The study of how children learn numbers has yielded one of the most productive research programs in cognitive development, spanning empirical and computational methods, as well as nativist and empiricist philosophies. This paper provides a tutorial on how to think computationally about learning models in a domain like number, where learners take…

Studies show that spatial interventions lead to improvements in mathematics. However, outcomes vary based on whether physical manipulatives (embodied action) are used during training. This study compares the effects of embodied and non-embodied spatial interventions on spatial and mathematics outcomes. The study has a randomized, controlled,…

Previous research on Montessori preschool education is inconsistent and prone to analytic flexibility. In this preregistered study, disadvantaged preschoolers in a French public school were randomly assigned to either conventional or Montessori classrooms, with the latter being adapted to French public education. Adaptations included fewer…

We explore whether training parents' math skills or playing number games improves children's mathematical skills. Participants were 162 parent-child dyads; 88.3% were white and children (79 female) were 4 years (M = 46.88 months). Dyads were assigned to a number game, shape game, parent-only approximate number system training, parent-only general…

Home math interventions often incorporate informational priming--explicit prompts emphasizing parental math input. While effective in increasing math talk, its impact on child outcome is mixed. This study examined how informational priming shapes the content and dynamic of math interactions. In year 2023, 122 Chinese parent-child dyads…

Different cross-domain trajectories in the development of students' ability self-concepts (ASCs) and their intrinsic valuing of math and language arts were examined in a cross-sequential study spanning Grades 1 through 12 (n = 1,069). Growth mixture modeling analyses identified a "Moderate Math Decline/Stable High Language Arts" class…

This article reports findings from a cluster-randomized study of an integrated literacy- and math-focused preschool curriculum, comparing versions with and without an explicit socioemotional lesson component to a business-as-usual condition. Participants included 110 classroom teachers from randomized classrooms and approximately eight students…

This study examined whether practice with arithmetic problems presented in a nontraditional problem format improves understanding of mathematical equivalence. Children (M age = 8;0; N = 90) were randomly assigned to practice addition in one of three conditions: (a) traditional, in which problems were presented in the traditional "operations…

This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be…

Latent growth models estimated developmental trajectories for adolescents' math and English self-perceptions (perceived talent, success expectancies), values (intrinsic, utility) and task perceptions (task difficulty, effort required). A longitudinal cohort-sequential study included 1,323 participants spanning Grades 7 to 11, with Occasion 1 mean…

In 2 studies, an expectancy-value framework was applied to investigate effort expended on mathematics homework. In Study 1 (2,712 students in grades 5, 7, and 9; mean age=13.37 years), lower homework effort was found in higher grades. The effects of intrinsic value on homework effort were higher in the older cohorts, whereas the effects of the…