). Fadeout in this trial is thus mostly not a story of the treatment group losing ground but of stable pre-existing differences reasserting themselves. What that decomposition could not do—stated explicitly in the paper—was (a) isolate which specific causal ingredients among the correlated candidates (prior mathematics achievement itself, literacy and language skills, family socioeconomic resources, domain-general cognitive ability, motivation, home conditions, time-varying family changes) actually produce the catch-up; (b) test whether schooling of substantially higher quality than the observed range in these low-resource communities would change the magnitude or mechanism of fadeout; and (c) distinguish whether the follow-through curriculum acted as a moderator of the original treatment or as a second treatment on its own, because no group received the cumulative professional development without the initial intervention. The authors specify the design that would settle the environmental part: re-randomize children from the original treatment and control groups into different types of subsequent environments. This agenda is known in the field as the sustaining environments hypothesis—the proposal that early-intervention effects persist only when subsequent environments are high-quality and aligned with what the intervention taught—which subsequent syntheses have framed but not causally resolved (Bailey, Duncan, Odgers, and Yu, 2017; Bailey, Duncan, Cunha, Foorman, and Yeager, 2020).

Problem Statement

The source study established that about 72% of the fadeout of the Building Blocks preschool mathematics intervention is attributable to pre-existing differences between treatment and control children who have the same mathematics achievement immediately after the intervention, and that this matched-group gap is statistically accounted for by measures of prior academic achievement—a domain-level attenuation that does not by itself isolate which specific ingredient is causal. Two linked questions remain open and jointly constitute the problem: (1) Causal ingredients: which specific pre-existing differences—prior mathematics achievement itself, literacy and language skills, family socioeconomic resources, domain-general cognitive abilities, motivation, home conditions, or time-varying family and environmental change—actually cause post-test matched control children to outlearn matched treatment children in the following years, and how malleable are those ingredients? (2) Subsequent environments: does substantially higher-quality schooling than the observed range in low-resource communities change the magnitude or mechanism of fadeout, and does instruction intentionally aligned with the intervention (a cumulative, follow-through curriculum) act as a moderator of the original treatment, as a second treatment effect, or neither? The source study left the environmental question untested: it did not establish whether aligned or higher-quality later schooling changes the magnitude or mechanism of fadeout. Together these questions define a causal account of fadeout in this intervention class: answering the causal-ingredients question requires saying which of the listed differences the available evidence can and cannot distinguish as the driver of the catch-up, together with how malleable each candidate is; answering the subsequent-environments question requires stating the conditions on later schooling under which early mathematics intervention effects persist, including the moderator, second-treatment, or neither distinction. Resolving the two questions requires observations that would distinguish the candidate ingredients, together with the identification or test strategy and assumptions under which that distinction is defensible. The source leaves generalizability untested: the problem is scoped to this intervention class, and whether these findings extend to other interventions, populations, or age groups remains unresolved.

References

  1. Bailey, D. H., Nguyen, T., Jenkins, J. M., Domina, T., Clements, D. H., & Sarama, J. (2016). Fadeout in an early mathematics intervention: Constraining content or preexisting differences? Developmental Psychology, 52(9), 1457-1469. DOI 10.1037/dev0000188, https://doi.org/10.1037/dev0000188 (source paper; full text via PMC5003741)
  2. Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127-166. DOI 10.5951/jresematheduc.42.2.0127, https://doi.org/10.5951/jresematheduc.42.2.0127
  3. Clements, D. H., Sarama, J., Wolfe, C. B., & Spitler, M. E. (2013). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies. American Educational Research Journal, 50(4), 812-850. DOI 10.3102/0002831212469270, https://doi.org/10.3102/0002831212469270
  4. Bailey, D. H., Duncan, G. J., Odgers, C. L., & Yu, W. (2017). Persistence and fadeout in the impacts of child and adolescent interventions. Journal of Research on Educational Effectiveness, 10(1), 7-39. DOI 10.1080/19345747.2016.1232459, https://doi.org/10.1080/19345747.2016.1232459
  5. Jenkins, J. M., Watts, T. W., Magnuson, K., Gershoff, E. T., Clements, D. H., Sarama, J., & Duncan, G. J. (2018). Do high-quality kindergarten and first-grade classrooms mitigate preschool fadeout? Journal of Research on Educational Effectiveness, 11(3), 339-374. DOI 10.1080/19345747.2018.1441347, https://doi.org/10.1080/19345747.2018.1441347
  6. Bailey, D. H., Jenkins, J. M., & Alvarez-Vargas, D. (2020). Complementarities between early educational intervention and later educational quality? A systematic review of the sustaining environments hypothesis. Developmental Review, 56, 100910. DOI 10.1016/j.dr.2020.100910, https://doi.org/10.1016/j.dr.2020.100910 (originally released 2019 as EdWorkingPaper No. 19-99, ERIC ED670888, https://eric.ed.gov/?id=ED670888)
  7. Bailey, D. H., Duncan, G. J., Cunha, F., Foorman, B. R., & Yeager, D. S. (2020). Persistence and fade-out of educational-intervention effects: Mechanisms and potential solutions. Psychological Science in the Public Interest, 21(2), 55-97. DOI 10.1177/1529100620915848, https://doi.org/10.1177/1529100620915848
  8. Dumas, D., McNeish, D., Sarama, J., & Clements, D. (2019). Preschool mathematics intervention can significantly improve student learning trajectories through elementary school. AERA Open, 5(4). DOI 10.1177/2332858419879446, https://doi.org/10.1177/2332858419879446
  9. Hart, E. R., Bailey, D. H., Luo, S., Sengupta, P., & Watts, T. W. (2024). Fadeout and persistence of intervention impacts on social-emotional and cognitive skills in children and adolescents: A meta-analytic review of randomized controlled trials. Psychological Bulletin, 150(10), 1207-1236. DOI 10.1037/bul0000450, https://doi.org/10.1037/bul0000450
  10. Kaestner, R., & Schiman, C. (2024). Do preschool investments depreciate and fadeout or result in dynamic complementarities? An assessment using the Head Start Impact Study. Review of Economics of the Household, 24(1), 61-97. DOI 10.1007/s11150-024-09735-4, https://doi.org/10.1007/s11150-024-09735-4
  11. Kang, C. Y., Duncan, G. J., Clements, D. H., Sarama, J., & Bailey, D. H. (2019). The roles of transfer of learning and forgetting in the persistence and fadeout of early childhood mathematics interventions. Journal of Educational Psychology, 111(4), 590-603. DOI 10.1037/edu0000297, https://doi.org/10.1037/edu0000297
  12. Little, M., Bastian, K. C., Cohen-Vogel, L., Bratsch-Hines, M., Burchinal, P., & Peisner-Feinberg, E. (2024). Is skill heterogeneity in kindergarten classrooms associated with the persistence of pre-K gains? Evidence from the IES Early Learning Network. Early Childhood Research Quarterly, 68, 35-44. DOI 10.1016/j.ecresq.2024.03.008, https://doi.org/10.1016/j.ecresq.2024.03.008
  13. McCormick, M. P., MacDowell, C., Weiland, C., Hsueh, J., Maier, M., Pralica, M., Maves, S., Snow, C., & Sachs, J. (2024). Instructional alignment is associated with PreK persistence: Evidence from the Boston Public Schools. Early Childhood Research Quarterly, 67, 89-100. DOI 10.1016/j.ecresq.2023.11.008, https://doi.org/10.1016/j.ecresq.2023.11.008
  14. Pearman, F. A., Springer, M. P., Lipsey, M., Lachowicz, M., Swain, W., & Farran, D. (2020). Teachers, schools, and Pre-K effect persistence: An examination of the sustaining environment hypothesis. Journal of Research on Educational Effectiveness, 13(4), 547-573. DOI 10.1080/19345747.2020.1749740, https://doi.org/10.1080/19345747.2020.1749740
  15. Wan, S., Bond, T. N., Lang, K., Clements, D. H., Sarama, J., & Bailey, D. H. (2021). Is intervention fadeout a scaling artefact? Economics of Education Review, 82, 102090. DOI 10.1016/j.econedurev.2021.102090, https://doi.org/10.1016/j.econedurev.2021.102090
  16. Watts, T. W., Botvin, C. M., Bailey, D. H., Hart, E. R., Mattera, S., Clements, D. H., Sarama, J., Farran, D. C., & Lipsey, M. W. (2026). Predicting persistence and fadeout across multi-site RCTs of an early childhood mathematics curriculum intervention. Educational Evaluation and Policy Analysis, 48(3), 1180-1205. DOI 10.3102/01623737251405258, https://doi.org/10.3102/01623737251405258
  17. Watts, T. W., Duncan, G. J., Clements, D. H., & Sarama, J. (2018). What is the long-run impact of learning mathematics during preschool? Child Development, 89(2), 539-555. DOI 10.1111/cdev.12713, https://doi.org/10.1111/cdev.12713