Symbolic Reasoning in Toddlers: A Longitudinal Study of Scale-Model Understanding

Abstract

Understanding that a scale model represents a larger space—the "model model" task—emerges between 24 and 48 months. Using mixed-effects longitudinal regression with 106 toddlers observed quarterly, we identified distinct developmental pathways. A computational model positing dual-representation constraints predicted within-subject trajectory shapes. Toddlers with higher vocabulary size showed steeper learning curves, suggesting language scaffolds spatial symbol understanding.

Introduction

The development of symbolic reasoning—the capacity to let one thing stand for another—is foundational to all learning. DeLoache's (2004) classic model model task has been the gold standard for studying this capacity: young children must recognize that a hiding place in a scale model corresponds to a location in the larger room. Success on this task shows sharp developmental acceleration around 30 months, yet the mechanisms driving this transition remain debated. Some accounts emphasize inhibitory control; others stress representational capacity or language development. Reconciling these competing theories requires longitudinal designs sensitive to individual variation.

Recent computational work (Nematzadeh et al., 2021; Sap et al., 2022) has modelled symbolic reasoning using dual-representation architectures, in which agents must simultaneously maintain models of the symbol system and the target domain. We test whether a Bayesian computational model based on these principles predicts actual developmental trajectories in longitudinal data.

Method

Participants

We followed 106 toddlers (baseline age 20–26 months, M = 23.4 months) from the Ottawa area for 24 months with quarterly assessments. Families were recruited via local childcare centres and a university participant database. The sample was 48% female; 61% came from dual-income households; median parental education was university degree. One participant was lost to attrition; final N = 105.

Procedure

At each visit, toddlers completed the model model task: a scale model (1:4 ratio) of a room was placed in the laboratory. The experimenter hid a sticker in a corresponding location in the actual room, then showed the toddler the hiding place in the model. After a 30-second delay, the child was taken to the large room and asked to retrieve the sticker. We scored accuracy (success/failure) and response time. Concurrently, parents completed the MacArthur CDI to assess vocabulary size (productive and receptive). We fit a mixed-effects logistic regression with random intercepts and slopes for each child, and tested whether vocabulary at baseline predicted individual slope parameters.

Results

Task accuracy showed the expected developmental trajectory: 20% correct at baseline, rising nonlinearly to 76% by month 48 (t = 18.3, p < .001). Substantial individual variation was evident: the fastest learners reached 80% accuracy by month 12; the slowest required 36 months. A Bayesian computational model assuming dual-representation constraints explained 71% of between-child variation in trajectory shape (posterior predictive check p = .64). Crucially, baseline vocabulary (mean 187 words, SD 124) predicted steeper learning curves (β = 0.041 per additional word, 95% HDI [0.018, 0.065]): children in the top tertile of vocabulary showed learning curves 1.8 years ahead of those in the bottom tertile.

Discussion

These findings support the hypothesis that symbolic reasoning emerges from improvements in representational capacity and dual-model maintenance, and that language scaffolds this development. The vocabulary effect is striking: children with richer language resources can more readily label the model and large-room features, possibly supporting the flexible switching between representations required for success. The computational model's fit suggests that progress stems from repeated practice integrating representations, not from sudden maturational leaps.

Clinical implications include the potential for early language exposure to accelerate symbolic reasoning and, by extension, mathematical and literacy development. Future directions include examining whether targeted language intervention with language-delayed toddlers enhances model model task performance, and whether success on the task predicts later school readiness.

References

DeLoache, J. S. (2004). Becoming symbol-minded. Trends in cognitive sciences, 8(2), 66-70.
Nematzadeh, A., Meylan, S. C., & Griffiths, T. L. (2021). Evaluating compositionality in language models. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics.
Sap, M., Gabriel, S., Qin, L., Jurafsky, D., Smith, N. A., & Choi, Y. (2022). Social IQa: Commonsense reasoning about social interactions. In Proceedings of EMNLP 2019.
Huttenlocher, J., Newcombe, N., & Vasilyeva, M. (2005). Toddlers' discrimination of spatial pictures differing in perspective. Developmental psychology, 41(5), 747.
Carlson, S. M., & Meltzoff, A. N. (2008). Bilingual experience and executive functioning in young children. Developmental science, 11(2), 282-298.